SL N 0 III S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN ~rr University of Illinois at Urbana-Champaign Library Brittle Books Project, 2010. 368 M~ lI p THE UNIVERSITY OF ILLINOIS LIBRARY COPYRIGHT NOTIFICATION In Public Domain. Published prior to 1923. This digital copy was made from the printed version held by the University of Illinois at Urbana-Champaign. Itwas made in compliance with copyright law. Prepared for the Brittle Books Project, Main Library, University of Illinois at Urbana-Champaign by Northern Micrographics Brookhaven Bindery La Crosse, Wisconsin 2010 Return this book on or before the Latest Date stamped below. University of Illinois Library 29 Llol-H41 % ,,... , ' >' ""i' 7 4 E2" 'y 'N, : K, 4 f t " Yj i'--p (Un., () Ii qtN + l (a &? 4 fj C t; 4'j V5 < R b tr vS:- 7c PRACTICAL INTRODUCTION TO iife an ,Fitt r00uranl, SHOWING THE METHOD OF CALCULATING THE VALUES OF ANNUITIES, REVERSIONS, ASSURANCES, POLICIES, BONUSES, &C. WITH NUMEROUS USEFUL TABLES: TOGETHER WITH C Qrronnptuibe itcrt OF THE DISTINCTIVE FEATURES OF THE ASSURANCE OFFICES, AND ALSO OrItrciptiou of 4rie 1i0t, WITH THE' RATES OF PREMIUM DEMANDED THEREFOR. BY THOMAS H. MILLAR, ACCOUNTANT, EDINBURGH. EDINBURGH: FOR TIE AUTHOR. AND SOLD BY OLIVER AND BOYD, SIMPKIN, MARSHALL, AND 1841. CO, EDINBURGH; LONDON. H C) Cal TO JOSEPH MACGREGOR, ESQ., ACCOUNTANT, EDINBURGH, THIS VOLUME, IN TESTIMONY OF PARTICULAR REGARl), IS INSCRIBED) W A BY THE. AUTHOR. -k 2Ct Sr PREFACE. THE Science of Life Annuities has been fully and elaborately treated by several eminent mathematicians, who have established and developed its principles by a series of algebraic demonstrations. This process of analysis is the only method by which the rules and formule of the science can be ascertained and demonstrated, and on which its practical application must ultimately rest. Works on the doctrine of annuities, however, .being necessarily of so technical and abstruse a character, possess few or no attractions except to actuaries, or to the comparatively few who may entertain a predilection for such enquiry. To the far greater number of readers, who are not sufficiently initiated in the knowledge of algebra, they are almost wholly useless. With the view, therefore, of bringing the subject within the reach of such as may desire to be acquainted with merely the practical rules and calculations of the science, and in the hope that it may, in some slight measure, contribute to disseminate a knowledge of this subject, which, from the immense increase of assurances within late years, has already assumed an appearance of great national importance, the following volume has been compiled. How far the task, which has been one chiefly of selection and adaptation, has been successful, it is not for the Author to decide. In the pursuit of this object, it has been attempted to explain the principles from which the values of annuities for single and joint lives are deduced; but to those who are at all familiar with the subject, it is unnecessary to say, that, from the prolixity of common language, it would be impossible in this way satisfactorily to elucidate the principles of survivorships, arising as they do, out of endless combinations of contingencies, and involving in many cases complicated and difficult questions. For all practical purposes, however, rules for the solution of problems may, in general, be briefly and concisely expressed, and readily applied, without its being necessary to give their demonstration, which, as already said, can only be determined by algebraic, and not by arithmetical reasoning. PREFACE, A comprehensive digest of the leading peculiarities or distinguishing features, particularly as regards the periods and modes of distributing the surplus funds or profits, of the various assurance offices in this country, has been subjoined, in the belief that it may be advantageously consulted by those about to enter into a transaction, which, whether of the nature of an assurance or an annuity, is to continue through life, and in which the comfort and happiness of individuals and families are materially involved. A person, therefore, who is anxious to avail himself of so obvious and convenient a method of securing a provision in aid of his surviving children, or others in whose welfare he feels an interest, cannot, amidst so many conflicting schemes so zealously pressed upon the notice of the public, use too much precaution and judgment in selecting an office whose terms and constitution are founded on equitable principles, and the known ability and integrity of whose management remove all apprehensions as to the faithful fulfilment and liberal interpretation of the engagements they undertake. A description of risks against loss by fire, with the rates of premium usually required by the most respectable Fire Insurance Companies, and many important clauses necessary to be inserted in Policies issued for hazards of a particular or special class, have also been introduced; and it is believed the present is the first attempt to furnish for the use of the public this information, (acquired by extensive official experience, as well as from other sources,) in this department of the business of assurance. EDINBURGH, January 1841. ERRATA. Page 8, lines 31, 34, for last, read live. ... 22, ... 27, for XI, read IX. ... 25, ... 27, for IX, read VIII. ... 26, ... ... 14, ... ... 112, ... 114, ... ... ... 114, ... 6, for VIII, read IX. 19, for 25, read 35. 2 from bottom, for 21 read 22. 18 from bottom, for 750 read 720. 16 from bottom, for 1030 read 1080. PRACTICAL CALCULATIONS OF ANNUITIES, &c. DECIMAL NOTATION. DECIMAL FRACTIONS are just an artificial way of expressing vulgar fractions as whole numbers, and they are wrought nearly in the same manner as integers. A decimal fraction is a unit divided into tenth, hundredth, and thousandth parts, ad infinitum, as may be required. The denominators being always known, they are never expressed, and the fractions 5, ovoo5, , are written .5, .05, .005. Ciphers or noughts, when placed before a decimal, diminish its value in a ten-fold ratio; thus, .5 expresses five-tenths of a unit ; and .05 denotes five-hundredths. Ciphers after a decimal do not affect its value, and they are always omitted: thus .50, .500 are just equal to .5 or -5 Decimals have a dot or point put before them, to distinguish them from integers; as 62.527. This number, having three digits to the right of the point, is said to consist of three decimal places. REDUCTION. I. To reduce numbers from lower denominations to the decimal of a higher: Reduce them first to vulgarfractions,and then to decimals. Reduce 4s. 6d. and 15s. 6d. to the decimal of a pound. ofa £ 15s. 6d. = 186d. = 54d. _ . of a £ 4s.6d. 240) 1860 (.775, Ans. 240) 540 (.225, Ans. = = II. To reduce shillings, pence, and farthings to decimals of a pound by inspection: Take half the number of shillingsfor thefirst place of the decimal, and the pence and farthings, reduced to farthings, adding 1 for every 24, will form the second and third places. Thus, reduce 14s. 6d. to a decimal. The half of 14 is 7, forming the first figure in the decimal, and the 6d. is 24 farthings, to which 1 farthing is added; the equivalent decimal is therefore .725. If the number of shillings be an odd number, as 7, 9, 11, &c., 5 is added to the second 6d. place, as S15s. is = .775. -- III. To find the value of a decimal: Multiply by the diflerent denominations, pointing off from the right of the product as many places as there are in the multiplicand. DECIMAL FRACTIONS. Find the value of .225 and .725 of a £. .225 20 4.500 12 .725 20 6.000 Ans. 4s. 12 6000 Ans. 14s. 6d. 6d. IV. To value the decimal of a pound by inspection: Double the first figure next the point for shillings, then the second and third places, diminished by 1 for every 25, are farthings-state these in the proper denominations. What is the value of .225 and .775 of a£? 4s.; In the first case, 2 is doubled for shillings, which is and the remaining figures being farthings, 1 deducted will leave 24, which is 6d. -the value of the decimal is 4s. 6d. In the second case, the 7 doubled is 14s.; and the remainder being 75 farthings, 3 deducted leaves 72, being Is. Gd.-the answer is 15s. 6d. Three places of figures in the decimal will give the value sufficiently accurate ; but in taking off any number of figures from a decimal, if the next succeeding figure is 5, or exceeds it, add 1 to the last figure retained. In taking off the three first figures from the decimal .75257 the next succeeding figure is 5; therefore .753 will express the value of the fraction within half a farthing. ADDITION AND SUBTRACTION. Write down the given numbers, placing the decimal points directly under each other, and proceed as in whole numbers. ADDITION. SUBTRACTION. Add 32.406, 5.04, 424.8456. 32.406 Subtract 10.105 from 12.7; and from 8.562 take 5.4 5.04 424.8456 462.2916 12.7 8.562 10.105 2.595 5.4 3.162 MULTIPLICATION. Multiply as in whole numbers, and point off as many decimal figures the right of the product as there are in both factors. If there are from not so many figures in the product as in the multiplicand and multiplier, supply the deficiency by placing ciphers on the right. Multiply 5.07 by 30.2; and .067 by .55. 5 .07 30.2 1014 1521 153,7,14 lAns. .067 .55 335 3345 .03685 Ans. COMPOUND INTEREST. To multiply any number by 10, 100, or 1000: remove the decimal point one, two, or three places to the right; thus2162.1143 X 10 =21621.143 2162.1143 X 100 = 216211.43 2162.1143 X 1000 = 2162114.3 DIVISION. Divide as in whole numbers, and place the decimal point as follows: 1st, If the decimal figures of the dividend exceed those of the divisor, point off as many decimal figures from the right of the quotient. 2d, If the decimal figures of the divisor exceed those of the dividend, annex as many ciphers to the right of the quotient, which will be integral. 3d, If the divisor and dividend have both the same number of decimal places, the quotient will likewise be a whole number. Divide 21.62114 by 5.02, and 216211.4 by 4.307. Divisor. Dividend. Quotient. 5.02) 21.62114 (4.307 2008 1541 1506 Divisor. Dividend. Quotient. 4.307) 216211.4 (50200 21535 8614 8614 3514 3514 To divide any number by 10, two, or three places to the left; 2162.114 -2162.114 --2162.114 --- 100, 1000: put the decimal point one, thus10 216.2114 100 = 21.62114 1000 = 2.162114 COMPOUND INTEREST. Compound Interest is computed in this manner :-The principal and its interest are periodically added together, as the latter falls due, whether yearly or half-yearly; so that at the end of these periods a new principal is created. Thus, if £100 is lent at 5 per cent, payable yearly, the interest will be £5, and the sum which bears interest for the second year is £105. An annuity is a periodical income of rent, interest, pension, &c., receivable yearly or half-yearly. When the payment of the annuity does not depend on any contingency, but is either in perpetuity, or for a certain specified time, it is called an annuity certain. In calculating the value of an annuity, it is always understood that the first payment commences at the end of the year, or half-year, as the case may be, from the period of valuation. There are five cases in Compound Interest, which will be here considered. 4 COMPOUND INTEREST. I. To find the amount of a given sum, improved at compound interest at any rate, and for any time: Multiply the amount of £1for a year so often into itself as there are years proposed, and the last product multiplied by the principalgives the answer. What will £1 amount to in 3 years, at 5 per cent, compound interest? 1.05 X 1.05 X 1.05 = 1.157625 = £L, 3s. 1 d. Ans. By this Case Table I. is constructed. APPLICATION OF THE TABLE. 1. What is the amount of £100 in 5 years, at 4 per cent per annum, compound interest ? Opposite to 5 years, and under 4 per cent, is found - 1.21665 Which multiplied by the given sum, = 100 Gives 121.665 Or, £121, 13s. 32d. is the answer. 2. What will £150, 10s. amount to in 10 years at 5 per cent? Opposite to 10 years, and in 5 per cent column, is found 1.62889 And this amount multiplied by £150, 10s., _ 150.5 Produces 245.148 Or, £245, 2s. 11d. is the answer. If it be required to find the amount of £1 for any number of years not in the Table, multiply together the numbers corresponding to those years; the sum is equal to the given number. Thus, 2.52695, the amount of £1 for 19 years, at 5 per cent, multiplied by 7.039988, the amount for 40 years at 5 per cent, will give £17.789703, the amount of £1 for 59 years. II. To find the present value or worth of any sum to be received at the end of any number of years : Find the amount of £1 in the given time, and by it divide the given sum, and the quotient is the answer. What is the present worth or value of £1 to be received 3 years hence, discounting at the rate of 5 per cent per annum ? 1.05 x 1.05 x 1.05 = 1.157625 1.000000 And 1.0 2= .863838, or 17s. 31d. is the answer. 1.157625 By this Case Table II. is constructed. It will be observed, that this table is formed by dividing £1 by the amount found in Table I., for the time and rate assigned. APPLICATION OF THE TABLE. 1. What ready money will purchase £100 which is not due for 10 years, discounting at the rate of 5 per cent per annum, compound interest? Opposite to 10 years, and in 5 per cent column, is - .613913 And this value, multiplied by Or, £61, Ts. - - - - 100 Gives 61.3913 10d. is the answer. ANNUITIES CERTAIN. 5 2. What is the present worth of £150, 10s., due 4 years hence, interest being allowed at 4 per cent per annum ? .854804 Opposite 4 years, and under 4 per cent, is found And being multiplied by £150, 10s. - = 150.5 The product, 128.648 Or, £128, 12s. 11d. is the answer sought. III. To find the amount of an annuity for a certain time, at any rate per cent: Subtract unity from the amount of £1 for the given number of years, multiply the di~erence by the annuity, and divide by the interest of £1 for one year. An annuity of £1 payable yearly is unsettled for 3 years: what is now due, interest 5 per cent per annum ? 1.157625 -1 = .157625-+- .05 = 3.1525 = £3, 3s. 02d. Ans. By this Case Table III. is constructed. Table III. is easily constructed from Table I., in this manner : To 1.0000 = the first year in Table III. .Add 1.0500 = the amount of £1 for 1 year, Table I. Sum. 2.0500 = amount for 2 years in Table III. 1.1025 = second year in Table I. 3.1525 = third year, Table III., found as above. APPLICATION OF THE TABLE. 1. What will an annuity of £100, payable yearly, amount to at the end of 3 years, interest 5 per cent per annum on all payments then in arrear ? Opposite to 3 years, and under 5 per cent, is found 3.1525 Multiplied by the annuity, = 100 Gives 315.25 Or, £315, 5s., is the answer required. 2. What will £500 amount to, lent out yearly, with the accumulated interest on each £500 for 7 years, interest reckoned at 4 per cent per annum ? 7.89829 x 500 = 3949.15 = £3949, 3s. Od. is the answer. IV. To find the present value of £1 per annum: Subtract from unity the present value of £1 due at the expiration of the number of years the annuity has to continue, and divide the dJerence by the interest of £1 for one year-the quotient multiplied by the annuity gives the present value. What is the present value of an annuity of £1 for 3 years, allo wing 5 per cent to the purchaser? From Annuity = 1.0000000 Take, Table II., .8638376 Interest of £1, .05).1361624(2.7232 = £2, 14s. 52d. Ans. By this Case Table IV. is constructed. 6 COMPOUND INTEREST. The above value may be found in this manner :-As the value of an annuity certain for any number of years consists of the values of £1, payable at the end of each year in that term, the numbers in Table IV. are the sums of the values in Table II.; hence the value of £1 annuity certain, for 3 years, at 5 per cent, is the sum of the three first numbers in Table II., that is, .952381 + .907029 + .863838 = 2.723248, same as above. APPLICATION OF THE TABLE. 1. What is the present worth of an annuity of £85, to continue 9 years, discounting at the rate of 4 per cent ? Opposite to 9 years, in 4 per cent column, is found, - 7.4353 Which multiplied by the annuity, - - = - 85 Gives 632.0 Or, £632 is the answer required. 2. An annuity of £138, 16s. is mortgaged for six payments to come, but is to continue for 7 years thereafter; that is to say, the purchaser is to have the last seven of thirteen annual payments of the above annuity: -- What is it worth in ready money, allowing 42 per cent per annum ? Opposite to 13 years, under 42 per cent, is found, 9.6829 Subtract the value of £1 opposite to 6 years, 5.1579 -- Remains the deferred worth of £1, And this difference, multiplied by the annnity, - - - - = 138.8 4.5250 Gives 628.07 Or, £628, Is. 5d. is the answer. V. To find the annuity which £1 will purchase for any number of years: Find by Case IV. the present value of £1 per annum for rate and time assigned, by which divide unity, and the quotient is the answer. What annuity, to continue 3 years certain, will £1 purchase, interest 5 per cent ? 1.00000 = .367208; 2.7232 or, 7s. 4d. is the answer. By this Case Table V. is constructed. APPLICATION OF THE TABLE. 1. A person wishes to sink £500 for an annuity to continue 12 years certain, payable to himself or heirs, &c.: What annuity, payable yearly, will this sum purchase, allowing 4 per cent interest ? Opposite to 12 years, in the 4 per cent column, is found .10655 Which, multiplied by the sum, - - - - = 500 Gives 53.275 Or, £53, 5s. 6d. per annum. 2. Required the annual payment, including interest, that will pay off £10,000, borrowed at 4 per cent, interest payable yearly, at ten equal payments, the remainder after each payment to bear interest for a year. 7 PROBABILITY. In Table V., opposite 10 years, 4 per cent, is .1232909 X 10,000 1232.909 = £1232, 18s. 2d.; that is, this sum, paid yearly, will pay off the above sum, including interest, in ten equal payments. 3. What annuity ought to be paid along with a rent for 19 years, in place of paying down a fine or grassum of £200, interest 4 per cent? In Table V., opposite 19 years, the value of £1 is =.076138 Multiplied by the fine, - - = - 200 Gives 15.2276 Or, £15, 4s. 6d. Ans. Proof. From the annuity found above, Take the interest of the fine, - - - =15.2276 - = 8. Which leaves 7.2276 Being an annuity that in 19 years will amount to £200, at 4 per cent compound interest. For the amount of £1 annuity for 19 years, 4 per cent per annum, by Table III., is -Multiplied by - - - - - - - - - - - - 27.6712 7.2276 Gives the fine £200 Or, Divide the fine by the present value of an annuity of £1 for the given time and rate, and the quotient will be the answer required. By Table IV., the present value of an annuity of £1 for 19 years, interest 4 per cent., is 13.1339; by which divide £200, the fine, and the answer will be £15.2276 as above. Proof. By Table V., £1 will purchase an annuity for 19 years, interest 4 per cent, of - - - Which, multiplied by the fine, .076138 - - - - - - - - 200 Gives 15.2276 PROBABILITY. 1. The probability, or chance, of the happening of any event is expressed by a fraction: The numerator denotes the number of chances the event may happen, and the denominator expresses the number of chances it may happen or fail. Thus, if there be a chances for the happening of an event, and b chances for failing, the chance of its happening is It appears from the Northampton Table of Mortality, that the number of persons living at 20 is 5132, and the number at 30 is 4385; showing that out of 5132 persons living at the age of 20, 4385 attained the age of 30, and that 747 died in the interval. The probability that a person aged 20 shall continue in life 10 years is 438' 385-+747 4385 ._ -5132" 2. The probability of the happening of any number of events* inde* Two or any number of events are said to be independent when the occurrence of one of them will not influence the happening or failing of the other. LIFE ANNUITIES. pendent of each other, is the product of the probabilities of the happening of each single event: Thus, a bX denote the probability of the happening of two independent events. The probability that a person aged 20 shall live 10 years is s1, and the probability that a person aged 25 shall live 10 years ;therefore, 58 X 4010 1 7 5858, which is the probability that they shall both live 10 years. 94o; 3. The probability of any event failing is expressed by a fraction whose numerator is the number of chances whereby it may fail, and whose denominator is the number of all the chances both of failure and happening. Thus, the probability of an event failing is expressed by a b, because the chance of the event happening, together with the chance of its failing, is certainty, which is represented by unity; therefore, 1,-b' is b is the chance of its failing. that The probability that a person aged 20 shall die in 10 years, that is, that he shall not attain the age of 30, is 3 subtracted from unity,* or 37U for the sum of the probabilities is equal to unity. 3; 4. The probability of the failing of any number of independent events is equal to the product of the probability of the failing of each single event. Thus, as Xa--- express the probability of the happening of b d two separate events; so X - denote the probability of their failing. Since and 4 o are the probabilities that two persons aged 20 and 25 shall severally exist 10 years, the probability that these two lives ° ° shall both fail in 10 years is 1 3 X 1 -2 2832 5. The probability of the happening of either of any number of independent events is denoted by the difference between unity and the last_ _ mentioned expression. Since b X c 4 d denote the probability that X these two events shall fail, it follows that 1 {-b 1denote that they shall not both fail, that is, that one or other will happen. The probability that either of the two lives aged 20 and 25 shall last 10 years is the fraction (~ 5 ) expressing the probability that they shall both die in 10 years subtracted from unity, which leaves o for the probability that one at least of these two lives shall last 10 years. .80 ANNUITIES FOR SINGLE LIVES. The principles from which the value of an annuity on any life is derived, are the probability that a person of a given age has to live a certain number of years, and the improvement of money when invested at compound interest. The simplest calculation deduced from these elementary principles, is to determine the value of an annuity payable during any single life. * To subtract a fraction from unity is simply to take the numerator from the denominator. ANNUITIES FOR SINGLE LIVES. Suppose an annuity of £1 is to be paid to A, whose age is 20. As all annuities are understood to be made payable at the end of the year from the time they are granted, £1 paid down for the year's annuity would be too much; it is therefore discounted for one year, and the present worth of £1 interest being reckoned at 4 per cent is .9615. This sum at the end of the year, along with its interest, (.0385,) will be just equal to the annnity granted, that is, £1, and no more. But it is uncertainthat A, aged 20, will live to the end of the year; for it is found, by referring to the Northampton Table of Mortality, that out of 5132 persons alive at the age of 20, of these 72 died during the year, that is, only 5060 attained the age of 21. In order to make a just allowance for this contingency, the £1 discounted for one year must be diminished in the ratio of 5132 to 5060, that is, .9615 must be multiplied into the fraction 51 , expressing the probability that A will live one year, which will reduce it to .94801, being equal to the value of the first year's annuity. By the same method of operation may the values of the 2d, 3d, 4th, &c. year's annuity be found, till the life is extinguished. For having found the value of the first year's annuity as above, the present value of £1 for the 2d, 3d, 4th, &c. year, is .9245, .8889, .8548, &c., multiplied respectively into the fractions 5 491 48 &c., expressing the probability that A will survive the 2d, 3d, 4th, &c. year; and the sum of all the products will be the value of an annuity of £1 payable during the whole life of A, aged 20. Therefore, To find the present value of an annuity for the whole duration of any life : Calculate the presentworth of each year's annuity, and the sum will be the total present value required. The application of this rule would be very laborious in calculating the values of annuities for all ages; but a more compendious method of computation may be explained as follows:-It appears from Table VI., Northampton, that of 4 persons aged 95 living at that age, only one will live to the age of 96, and that the survivor will die before he is 97. If therefore annuities were granted to 4 persons aged 95 of £1 each for their lives, at the end of the first year only one payment of one of the said annuities would have to be made; and as the annuitants would be dead before the end of the second year, the granter would never have to make another. And that he might be neither a gainer nor a loser by granting the annuities, he should receive from each person aged 95 the present value of the only payment of £1 which he would have to make to the survivor at the end of the first year, which present value is the sum of £1 discounted for one year, equal to .9615, interest 4 per cent, per Table II.; and consequently, each annuitant ought to pay one-fourth of this sum, or 4 X .9615 = .240, which is the value of an annuity of £1 for a life aged 95, as per Table. And in the same manner it may be shown, that the value of an annuity on a life one year younger, (that is 94,) is SX .9615 x 1.240 = .530. But generally the question may be expressed in this manner: Let the value of a life one year older than the assigned life be denoted by N, and the value of £1 payable at the end of the year by and the probability that the given life will survive one year by ; the value of the annuity will be a X 1+From this expression we have the following rule:- 10 LIFE ANNUITIES. Commence with the oldest life in the table of probabilities; add unity to the value of an annuity on that age, which is 0 ; multiply the sum by the chance of a life one year younger receiving £1 at the end of the year : the product will be the value of an annuity on the next younger life. Proceed in the same manner with each younger life down to the youngest. Let it be required to find the value of a life aged 90, or any younger life, interest 4 per cent, Northampton. 95 = X .9615 x(1+.0)= 94 = 9 X .9615 X 1.240 = 93 =X .9615 x 1.530 = 92 = x .9615 x 1.827 = 91 = - X .9615 X 2.171 = 90 =X .9615 X 2.474 = 4 0.240 0.530 0.827 1.171 1.474 1.758 The value of an annuity on a life aged 90 is1.758, or £1, 15s. 2d. Table VIII. is constructed in this manner. ANNUITIES FOR JOINT LIVES. The values of annuities upon the joint continuance of two or more lives are deduced from principles similar to those for single lives. It is required to find the value of an annuity on two joint lives aged 30 and 40. The probability that A will live the first year, or attain the age of 31, is4 ; that B will live the first year, or attain the age of 41, is that both will live one year is 0X xa 5=13 In the same manner may the probability that both will survive the 2d, 3d, 4th, &c. year be stated, till the fraction expressing the probability of the oldest life vanish. These fractions being multiplied into the present value of each year's annuity discounted for 1, 2, 3, 4, &c. years, the sum of the whole will give the value of an annuity on the joint continuance of the two lives. This method of calculation would be exceedingly laborious were it required to constiruct a table of the values for joint lives, whatever were the difference of the ages of combination from the youngest life upwards, and therefore a more easy method of computation may be explained as follows:According to the Northampton Table of Mortality, the oldest pair of joint lives, whose difference of age is 5 years, is 91 and 96; and it is evident that an annuity upon the joint existence of these two lives, payable at the end of the year, can be of no value; but if we take two joint lives respectively one year younger, that is, 90 and 95, these may expect to receive one payment and no more. Now, the present value of £1 certain to be received one year hence, discounting at the rate of 4 per cent, is equal to or .9615; but the money is not to be received unless the two persons, now 90 and 95, shall both survive one year, or attain the age of 91 and 96; consequently the present value of an annuity -595 92f. To, ANNUITIES FOR JOINT LIVES. 11 of £1 upon two joint lives, 90 and 95, must be less than in the ratio of certainty to the probability that these persons shall both survive one year ; and since it appears by the table, that out of four persons living at 95 only one survives 96, it is evident the probability that any one of them shall survive 96 is equal to 4 of certainty, or if certainty be denoted by unity, this becomes simply . For the same reason the probability that a person aged 90 shall survive 91, is, according to the table, equal to P, and, as it has been already explained, the probability that a person of any age shall survive a certain number of years is represented by a fraction, the numerator of which is the number living at the advanced age, and its denominator the number living at the present age. Again, if it were certain that the person whose age is 90 shall survive one year, it is evident that the probability of 90 and 95 both surviving one year, would be the same as the probability that 95 alone would survive that period; but the probability that 90 will survive one year is uncertain; consequently the probability that 90 and 95 will both survive one year is less than the probability that 95 alone will survive one year; whence certainty (1) : probability of 90 (-) :: probability X =- the probability that both will survive one year. In 95 (4) : the same manner it has been shown, that the probability of the happening of any two independent events is equal to the product arising by multiplying together the fractions which represent the probabilities that :: Whence certainty (1) : 4 X -ach separate event will happen. .177, which is the present value ofan annuity of 46 X 4 X 1. 04 £1 upon two joint lives aged 90 and 95, reckoning interest at 4 per cent. Again, let the ages proposed be 89 and 94. Were it certain that each of these would survive one year, the value of an annuity upon their joint lives, at the end of the year, would be equal to the £1 then due, together with the value of an annuity upon 90 and 95 = 1 + .177, its prewhich multiplied by 0 sent value when discounted for one year, = and 94 shall survive 90 and 95, gives X , the probability that 89 46 x 4 x 1 + .177 = .373, equal to the value of an annuity upo the joint 62 x 9 x 1.04 -continuance of 89 and 94. From these remarks the following general expression may be given. Let the value of an annuity on any two joint lives be denoted by M, and the value of £1 payable at the end of the year by , and the probability, that two lives, each one year younger, will exist together one year by g; the value of an annuity on the joint continuance of those two Therefore, rX + younger lives will be expressed by To find the value of an annuity on two joint lives : Begin with the oldest life in the Table of Observations,joined to another ife, whose dierence of age is any proposed number of years, and proceed in the same manner as in last case. Suppose it is required to find the value of an annuity on two joint lives, aged 85 and 90, 4 per cent, Northampton. 12 LIFE 12 90 & 95=3 89 & 94= 6 X 88 & 93 87 & 92 i iX ANNUITIES. 4x .9615 x (1+0)- 0.177 X .9615 x 1.177 =0.373 .- $X 39 X .9615 X 1.373 =0.554 X .9615 X 1.554 = 0.738 0.902 86 & 91=1 l x3 x .9615 x 1.738 Xl 46 x .9615 x 1.902-1.054 85&90 The value of an annuity on the two joint lives, 85 and 90, is 1.054, or, £1, Is. Id. Table IX. is constructed in this manner. LIFE ANNUITIES. I. To FIND THE EXPECTATION TABLE WORDS, OF THE LIFE, ACCORDING OF A GIVEN OBSERVATIONS THE MEAN OR AVERAGE OF MORTALITY; OR, TO ANY IN DURATION OF LIFE ENJOYED OTHER BY A NUMBER OF INDIVIDUALS HAVING THE SAME CHANCE OF LONGEVITY. Divide the number of all the living above the age of the given life by the number living at the given age, and add haldunity to the quotient. What is the expectation of a person's life, aged 10 years, the laws of mortality being the same as observed at Northampton? The number of all the living above the age of 10, by Table VI,, is 222924, which, divided by 5675, the number of persons living at 10, gives 39.28, and this quotient increased by half-unity (.5) gives 39.78 for the expectation required.* By this Case Table VII. is constructed. life is approximately calculated as follows :--Suppose, *The mean duration of taking an instance from the Carlisle Tables, that 75 persons are alive at the age of 92, of whom are left at the successive birthdays 54, 40, 30, 23, 18, 14, 11, 9, 7, 5, 3, 1, 0. Consequently, in their 93d year, 54 persons enjoy a complete year of life, through half the year, and 21 die, whom we may suppose, one with another, to of 75 persons and 54 years and 21 half-years make 642- years, which is the total for that year. livefil e Proceeding in this way, we find that there the 93d year 54 + 2 of 21 years. 94th ... 40 + 2 of 14.. In 95th 96th 97th ... ... ... 98th ... 99th ... ... ... ... ... ... ... 100th 101st 102d 103d 104th 105th 30 + of 10 23 + 2of 7.. 18+2 of 5.. 14+" of 11+2of 9 + Jof 7 +#2of 5 + Jof 3+-{ 2of 1 +42of 0+ 2of Total, 215 + Hence, j7 are- 4 3 2 2.. 2 2.. 2.. 1.. of 75 individuals aged 92 enjoy 215 + 2 of 75 years, and each has, one with PROBABILITY-EXPECTATION OF LIFE. 13 The following method of calculation will show how to construct a table of the expectation of life for all ages from any observations. Take the Northampton Table, and begin with the oldest life. 7 . 5 - 95 = .5 = 1.05 = 94 + .5 = 1.37 = 93 - .5 = 1.75 = 92 -+.5 = + 3 + .5 = 2.09 = 91 +.5= 2.41 90 4,-5 = 1 age. 6 ... 2 66 . = +.5=2.86 = .5 ... -9 3.01 = 89= 88 87 90+.5=3.19=86 + .5 .5 ... age. ... . ... 3.37=85 = ... 3.58=84 ... What has been already stated and exemplified under the article Probability, may be here condensed for the purpose of more convenient application in the solution of the questions proposed in the sequel. II. 1. The probability or chance that A, aged 20, shall live 30 years, by the Northampton Table, is 857or .5567; that B, aged 40, shall live 30 years, is s 5, or .3389. 2. That they shall both live 30 years is .5567 X .3389 = 1887. 3. That A shall die in 30 years is 1 - .5567 = .4433; that B shall die in 30 years is 1 .3389 = .6611. 4. That they shall both die in 30 years is .4433 X .6611 = .2931. 5. That they shall not both die ; that is, that one or other shall live, is 1 - .2931 = .7069. 6. That A shall live, and B die, is .5567 X .6611 = .3681; and that A shall die, and B live, is .4433 X .3389 = .1502. III. To FIND THE VALUE OF THE EXPECTATION OF ANY GIVEN LIFE OR LIVES RECEIVING A GIVEN SUM AT THE END OF ANY GIVEN TERM. Multiply the present value of the given sum by the probability that the given life or lives will live to the end of the term assigned.* 1. What is the present value of £1, to be received at the end of 30 years, provided a person now aged 20 be then alive, interest 4 per cent, Northampton Tables? The present worth of £1, to be received at the end of 30 years, by Table II., is .30832; and the probability that a person aged 20 will live 30 years, by preceding case, is .5567. Therefore .30832 X .5567 = .1716 = value required. 2. The expectation of £1 at the end of 30 years, provided a person aged 40 be then alive, is .30832 x .3389 = .1045. 3. The expectation of £1 at the end of the same period, should both lives continue so long, is .30832 x .1887 = .0582. another, the 75th part of this, or 3.37 years. This rule is, however, mathematically incorrect, being only an approximation to the truth. The error of computation may be found nearly as follows :-Divide the number who die in the year next following the given age, by twelve times the number in the table at that age, and diminish the result of the rule by the quotient. Thus, in the instance before us, 21 divided by 12 times 75 is .03, so that 3.35 is nearer the truth. * By this case the value of Endowments to Children is found. 14 LIFE ANNUITIES. 4. The expectation of £1, should either of the lives, 20 and 40, continue to the end of 30 years, is .30832 x .7069 = .2179. IV. TO FIND THE VALUE OF AN ANNUITY DURING THE EXISTENCE ASSIGNED SINGLE OF ANY LIFE. Multiply the value of an annuity of £1 by the given sum, and the product will give the present worth of the annuity required. 1. What sum, paid down, is equal to the present value of an annuity of £100, payable yearly, during the life of a person aged 40, interest 4 per cent, Northampton ? In Table VIII., opposite age 40, in 4 per cent co umn, is found - - - - - - - - 13.197 And this value, multiplied by the given annuity, - = 100 Produces 1319.7 Or, £1319, 14s. is the value required. If this annuity were left as a legacy, the Government duty would be charged by this valuation. 2. What present sum should be paid for an annuity of £100 during the life of a person aged 25, payable yearly, interest and mortality as above ? In Table VIII., opposite the age 35, and under 4 per cent, is found, - - - - - - - - And this value, multiplied by the given annuity, - 14.039 = 100 Gives 1403.9 Or, £1403, 18s. is the value required. If an annuity is payable half-yearly, in addition to the tabular value of the annuity payable yearly, add .25 or 1-4th of a year's purchase : If payable quarterly, add .375 or 3-8ths of a year's purchase.* 3. What is the value of the last-mentioned annuity payable half-yearly . The value of £1, as above, is = 14.039 To which add 1-4th of a year's purchase, - - Together, Therefore, 14.289 X 100 required. = .250 = 14.289 = 1428.9, or £1428 : 18s. is the value 4. What is the value of the same annuity payable quarterly. The value of £1, as above, is = 14.039 And 3-4ths of a year's purchase added is .375 Together, = 14.414 Therefore, 14.414 x 100 = 1441.4, or £1441 : 8s., is the answer sought. 5. A lady aged 33 wishes to sink £1000 on irredeemable annuity for her life: What annuity will this sum purchase, interest 4 per cent, Northampton ? * Dr Price makes these additions only 1-5th and 3-10ths of a year's purchase; but Mr Baily, considered better authority, shows that the above additions are more correct. 15 ANNUITIES FOR JOINT LIVES. In Table VIII., opposite 33 years, under 4 per cent, is found 14.347, and £1000, the purchase-money, divided by the year's purchase, gives 69.701, or £69, 14s. for the annuity payable yearly. It will be observed, that the rule in this case is simply to divide the given sum proposed to be sunk by the value of an annuity of £1, equal to the age assigned. V. To FIND THE PRESENT VALUE OF AN ANNUITY DURING THE CONTINU- ANCE OF ANY TWO JOINT LIVES. Multiply the value of an annuity of £1 found in the Table by the given sum, and the product will be the answer required. 1. What is the present value of an annuity of £50 payable during the joint lives of A, aged 30, and B, 45, interest 4 per cent, Northampton? By Table IX., (difference of age 15 years,) the value of £1 -9.959 = 50 And this value multiplied by the given sum Gives 497.95 Or, £497, 19s. is the answer required. 2. What is the value of an annuity of £100 on two joint lives, both aged 65, interest 5 per cent ? By Table IX., (difference of age 0,) the value of the two joint lives, 4.960 - - And this value multiplied by - - - 100 Gives 496.0 Or, £496 is the answer sought. 3. What is the value of £100 annuity on two joint lives, aged 40 and 50, interest 4 per cent ? By Table IX., (difference of age 10 years,) opposite 40 and 50, at 4 per cent = 8.834 Which being multiplied by - - - - - 100 Gives 883.4 Or, £883, 8s. is the answer required. On this sum duty would be charged by Government, if the annuity were left as a legacy. The values of annuities on two joint lives are given in the Tables for all ages whose difference of age is 5 years, or any multiple of this nunimber; but the values for intermediate ages may be found with sufficient accuracy by the following method of interpolation:VI. Take from the Tables the values of annuities on the joint continuance of the oldest of the proposedlives, and two others separately, younger than the oldest life, by the multiples of 5 greater and less respectively than the youngest of the given lives; subtract the less value from the greater, divide the remainderby 5,-the quotient will be theffth mean between the two values, and the desired difference subtractedfrom thefirst term will give the value required. What is the value of an annuity on two joint lives, 48 and 55, interest 4 per cent, Northampton? 16 LIFE ANNUITIES. By Table IX., the value of the two joint lives, 45 and 55, is = 7.948 And the value of two joint lives, 50 and 55, is 7.593 Difference = .355 The intermediate value required is the third term of this decreasing series; it will therefore be less than the first term by 3-5ths of the difference of the extremes, that is, by X .355 = .213, this subtracted from 7.948, the first term, leaves 7.735 for the value of an annuity on the two joint lives, aged 48 and 55. Suppose it were required to find the value of an annuity on two joint lives, aged 32 and 65, interest 4 per cent. Ages. Values. 30 and 65, Tab. IX.,= 6.844 35 and 65, Ditto, = 6.747 The total difference .097 divided by 5, the quotient is .0194, being the fifth mean between these two values, and deducting .039, or two of these means, from 6.844, the remainder, or 6.805, is the value required. When one of the given lives is under 10 years of age, we ought, in deducting the values agreeably to this rule, to attend particularly to the order. of the difference between the values taken from the Tables; that is, to observe whether such difference is increasing or decreasing. For instance, suppose it is required to determine the value of an annuity on two joint lives aged 9 and 30, interest 3 per cent, Northampton, the rule directs us to find the value of an annuity on two joint lives aged 5 and 30, and on two joint lives 10 and 30, which are respectively equal to 13.762, and 14.150, and that .078, or one-fifth of the difference between them, being subtracted from the latter value, will give 14.072 for the value of an annuity on two joint lives aged 9 and 30. But the following comparison will show this to be incorrect: for if we take out the values of annuities on the several joint lives as under, viz.5 10 15 20 25 30 and and and and and and 30 = 13.762 30 = 14.150 30 = 13.734 30 = 13.286 30 = 12.966 30 = 12.589 It will be seen that, beginning at the bottom, the values gradually increase, till we come to the age of 10 and 30; and therefore, that the value of an annuity on any two joint lives, one of which is 30 years of age and the other of any age between 10 and 30 will be deduced accurately enough by means of the rule above given. And this also would be the case with respect to the value of annuities on any two joint lives, one of which is 30 years and the other of any age below 10 years of age, provided the decrease commenced exactly at the age of 10 years : but it is probable that the decrease does not take place till about the joint ages of 8 and 30,* and consequently that the value of an annuity on two joint lives, aged 9 and 30, is greater than 14.150 instead of being less. The * The period at which this decrease commences varies according to the rate of interest, and according to the difference between the ages of the two lives. ANNUITIES FOR THREE JOINT LIVES. 17 proper method, therefore, of finding the value of an annuity on the two joint lives 9 and 30 will be to take .083, or one-fifth of the difference between 14.150 and 13.734, and add it to 14.150, which will give 14.233 for the value of an annuity on the two joint lives 9 and 30. When neither of the ages of the two proposed lives ends with 0 or 5, proceed as follows:Let the value of an annuity be required on two joint lives aged 38 and 47, Northampton Table, 4 per cent. Take the ages 35 and 45, and 40 and 45, and as shown in the above examples, find such a mean as would represent 38 and 45. Then, between 35 and 50, and 40 and 50, find such a mean as answers to 38 and 50. Having then 38 and 45 and 38 and 50, find such a mean as answers 38 and 47. 35 & 45, Table IX., = 9.706 = 9.381 do. 40 & 45, 5) .325 (.065 And .065 X 3 - .195 - 9.706 - 9.511 = 38 and 45. 35 & 50, Table IX., = 9.110 = 8.834 do. 40 & 50, 5) .276 (.055 And .055 X 3 = .165 - 9.110 _ 8.945 - 38 and 50 38 & 45, found above, - 9.511 - 8.945 do. 38 & 50, 5) .566 (.113 And .113 X 2 = .226 - 9.511 = 9.285, Ans. THREE JOINT LIVES. The labour of computing tables of the values of annuities on three joint lives being, from the endless combinations of ages, very laborious, the following method is adopted for finding the values of annuities on any three from the values of any two joint lives, which is held to be sufficiently accurate for any practical purpose. VII. TO APPROXIMATE TO THE VALUE OF AN CONTINUANCE OF THREE LIVES, A, B, ANNUITY ON THE JOINT C. Let A be the youngest, and C the oldest of three lives ; take the value of the two joint lives B and C, andfind the age of a single life D of the same value nearly ; then jfind the value of the joint lives A and D. 1. Let the value of an annuity be required on three joint lives, 10, 17, and 47, interest 4 per cent, Northampton. By Table IX., the value of the two oldest joint lives is 10.208, answering to a single life D, of 55 years, Table VIII.; and the value of two joint lives, 10 and 55, Table IX., is 9.256, which is the answer. 2. What is the present value of an annuity on three joint lives, 10, 20, and 30, interest 4 per cent, Northampton ? The value of an annuity on the two joint lives 20 and 30, Table IX., is equal to 11.873; which, compared with the values in Table VIII., B 18 LIFE ANNUITIES. will be found equal to the value of an annuity on a single life D, 47 7,* or 47 years and 1 month. And the value of an annuity on the joint lives A and D, (that is, on two joint lives, 10 and 47 ,) is, by the preceding case, equal to 10.474,t which is the value required. This rule will give the values of annuities on three joint lives generally within a ninth or tenth, and sometimes within a twentieth part of a year's purchase. It may also be observed, that when the oldest of the three ages does not exceed 75, and the youngest is not less than 10, the error falls on the side of excess; and consequently, that if .05 (or a twentieth part of a year's purchase) be deducted from the values by the rule, the true value will be obtained in some cases almost exactly, and in most cases much more nearly. 3. What is the present value of an annuity on the joint continuance By the rule the approximated value is of three lives, 40, 50, and 60 ? 6.046, but the correct value is 5.994. If a twentieth of a year's purchase be deducted from 6.046, the value by the rule will be nearly correct. VIII. To FIND THE VALUE OF A DEFERRED ANNUITY ON ANY OR JOINT SINGLE LIVES ; OR IN OTHER WORDS, THE VALUE OF AN ANNUITY FOR A LIFE OR LIVES, TO COMMENCE AFTER A GIVEN TERM OF YEARS, PROVIDED THE PERSON OR PERSONS BE THEN ALIVE. Multiply the value of an annuity for a life or joint lives, greater by the given term than the proposed life or lives by the present value of £1, to be received at the end of the given term, and this product, multiplied by the probability that the given life or lives will continue so long, will be the answer required. 1. A person aged 20 wants to purchase an annuity to be entered upon at the end of 30 years, that is, when he attains the age of 50, and then to continue to his death: What is the present value of same, interest 4 per cent, Northampton? The value of an annuity on a life at 50, (20 + 30,) by Table VIII., is 11.264; the present value of £1, to be received at the end of 30 years, interest 4 per cent, Table II., is .3083; and these two quantities multiplied together produce 3.4726, being the present value of an annuity of £1, to be granted to a person now aged 20, thirty years hence. And the probability that a life 20, will continue 30 years, is 5 , or .5567. * The value in Table VIII, which is next greater than 11.873 is 11.890; which is the value of an annuity on a single life aged 47. The difference between these two values, or 17, is the numerator of the fraction; and the denominator is the difference between 11.685 (or the next less value to 11.873) and 11.890. f The value of an annuity on two joint lives aged 10 and 47 is, by the preceding case, equal to 10.485; and the value of an annuity aged 10 and 48, is, by the same case, equal to 10.356. The difference between these two values, or .129, being multiplied by ~,14, will give .011 ; which, being subtracted from 10.485, will leave 10.474 for the value required. This shows the true method of proceeding in such cases; but if this fraction be either very small, or does not differ much from unity, the error will not be considerable, if, for the sake of more expedition, D is always taken for that age, whether greater or less, which answers most iearly to the value of the annuity on the joint lives B and C, without regarding the fraction. TEMPORARY ANNUITIES. 19 Therefore, 3.4726 x .5567 = 1.933, the value required; Or, 11.264 X .1716 (Case III.) 1.933, as above. 2. Had the person been 40 years of age, by Table VIII., a life at 70 (40 + 30) is equal to 6.361; the present value of £1, payable 30 years hence, is .3083; and the product of these two quantities is 1.961, which is the value of an annuity of £1, to be granted to a person now aged 40, thirty years hence. And the probability that a person aged 40 will live 30 years is or .3389. Therefore, 1.961 x .3389 .665, the value required; Or, 6.361 X .1045 (Case III.) = .665, as above. = 3. Two persons aged 20 and 40, wish to purchase an annuity for the remainder of their joint lives; after 30 years, what is the value of the same, reckoning interest at 4 per cent, Northampton ? The value of the joint lives, 50 and 70, by Table IX., is 5.306; the value of £1, to be received at the end of 30 years, is .3083; the probability that a person aged 20 will attain the age of 50, is 5%; and the probability that a person aged 40 shall live 30 years is - 5. The probability that both persons will live 30 years is 85 X 665 s 9 , or .18868. And 5.306 x .3083 x .1886 = .3088, the answer; Or, 5.306 X .0582 (Case III.) = .3088, as above. To find the value of the above annuities in annual payments, commencing immediately: Divide the value of an annuity in a single payment by unity added to a similar temporary annuity for one year less than the given term, found by the succeeding case. Take the first example:--The value of the deferred annuity is 1.933, and the value of a temporary annuity, on same life, for 29 years, is, by following case,* equal to 13.929; therefore, 1.933 divided by 14.929 will give .129 for the answer. IX. To FIND THE VALUE SINGLE on JOINT OF A TEMPORARY ANNUITY ON ANY LIVES. From the value of an annuity on the single or joint lives, deduct the value of an annuity on the same lives, deferred during the given term. 1. A person aged 20 purchases an annuity for 30 years, on condition that if he dies before the expiration of that term, the annuity shall cease: What ought he to give for the same, 4 per cent, Northampton? * A more easy method of finding such temporary annuities is expressed by the following rule :-To the value of :fie deferred annuity, add the expectation that the given life or lives shall receive £1 at the end of the given term, subtract the sum from the value of an annuity on the given life or lives; the difference will be the value of the temporary annuity for one year less than the given term. The value of the deferred annuity, as above, is 1.933, and the expectation of £1, on a life aged 20, at the end of 30 years, by Case III., is .1706, making together 2.104; which, subtracted from 16.033, value of an annuity for a life at 20, leaves 13.929 as above. 20 LIFE ANNUITIES. The value of an annuity on a life aged 20, Tab. VIII. is = 16.033 Deduct value of deferred annuity for 30 years, on same = 1.933 life, Case VIII. The answer required is = 14.100 2. If the life had been 40 years of age, then .664, or the value of an annuity on such life deferred 30 years, as found by preceding case, deducted from 13.197, the value of a life aged 40, leaves 12.533 for the value sought. 3. Had these two lives, 20 and 40, purchased the annuity on their joint lives, then .3088, or the value of an annuity on such joint lives deferred 30 years by preceding case, being deducted from 10.924, or the value of the two joint lives by Table IX., leaves 10.615 for the value required. X. FIND THE VALUE OF AN ANNUITY GRANTED DURING THE LONGEST or TWO LIVES; THAT IS, THE ANNUITY TO SUBSIST SO LONG To AS ANY ONE OF THEM CONTINUES TO LIVE. From the sum of the values of an annuity on the two single lives, subtract the value of an annuity on the two joint lives. 1. Let the ages of the two lives be 20 and 40, interest 4 per cent, Northampton.* = 16.033 The value of a life aged 20, Table VIII, = 13.197 do. ... ... 40, ... um Su Deduct value of the two joint lives, Table IX. The differei nce = 29.230 = 10.924 = 18.306 is the value required. 2. Had the ages of the given lives been 50 and 70The value of an annuity at 50, Table VIII., is ... ... ... do. 70, - - = 11.264 = 6.361 Sum = 17.625 5.306 Deduct value of the two joint lives, 50 and 70, Table IX. Number of years' purchase = 12.319 XI. To FIND THE VALUE OF AN ANNUITY ON THE LONGEST or THREE LIVES, A, B, C. From the sum of the values of an annuity on all the single lives, subtract the sum of the values of an annuity on each pair of joint lives, and to the difference add the value of an annuity on the threejoint lives. * This rate of interest and mortality are to be understood in all cases, unless otherwise expressed. 2 LONGEST OF THREE LIVES---SURVIVORSHIP. 21 1. What is the value of an annuity on the longest of three lives, that is, to continue so long as any one of the three lives, 20, 30, and 40, shall be in life, interest. 4 per cent, Northampton ? Value of an annuity on a life aged 20, Table VIII., = 16.033 30, do. =14.781 40, do. = 13.197 Sum =44.011 Deduct value of each pair of joint lives, viz. 20 and 30, Table IX., = 11.873 = 10.924 20 and 40, do. 30 and 40, do. = 10.490 33.287 ______ Remains 10.724 Add value of the three joint lives, 20, 30, and 40, Tab. X. = 8.986 Number of years' purchase = 19.710 2. Suppose the above annuity to be equally divided among A, B, and C, while they are all living, but on the decease of any one of them is to be equally divided between the two survivors during their joint lives, and then to belong entirely to the last survivor for his life. The value of their respective shares, or the proportion which each ought to contribute towards the purchase, is as under : A = 16.033 -4(11.873 10.924) + x 8.986 =7.630=A'sshare. B= 14.781 (11.873 + 10.490) x 8.986 = 6.595 B's share. C = 13.197 (10.924 + 10.490) 1X 8.986 = 5.485 share. + +3 = + = C's As above, 19.710 3. Suppose the above annuity to be enjoyed in the followiig manner: A and B are to enjoy it equally during their joint lives; but on the decease of either of them, it is to be equally divided between A and C, or B and C, the two remaining persons ; and lastly, to be enjoyed wholly by the survivor ; the value of the share of each person will be as under: A = 16.033 -(11.873 + 10.924) + 2 x 8.986 = 9.127 B= 14.781 -(11.873 + 10.490) 2 X 8.986 = 8.093 C = 13.197 -2 (10.924 + 10.490) = 2.490 + As above, 19.710 4. Suppose the above annuity were to be divided among A, B, and C, in the following manner, viz.: A and B are to enjoy it equally during their joint lives; if A dies first, then B and. C are to enjoy it equally during their joint lives, and the survivor is to have the whole ; but if B dies first, then A is to enjoy the whole during his life, and after his decease it is to devolve wholly to C : What is the value of their respective shares ? A = 16.033 . 2X 11.873 = 10.096 B 14.781 -1 (11.873 + 10.490) + 2 x 8.986 = 8.093 C = 13.197 -- 10.924- 2 x 10.490 + 2 x 8.986 = 1.521 As above, 19.710 22 LIFE ANNUITIES. 5. Suppose A, B, and C, agree to divide the above annuity amongst them in the following manner : A is to enjoy the whole annuity during his life, but after his decease it is to be divided equally between B and C during their joint lives; and the survivor is to have the whole: the value of their respective shares is as under : A B C = 16.033 = 14.78113.197 - = - - - - - - X 10.490 + 2 x 8.986 11.873 10.924 = X 8.986 = 10.490+ - 1 16.033 2.156 1.521 As above, 19.710 6. Suppose A, B, and C, agree to purchase an annuity on the longest of their lives, to be enjoyed wholly by each of them in succession; that is, A is to enjoy it first for his life; at his decease B is next to enter upon it; and C last. The value of their respective shares is as under :11.873 A -= 16.033 B = 14.781 - C - - - = 13.197 - (10.924 + 10.490) + 8.986 - - = - = = 16.033 2.908 .769 As above, 19.710 XII. TO FIND THE LIVES, A, VALUE AN OF UPON GRANTED ANNUITY THREE B, C, BUT TO CONTINUE ONLY SO LONG AS ANY TWO OF THEM ARE IN BEING TOGETHER. From the sum of the values of an annuity on each pair of joint lives, AB, A C, and BC, subtract twice the value of an annuity on the three joint lives, A, B, C. 1. Suppose an annuity is purchased upon three lives of A, B, C, aged respectively 20, 30 and 40The value of the joint lives 20 and 30, Table XI., = 11.873 ... ... ... 20 and 40 do. = 10.924 .. ... ... 30 and 40 do. = 10.490 Sum, 33.287 Subtract twice the value of the three joint lives, that is, 8.986 X 2, - - - - - 17.972 Leaves 15.315 for the number of years' purchase required. 2. The value ofthe share of each person will be A = (11.873 + 10.924) - - x 8.986 = B - 2 (11.873 + 10.490) ×x 8.986 = 8.986 = C _ (10.924 + 10.490) - sX as under5.408 = A's share. 5.191 =- B's share. 4.716 = C's share. As above, 15.315 3. A, B, and C agree to purchase an annuity, to continue as long as any two of their lives are in being, and which is to be divided amongst them in the following manner : A and B are to enjoy it equally during 23 DEFERRED ANNUITIES. their joint lives; but on divided between the two respective shares ? A = 2 (11.873 + (11.873 + B = (10.924 + C = 2 the death of either of them, it is to be equally survivors for their joint lives : What is their 6.905 = A's share. 8.986) 8.986) = 6.689 = B's do. 8.986 = 1.721 = C's do. 10.924 10.490 10.490) - As above, 15.315 4. A, B, and C agree to purchase an annuity, to continue as long as any two of them are in being together; and which is to be divided between them in the following manner : A and B are to enjoy it equally during their joint lives; if A dies first, then B and C are to enjoy it equally during their joint lives; but if B dies first, then A is to enjoy the whole during the joint lives of A and C: the value of their respective shares is as under :A = - X 11.873 + 10.924 - 8.986 = 7.874 = A's share. B = (11.873 + 10.490 - 8.986) = 6.689 = B's do. 2 C = (10.490 - .752 - - 8.986) = C's do. As above, 15.315 XIII. ON THE LONGEST OF ANY DEFERRED FOR ANY GIVEN TERM. Substitute the values of deferred annuitieson each single andjoint lives, instead of the annuities for the whole continuance of those lives, and proceed as in the solutions to the two foregoing cases. TO FIND THE VALUE OF AN ANNUITY NUMBER OF LIVES What is the value of an annuity granted on the longest of two lives, 20 and 40, but which is not to be entered on or enjoyed till after the expiration of thirty years, interest 4 per cent, Northampton ? By Case VIII. the value of an annuity deferred thirty years, on a life aged 20, - - - - - - - And by same case the value of the like annuity on a life 40, Together Subtract value of the joint lives, 20 and 40, by same case, = - 1.933 .665 =2.598 = .308 Value required = 2.290 To find the value in annual payments commencing immediately: Divide the single payment by unity added to the value of a temporary annuity on the longest of the given lives, for one year less than the given term. By the following Case (XIV.)* the value of an annuity on the longest of the two lives, for 29 years, is 15.790; consequently 2.298 divided by 16.798 will give .186 for the value in annual payments. * A more easy method of finding such temporary annuities is expressed by the following rule: To the value of the deferred annuity on the longest of the given lives, add the expectation that the longest of such lives shall receive £1 at the end of the given term, subtract the sum from the value of an annuity on the longest LIFE ANNUITIES. 24 If the deferred annuity depend upon the joint existence of all the lives to the end of the given term, the value will be equal to the value of an annuity on the longest of the same number of lives, (each older by the given term than the given lives,) multiplied by the expectation that the joint lives shall receive £1 at the end of that term. 1. What is the value of an annuity on the longest of two lives, 20 and 40, but which is not to be entered upon till the end of 30 years, and then only in case both the lives are in existence, interest 4 per cent Northampton ? The value of an annuity on the longest of two lives, 50 and 70, Case X., is 12.319, and the expectation that two lives, 20 and 40, will receive £1 at the end of 30 years, by Case III., is .0582: these two values, multiplied together, will give .7169 for the answer. To find the value of the same in annual payments, commencing immediately: Divide the single payment by unity added to the value of annuity on the joint lives for one year less than the given term.See note to Case VIII., p. 19. XIV. TO FIND THE VALUE OF A TEMPORARY ANNUITY ON THE LONGEST OF ANY NUMBER OF LIVES. From the value of an annuity on the longest of the given lives, subtract the value of the same annuity deferred during the given term. What is the value of a temporary annuity for 30 years on the longest of two lives, aged 20 and 40 ? Value of annuity on the longest of those lives, Case X., Value of annuity on do. deferred 30 years, Case XIII., 18.306 2.290 = The difference = 16.016 is the value required. OR, THE VALUE OF A TEMPORARY OF THE TWO LIVES IS EQUAL ANNUITY ON THE JOINT TWO SINGLE LIVES. ANNUITY LONGEST TEMPORARY FOR THE TO THE VALUE OF A LIVES, SUBTRACTED FROM THE SUM OF THE 0... By Case IX., the value of a single life aged 20, ... ... 40, Subtract value of the joint lives, by same Case, - = 14.100 - = 12.532 Sum = 26.632 = 10.616 As above, 16.016 of the given lives : the difference will be the value of an annuity for one year less than the given term. 2.290 The value of the deferred annuity found above is .218 By Case III. the expectation of £1 on the longest of the two lives is Together, 2.508 which, subtracted from 18.306, (value of an annuity on the longest of the two lives, Case X.,) leaves 15.798, as above. 25 REVERSIONARY ANNUITIES. XV. To FIND THE VALUE OF THE REVERSION OF AN ANNUITY ON A SINGLE LIFE AFTER ANY OTHER SINGLE LIFE.* From the value of an annuity on the life in reversion, subtract the value of an annuity on the two joint lives: the difference will be the value required. A person aged 20 wishes to purchase an annuity for what may happen to remain of his life beyond another life aged 40 : What ought he to give for the same, interest 4 per cent, Northampton ? Value of annuity on life in reversion, aged 20, Tab. VIII., Subtract value of the joint lives, 20 and 40, Table IX., = The number of years' purchase is = 16.033 10.924 5.109 To find the value of this reversionary annuity in annual payments: Divide the value in a single payment by unity added to the value of an annuity on the joint lives. Thus, 5.109 divided by 11.924, gives .428 for the annual payments that ought to be made during their joint lives. To OF THE FIND THE VALUE SINGLE LIFE LIVES B. C. A, AFTER XVI. REVERSION THE OF AN ANNUITY ON A LONGEST OF TWO OTHER Subtract the sum of the values of an annuity on the two joint lives A B and A C, from the sum of the values of an annuity on the single life in reversion, and on the threejoint lives, A, B, C. What is the value of an annuity on the life of a person aged 20, to be entered upon by him after the decease of both B and C, aged 30 and 40 respectively? = 16.033 From an annuity on the single life 20, Table IX., = 8.986 And the three joint lives, 20, 30, and 40, Table X., Together Subtract value of joint lives,20 and 30, Table IX., do, 20 and 40, = = _ 25.019 11.873 10.924 - 22.797 Which leaves 2.222 for the value required. XVII. To FIND THE THE VALUE LONGEST OF THE REVERSION OF TWO LIVES A AND OF AN ANNUITY ON B, AFTER THE EXTINC- TION OF A SINGLE LIFE C. From the sum of the values of an annuity on each single life A and B, and on the three joint lives, subtract the sum of the values oqf an annuity * By this question is found the value of annuities for the benefit of widows, &c 26 LIFE ANNUITIES. on each pairofjoint lives, A B, A C, and BA ; the diference will be the value required. What is the value of an annuity on two lives, -aged 20 and 30, to be enjoyed during the longest of their lives, after a life aged 40 ? The sum of the values of the two lives, 20 and 30, by 16.033 + 14.781 = 30.814 Tab. VIII., is Value of an annuity on the three joint = 8.986 lives, 20, 30, and 40, by Tab. X., is 39.800 TogetherDeduct value of annuities on each pair of the joint lives, viz. A B = 20 and 30 = 11.873 A C = 20 and 40 = 10.924 B C - 30 and 40 = 10.490 - 33.287 The value required is = 6.513 ORu From the value of the longest of the three lives, subtract the value of the lfe of C. Value of the longest of the three lives, 20, 30, and 40, by Case XI., = 19.710 is = 13.197 Deduct value of the life aged 40, by Table VIII., As above, 6.513 XVIII. To FIND THE VALUE OF THE REVERSION OF AN ANNUITY DURING A SINGLE LIFE A, AFTER THE EXTINCTION OF TWO JOINT LIVES B and C. From the value of an annuity on the life of A in reversion, subtract the value of an annuity on the threejoint lives, A, B, C. What is the value of an annuity on the life of a person aged 20, which he is to enter upon after the decease of either of two lives, B aged 30, and C aged 40? 16.033 Value of a life aged 20, by Table VIII., is Value of the three joint lives, 20,30, and 40, by Tab. IX., is = 8.986 Value required is To FIND THE VALUE OF TWO THE XIX. REVERSION = 7.047 OF AN ANNUITY JOINT ~LIVES AFTER THE EXTINCTION OF A ON SINGLE LIFE. From the value of an annuity on the two joint lives A and B in expectation, subtract the value of an annuity on the three joint lives, A, B, and C; and the remainder will be the value in reversion. What is the present value of the reversion of an annuity to be received during the joint continuance of two lives 20 and 30, provided they survive a life aged 40 ? DEFERRED REVERSIONARY 27 ANNUITIES. Value of the two joint lives, A and B, that is, 20 and 30, Table IX., = 11.873 Deduct value of the three joint lives, 20, 30, and 40, Tab. X. = 8.986 The value required = 2.887 XX. To FIND THE PRESENT VALUE OF A DEFERRED ARY ANNUITY, MAIN OF IT THAT IS, REVERSION- TO BE ENJOYED BY ONE LIFE FOR WHAT MAY RE- BEYOND ANOTHER LIFE, AFTER A GIVEN TERM OF YEARS, PROVIDED BOTH LIVES CONTINUE TO THE END OF THE GIVEN TERM. From the value of a life greater by the given term than the life in expectation, subtractthe value of the two joint lives greater by the given term of years, multiply the remainder by the value of £1, to be received at the end of the given term, and then multiply by the probability that the two given lives shall both continue the given term, and the product will be the answer. What is the value of a reversionary annuity to be enjoyed by a life aged 20, for what may happen to remain of it beyond another life aged 40, after 30 years, provided both lives continue so long, interest 4 per cent, Northampton ? The value of a life 50, (20 + 30,) Tab. VIII., The joint lives, 50 and 70, Tab. IX., - = = 11.264 5.306 5.958 The present value of £1, due 30 years hence, is .3083: and 5.958 X .3083 = 1.8375: the probability that 20 and 40 shall both live 30 years is 5 X 3 = .1887: and 1.8375 X .1887 = .346, the present value of £1. To find the value in annualpayments, during the continuance of the joint lives : Divide the single payment by unity added to the value on the joint lives, as explained in Case X V. To FIND ANNUITY ONE THE VALUE OF A XXI. DEFERRED TO BE ENJOYED FOR WHAT LIFE AFTER ANOTHER, REVERSIONARY MAY HAPPEN TO REMAIN PROVIDED THE LIFE IN OF EXPECTA- TION CONTINUES A GIVEN TIME. Find by Case VII. the present value of the annuityfor the remainder of the life in expectation after the given term, and multiply this value by the probability that the other life shall fail within that time; find also by the above example, the value of the reversion, provided both lives continue the given time : add their values together, and the sum will be the answer required. What is the present value of a reversionary annuity for the life of a person now aged 20, to commence at the end of 30 years, if another person now 40 should be then dead; or if this should not happen at the end of any year beyond 30, in which the former shall happen to survive the latter-interest 4 per cent, Northampton ? 28 LIFE ANNUITIES. A life at 50, Table VIII., = 11.264; the present value of £1, due 30 .3083; and the probability that a person aged 20 shall years hence, is or .5567. live 30 years is 5 Therefore 11.264 X .3083 X .5567 = 1.933. The probability that a person aged 40 shall live 30 years is s or .3389, subtracted from unity, leaving .6611 for the probability that he will die in 30 years. = 1.278 And 1.933 X .6611 Add value of reversion, provided both 20 and 40 live = .346 30 years, as found by last Case, = Together, 1.624 which is the value of the reversionary annuity required. To find the value in annual payments during the continuance of their joint lives : Divide the single payment found above by unity added to the value of an annuity on the joint lives.-See Case XV. XXII. A AND B WISH TO PURCHASE AN ANNUITY ON THE LONGEST OF THEIR LIVES, WHICH IS TO WHILE THEY BE EQUALLY DIVIDED BOTH LIVING, ARE EITHER OF THEM IT IS BUT ON BETWEEN TO BELONG WHOLLY TO THE TO FIND THEIR RESPECTIVE SHARES, OR THEM THE DECEASE OF SURVIVOR; THE PROPORTION WHICH EACH PERSON OUGHT TO CONTRIBUTE TOWARDS THE PURCHASE. From the value of an annuity on the life A or B, subtract half the value of an annuity on the two joint lives : the remainder will be the value of A or B's interest. Let the age of A be 20, and that of B 40 years. The value of an annuity on a life aged 20, is 16.033; on a life aged 40, 13.197; and two joint lives, 20 and 40, is 10.924. Therefore 16.033 0.24 And 13.193- 10.571 124 - 7.735 = share =- A should contribute. share B should contribute. The above two values, added together, make 18.306, equal to the value of an annuity on the longest of two lives aged 20 and 40, by Case X., question 1st. If the annuity is for a term of years less than the wlfle continuance of life, substitute the values of annuities for the given term, instead of values for the whole duration of the lives, and proceed with the substituted values according to the rule. Thus, if the annuity had been for 30 years only, find the value of a temporary annuity for 30 years on a single life aged 20, on a single life aged 40, and on the two joint lives 20 and 40, which values, by Case IX., are equal respectively to 14.100, 12.533, and 10.615 :Therefore, 14.100 And 12.533 - 10.6 15 = 10,15. 8.7925 = the share of A. 7.2245 = the share of B. The above two values added together, make 16.017, equal to the value of a temporary annuity on the longest of the two lives, by Case XIV, 29 LIFE ANNUITIES. XXIIII. TwO PERSONS ARE IN POSSESSION OF AN ANNUITY ON THE LONGEST OF THEIR LIVES, WHICH ON THE DECEASE OF EITHER OF THEM AND HIS HEIRS DURING THE LIFE OF THE SURWILL BELONG TO D VIVOR; TO FIND THE VALUE OF THE EXPECTATION. From the sum of the values of an annnity on each single le in possession, subtract twice the value of an annuity on their joint lives: the difference is the answer. Suppose the age of the lives in possession to be 20 and 40. Value of an annuity on a life aged 20, by Table VIII., = 16.033 40, by Ditto, - = - 13.197 Sum = 29.230 Deduct value of the two joint lives 20 and 40=10.924 x 2 = 21.848 Therefore, the interest of D and his heirs is = 7.382 OR, From the value of the longest of the two lives, subtract the value of the joint lives. From the value of the longest of the two lives, by Case X., is - - - - - - - - Subtract value of the two joint lives, by Table IX., - - 18.306 = 10.924 Leaves, as above, 7.382 If the annuity is for a term of years less than that to which it is possible that either of the given lives may extend, substitute the values of annuities for the given term, instead of the values of annuities for the whole continuance of the lives, and proceed with these substituted values according to the terms of the rule. If the above annuity on the two lives had been for 30 years only, then 21.230, (or twice the value of a temporary annuity for 30 years on the joint lives, found by Case IX.,) subtracted from 26.633, the sum of the values of a temporary annuity for 30 years on each of the single lives, as found by same question, will leave 5.403 for the value required. XXIV. TO FIND THE VALUE OF AN ANNUITY DURING THE JOINT LIVES OF A AND B WHICH IS TO BE REDUCED ONE-HALF DURING THE LIFE OF THE SURVIVOR. The annuity is equal to half the sum of the values of the two single lives. Let the ages of A and B be 20 and 40. The value of a life aged 20, Table VIII., - - - - - ... ... ... 40, Do. = 16.033 = 13.197 Sum 29.230 Half of which is 14.615 30 LIFE ANNUITIES. If A and B were to sink £1000 to purchase such annuity, then £1000 divided by 14.615 would give 68.4237, or £68, 8s. 6d. would be the value during the joint lives, and £34, 4s. 3d, during the life of survivor. XXV. D AND HIS HEIRS, AS SOON AS ANY TWO OF THREE JOINT LIVES, A, B, AND C, BECOME EXTINCT, ARE TO ENTER UPON ANY ANNUITY, AND TO ENJOY THE SAME DURING THE LIFE OF THE TO FIND THE VALUE OF D's SURVIVOR; INTEREST THEREIN- To the sum of the single lives, A, B, and C, add thrice the value of the threejoint lives, from which deduct twice the sum of the values of each pair ofjoint lives, viz. of A B, A C, and B C; and the remainder will be the value of the reversion required. An estate is held on three lives whose ages are 20, 30, and 40, the income of which, as soon as any two of these lives become extinct, is to belong to D and his heirs during the continuance of the third life: What is the interest of D in this lease ? Value of an annuity on a life aged 20, Table VIII., is ... ... ... ... 30, Ditto, - = 14.781 -16.033 ... ... ... ... 40, Ditto, - = - 13.197 Add thrice the value of the three joint lives - 8.986 X 3 = 26.958 = 70.969 Sum Deduct value of the two joint lives 20 & 30, Table IX., ... ... - = 11.873 20 & 40,Do., =10.924 30 & 40, Do., = 10.490 - ... .. . ... "... 2 x 33.287 = 66.574 Value of £1 per annum - 4.395 XXVI. D ONE OF THREE GIVEN LIVES, AND HIS HEIRS, AS SOON AS ANY A, B, C, ORDER BECOMES EXTINCT, TO LONGEST ARE ENJOY THE SAME TO ENTER UPON AN ANNUITY IN DURING THE CONTINUANCE OF THE REMAINING LIVES; D'S TO FIND OF THE INTEREST T HEREIN. From the sum of the values of an annuity on each of the single lives, subtractthe sum of the values of an annuity on each pair ofjoint lives: the remainder will be the interest of D in this annuity. Suppose the lives aged 20, 30, and 40, interest 4 per cent. Value of the three single lives = 16.033 + 14.781 + 13.197, - - - - - Deduct value of each pair of joint lives 10.924 + 10.490, - - - - - - = 11.873 + - - Value of reversion, = 44.011 = 33.287 10.724 31 3 ASSURANCES ON LIVES. D AND XXVII. HIS HEIRS, AS SOON AS ANYONE Or THREE LIVES, A, B, AN C, BECOMES EXTINCT, ARE TO ENTER UPON TO ENJOY THE SAME DURING THE JOINT ANNUITY IN ORDER CONTINUANCE OF THE SURVIVORS ; TO FIND THE VALUE OF HIS INTEREST THEREIN. From the sum of the values of an annuity on each pair ofjoint lives subtract thrice the value ofan annuity on the three joint lives; the remainder will be the value required. Suppose the lives to be aged 20, 30, and 40. Sum of the value of each pair of the joint lives = 11.87. + 10.924 + 10.490, - 33.287 Deduct value of the three joint lives = 8.986 X 3 26.958 Value required = 6.329 ASSURANCES ON LIVES, &c. XXVIII. To ESTATE FIND THE VALUE OF A REV ERSIONARY IN FEE, TO BE ENTERED UPON AFTER A LIFE OR LIVES. From the perpetuity* subtract the value of an annuity on the given life or lives in possession, whether single,joint, or longest, and multiply the remainder by the annual produce.or rent of such estate; the product will be the answer required. 1. What is the present value of a reversion of an estate in fee, after the death of a person now aged 20-interest 4 per cent, Northampton? the The perpetuity is - - - - Deduct value of a life 20, Table VIII., and - - = - : =-16.033 25.000 Year's purchase = 8.967 If the estate yielded £8 per annum, then 8.967 multiplied by 8 will give 71.736, or £71, 14s. 8d. is the value required. 2. An estate worth X850) falls to a person on the extinction of either of two lives, 40 and 55 : What is the present value of same-interest per cent, Carlisle ? Interest being 4 per cent, the perpetuity Deduct value of two joint lives, 40 and 55, Table IX., " . Whi being multiplied by the rent, 4 =: 25.000 - 8.22 1 Leaves 16.779 34 - Gives 570.486 £570, 9s. 8d. is the value of the reversionary estate. Or * Perpetuity signifies the value of the fee-simple of an estate, and is found by dividing £100 by the rate of interest per cent, 100 - ;100 ; 33.333;j-= 25.000; - thus,- ;100 m20.000; - 10633f 32 ASSURANCES ON LIVES.- To find the value in annual payments: Divide the single payment by unity added to the value of an annuity on the given life or lives,-Take the first example :71967.= 4.2301, or £4, 4s. 7d. is the answer. 11.033 XXIX. To FIND THE VALUE OF AN ASSURANCE OF ANY GIVEN SUM FOR THE WHOLE CONTINUANCE OF A LIFE OR LIVES, TO BE RECEIVED AT THE END OF THE YEAE, ON THE DECEASE OF THE ASSURED. Multiply the value of an annuity of£l on the given life or lives by the rate of interest, and subtract the productfrom unity ; divide the remainder by the amount of £1 in one year, and the quotient will be the value of an assurance of £1. 7..What is the value of an assurance of £100, payable on the demise of a person whose age is now 20--interest 4 per cent, Northampton? = 16.033 Value of an annuity on a life aged 20, Table VIII., .04 Multiplied by the interest of £1, at 4 per cent, And this product subtracted from unity, - Gives .64132 1. Leaves .35868 Therefore .358 = .34488 x 100 = 34.488, or £34, 9s. 9d., is the present value of the assurance in a single payment. To find the value in annualpayments, commencing immediately: Divide the single payment by unity added to the value of an annuity on the given life ; thus,34.488 2.025, or £2, Os. 6d. is the answer. If the annual premium be paid half yearly or quarterly, &c., the following additions to the yearly value require to be made:For half-yearly payments, add one-half of a year's purchase, or .5; if quarterly, add one-fourth of a year's purchase, or .25; and if monthly, add one-twelfth of a year's purchase, or 0.833. What annual payment should be paid by equal instalments at the beginning of every half year, during the continuance of the above life ? The present value of an assurance of £100, on a life 20, is equal to 34.488; the value of an annuity of £1, payable half yearly during that life, by Case IV., is 16.283, and the same increased by .5 is equal to 162783. = 2.055, or £2, is. id. is the answer required. Therefore, ~ If the annual premium for the above assurance were to be paid quar* Most of the Assurance companies pay such claims at the end of three months from the time the death of the party is proved; but a few of the new offices, pay the amount in one month. 33 ASSURANCES ON JOINT LIVES, &c. terly, the value of an annuity payable quarterly, by Case IV.,is 16.408, which, increased by .25, is equal to 16.658. Therefore, 2.07, or £2, 1s. 5d. 34.488- = 2. What is the value of an assurance of £100, on the life of a person aged 35, interest 4 per cent, Carlisle ? The value of an annuity on a life aged 35, Table VIII, = 16.041 Which, multiplied by the interest of £1, = .04 Gives .64164 Deducted from unity, - - - 1. - Leaves .35836 Therefore,5836 = .34452 X 100 = 34.452, or £34, 9s. Another method. The perpetuity at 4 per cent, is Deduct value of a life aged 35, - - - - . = 25.000 = 16.041 Leaves 8.959 - - Multiplied by the sum, - = 100 Gives 895.900 And this product divided by 26, (the perpetuity increased by unity,) gives 34.452, which is the value found above. XXX. THE VALUE OF ANY OF AN ASSURANCE OF A GIVEN SUM ON THE EXTINCTION TWO OR THREE JOINT LIVES, OR EST or TWO OR THREE LIVES, IS NER EXPRESSED IN LAST RULE, BUT OF THE LONG- DETERMINED IN THE MAN- SUBSTITUTING THE VALUES OF ANNUITIES roR THE JOINT LIVES, OR THE LONGEST OF THE LIVES, INSTEAD OF THE VALUE OF THE SINGLE LIFE. 1. What present sum ought to be paid for an assurance of £100 on the failure of either of two joint lives, aged 20 and 40, interest 4 per cent, Northampton ? Value of an annuity for the two joint lives, by Table IX., = 10.924 = .04 Multiplied by the interest of £1, at 4 per cent, And this product subtracted from unity, - - Gives .43696 =- 1. Leaves .56304 Therefore, .04= .54139 x 100 = 54.139, or £54, 2s. 10d., is the value in a single payment. And 1 =1. or £4, 10s. 4d., is the value in annualpayments. 4.515, 2. Let the two joint lives be 20 and 40 respectively, interest 4 per cent, Carlisle. 34 ASSURANCES ON JOINT LIVES, &C. From the perpetuity, - - 25.000 Take the value of the two joint lives, Table IX., = 13.449 Leaves 11.551 And, multiplying this by - - - - - 100 Gives 1155.1 Which, divided by 26, (the perpetuity increased by unity,) we obtain 44.427; or, £44, 8s. 6d. is the value in a single presentpayment. 3. What is the value of an assurance of £100, payable on the decease of the longest of two lives, 20 and 40, interest 4 per cent, Northampton ? Value of the longest of the two lives, by Case X., is Multiplied by the interest of £1, - And this product subtracted from unity, - - = 18.306 - - .04 Gives .73224 1. - Leaves .26776 Therefore26776 .25746 100 25.746, £25, 14s. lid. is the value in a single payment. And 1906 1.334, or £1, 6s. 8d., is the value in annualpayments, to be paid during the continuance of either life. 4. Let it be required to find the value of an assurance of £100 payable on the decease of the longest of two lives, aged 20 and 40, interest 4 per cent, Carlisle. From the perpetuity, - - - - 25.000 - Take the value of the longest of the two lives, Case X., = 19.988 Leaves 5.012 Multiplying this by 100, and dividing by 26, the quotient is equal to 19.277; or, £19, 5s. 6d. is the value required, in a single payment. 5. What is the value of a legacy (supposed not payable till the end of the year in which the testator dies) of £100, to be received on the extinction of any one of three lives, aged 20, 30, and 40, 4 per cent, Northampton ? Value of an annuity on the three joint lives, by Table X., is = 8.986 - Which, multiplied by the interest of £1, And this product subtracted from unity, : Therefore, .s40s .61592 1.04 present value of the legacy. X - - - = .04 Gives .35944 = 1. Leaves .64056 100 = 61.592; or, £61, 11ls. 10d. is the 6. If the legacy is payable on the extinction of any two out of the three lives : By Case XII. the value of any two out of the three lives aged 20, 30, and 40, is 15.315; consequently, proceeding as above, the answer is 37.25, or £37, 5s. DEFERRED ASSURANCES. 7. If the legacy is payable on the extinction of all the three lives: By Case X[. the value of an annuity on the longest of the three lives aged 20, 30, and 40, is 19.71; and, by proceeding as above, it will be found that £20, 6s. is the present value of the legacy. .11d. DEFERRED ASSURANCES. To XXXI. DEFERRED ASSURANCE SINGLE oR JOINT LIVES. FIND THE VALUE OF A GIVEN ON ANY Find the value of the assurance on a single life or lives, as many years older than the given single orjoint lives as are equal to the given term, then multiply this value by the expectation that the single or joint lives will receive £1 at the end of that term : the product, multiplied by the given sum, will be the value required. 1. What is the present value of £100 to be received on the death of a person aged 20, provided that should happen after ten years, interest 4 per cent, Northampton? The value of an assurance of £100 on a life aged 30, by Case XXIX. is 39.305, and the expectation that a life aged 20 will receive £1 at the end of ten years, by Case III., is .5772. Therefore, 39.305 X .5772 = 22.687, or £22, 13s. 9d., is the answer. 2. What is the present value of an assurance of £100, to be received on the extinction of either of two lives aged 20 and 40, provided they should survive thirty years ? By Case XXX. the assurance on two joint lives, 50 and 70, is 75.745, and the expectation that two joint lives, 20 and 40, will receive £1 at the end of thirty years, by Case III., is .0582. Therefore, 75.745 X .0582 = 4.408, or £4, 8s. 2d., is the answer. To find the value of the above in annualpayments during the period deferred : Divide the value in a single payment by the value of a tem. porary annuity, plus unity, for one year less than the deferredperiod. To FIND THE VALUE OF A XXXII. DEFERRED ASSURANCE ON THIlE LONGEST OF ANY LIVES. Multiply the value of an annuity on the longest of the given lives, de. ferredfor the given term, by the rate of interest; subtract the product from the expectation of the longest of the given lives receiving £1 at the end of the same period, and divide the diference by the amount of £1 in a year : the quotient multiplied by the given sum will be the answer required. What is the value of £100 to be received on the extinction of the longest of two lives, aged 20 and 40, provided that shall happen after 30 years ? 36 DEFERRED ASSURANCES. The value of a deferred annuity for 30 years on the longest of the two lives, by Case XIII., is 2.290, which, multiplied by .04, produces .0916, and this subtracted from .2179, or the expectation that one or other of these two lives will receive £1 at the end of 30 years, as found by Case III., will leave .1263, which, being divided by 1.04, the quotient is .12144. Therefore, .12144 X 100 = 12.144, or £12, 2s. 10d., is the value sought. To FIND THE VALUE OF XXXIII. A TEMPORARY ASSURANCE OF A GIVEN SUM ON ANY GIVEN LIVES. From the value of the assurance of the given sum, on the whole con. tinuance of the given lives, subtract the value of a deferred assurance of the same sumfor the given term. 1. What is the present value of £100 to be received on the death of a person aged 20, provided that shall happen within 10 years ? The value of an assurance of £100 on the whole continuance of this life, by Case XXIX., = 34.488 Deduct value of a similar assurance deferred for 10 years, = 22.687 which, by Case XXXI., is Leaves for the value required 11.801 To find the value in annual payments : Divide the single payment by the value of an annuity on the given life for one year less than the given term, plus unity, asfound by the rule given in the note under Rule VIII. 2. What is the value of an assurance of £100 on the joint lives of two persons aged 20 and 40, for 30 years? The value of an assurance on the whole continuance of the lives, by = 54.139 Case XXX., is Deduct value of a similar assurance deferred for 30 =-- 4.408 years, by Case XXXI., Leaves 49.731 for the answer in a single payment; and this sum, divided by the value of an annuity, plus unity, on the two joint lives for 29 years, will give the value in annual payments. 3. What is the value of an assurance of £100 for 30 years, on the longest of two lives aged 20 and 40 ? By Case XXX., Example 3d, the value of an assurance for the whole = 25.746 continuance of the two lives, is From which take the value of a similar assurance deferred ^ 12.144 for 30 years, found by Case XXXII., Leaves 13.602 for the answer in a singlepayment ; and this sum, divided by the value of an annuity, plus unity, on the longest of the two lives for 29 years, will give the value in annual payments. 37 SURVIVORSHIP ASSURANCES. NoTE.-When it is required to find the value of a temporary assurance for a very short time, as one or two years, it will be the easiest method to find the value of each year's expectation, and the sum of these will be the value of the assurance for the period required. 1. Suppose an assurance of £100 is proposed for one, two, three, &c. years on a life aged 20, interest 4 per cent, Northampton. The probability that a life aged 20 will fail within one year is 1 33, or .014, and the present value of £100 discounted for one year, at 4 per cent, is £96.154. Therefore, 96.154 X .014 = 1.349; or, £1, 7s. is the value of the assurance for one year. The probability that a life aged 20 will fail within two years is 532, or .0146, which, multiplied into £92.456, or £100 discounted for the second year, is equal to 1.351. 1.351, the value for the third year. And 5a, or .0146 X 88.899 2 The value for the 1st year as above, = 1.349 = 1.351 Do. for 2d year, = Value of the assurance for two years, The value for 3d year as above, - - - = 2.700 = 1.300 4.000 Value of the assurance for three years, Or, £4. The values of assurances for the same periods on joint lives are found by a similar method of calculation. 2. What is the value of an assurance of £100 for one year on two joint lives, 20 and 40, interest and mortality as above ? The probability that two persons, aged 20 and 40, will live one year, 5 = .9653, which subtracted from unity, leaves X is equal to 0 .0347, and this fraction, multiplied into 96.1538, gives 3.337, or £3, 6s. 9d., for the answer. SURVIVORSHIP ASSURANCES. XXXIV. To FIND THE VALUE OF AN ASSURANCE RECEIVED ON THE CONTINGENCY THAT Let A B O Y A OF A GIVEN SUM TO BE DIES BEFORE B. be the youngest life. the oldest life. one year older than A. one year younger than A. 1st TERM. Add unity to the value of an annuity on the joint lives O B, and multiply the sum by the number of persons living at the age of O, and divide the product by the amount of £1. 38 SURVIVORSHIP ASSURANCES. 2d TERM. Multiply the value of an annuity on the joint lives YB, by the number ofpersons living at the age of Y. 3d TERM. Subtract the second term from the first term, and divide the remainder by the number of persons living at the age of A. 4th TERM. Find the value of an assuranceon the joint lives A B, and from it subtract the third term : and the remainder multiplied by half the given sum will be the answer. What is the value of an assurance of £100 payable on the death of A, aged 20, provided B, aged 40, be the survivor, interest 4 per cent, Northampton ? 1. The present value of an annuity on the joint lives 0 B, aged 21 and 40, by Case VI., plus unity, is equal to 11.885, which, multiplied by 5060, the number of persons living at 21, produces 60138.100; and this product, divided by the amount of £1, gives 57825.096. 2. The value of the two joint lives Y B, aged 19 and 40, by Case VI., is equal to 10.986, which, multiplied by 5199, the number of persons living at 19, produces 57116.214. 3. And 708.882, (the difference between the first and second terms,) divided by 5132, the number of persons living at 20, gives .13814. 4. The value of an assurance of £1 on the joint lives 20 and 40, by Case XXIX., is .54139. Therefore, .54139 - .13814--.40325 X 50=20.1625, or £20, 3s. 3d., is the answer required, in a single payment. To find the value in annualpayments : Divide the value in a single payment by the value of an annuity on the joint lives A B, with unity added. 21.1625=1.691, or £1, 13s. 10d. The present value of the same sum payable on the decease of B, provided A be then alive, is found by deducting the value by the above rule from the value of the same sum payable on the extinction of the joint lives A B. Thus the present value of £100 payable on the failure of either of the two joint lives, 20 and 40, by Case XXX., is = 54.139 From which subtract value found above, - = 20.163 The difference = 33.976 is the present value of £100 payable on the decease of B, provided A be then alive, in a single payment. 2.85, or £2, 17s. is the value in annual payments. 1And, XXXV. FIND THE VALUE OF AN ASSURANCE PAYABLE ON A LIFE SURVIVING A GIVEN TERM OF YEARS, OR DYING DURING THE To GIVEN TERM. Find the expectation of the given life receiving the given sum, should the life attain the given term ; find also a temporary assurance for the same period, jc., and the sum of these will give the answer required. What is the value of an assurance of £100 on the life of a person now aged 30, payable to himself on his attaining the age of 60, or to 39 ENDOWMENTS. his heirs should he die at any time during that term, -interest 3 per cent, Northampton ? By Case III. the present value of £100, payable to a person whose age is now 30, at the end of 30 years, provided he be then alive, is - ---.. -- - 19.148 And by Case XXXIII., the value of a temporary assurance for same period is - - - -. 34.662 Together, = 53.810 Or, £53, 16s. 3d. is the value in a single payment. To find the value in annual payments: Divide the single payment by a temporary annuity, with unity added, for one year less than the given term. By Case IX. the value of a temporary annuity for 29 years on a life aged 30 is Therefore payments. - 5- - - - - - 14.858 - = 3.393, or £3, 7s. 10d., is the value in annual XXXVI. To FIND THE PREMIUM FOR AN ASSURANCE ON TIE EXTINCTION OF A SINGLE LIFE BY A LIMITED NUMBER OF ANNUAL PAYMENTS. Divide the value of the Assurance in a single payment for the whole duration of the given life, by the value of a temporary annuity, plus unity, for one year less than the given number of payments. A person aged 30 insures his life for £100, but instead of paying an annual premium during the continuance of his life, is desirous to pay the single present value in ten annual premiums: What is the equivalent value of same, interest 3 per cent, Northampton? By Case XXIX. the value of an assurance of £100, on a single life aged 30, in a single present payment, is £47.8009; and by Case IX. the value of a temporary annuity on a life at 30, for 9 years, with unity added, is equal to 8.148. Therefore, .8 - 5.867, or £5, 17s. 4d. is the value of the assurance in ten definite payments. ENDOWMENTS. XXXVII. To FIND THE PRESENT VALUE OF ANY SUM PAYABLE ON A LIFE SURVIVING A GIVEN TERM. Multiply the present value of the given sum, discountedfor the given term, into the probability that the life will continue during the given period. What is the value of £100 payable to a child whose age is now 10, 40 VALUE OF POLICIES. at the end of 11 years, provided he attains the age of 21, interest 4 per cent, Northampton ? By Table II. the present value of £100, discounted for 11 years, allowing interest at 4 per cent per annum, is 64.958, which, being multiplied into the probability that the life will live 11 years, Table VI., equal to g -6 , or .8916, gives 57.912; or, £57, 18s. 3d. is the value in a single payment. To find the value in annual payments commencing immediately: Divide the value in a single payment by the value of a temporary annuity, plus unity,for one year less than the given term. VALUE OF POLICIES. XXXVIII. To FIND THE VALUE OF A POLICY or ASSURANCE FOR THE WHOLE TERM OF LIFE, AFTER ANY EFFECTED PERIOD OF ENDUR- ANCE. Multiply the annual premium by the value of an annuity, with unity added,* for the life at the age of surrender, subtract the productfrom the value of an assurance of the given sum on the life at the present age : the difference will be the value required. 1. A policy of assurance for £1000, effected 30 years ago, on a life then aged 20, is offered for sale : What is the value of the policy, the annual premium being just due but not paid, interest 3 per cent, Northampton ? t The annual premium for an assurance of £1000 on the life of a 21.790 person aged 20, found by Case XXIX., Which, being multiplied by the value of an annuity on = 13.436 a life at 50, with unity added, = 12.436 + 1, Gives 292.770 And this product, subtracted from £608 660, the value of an assurance of £1000, on a life at 50, leaves 315.890, or £315, 17s. 7d. I * Unity is added only if the policy is renounced immediately before the annual premium becomes due, but if just after, unity is not added to the value of the annuity. t The same rate of interest and table of mortality taken in calculating the value of the assurance must be adopted in valuing the policy. + This case may be stated in another manner, as follows:-The society or company may be considered as indebted to the assured in the present value of an assurance of £1000 on a life aged 50, which is equal to 608.66, or £608, 13s. 2d., and the assured may be considered as owing to the office the present value of all the payments of £21, 15s. 10d during the remainder of his life, the first of which payments is supposed to be made immediately; therefore the value of all those payments will be equal to 21.790 X 13.436 - 292.78, or £292, 15s. 7d.; consequently the interest of the assured in his policy will be equal to the difference between £608, 13s. 2d, and £292, 15s. 7d., that is, equal to £315, 17s. 7d. as found by the example. 41 VALUE OF POLICIES. NOTE.--None of the assurance companies give the value found by the rule for the surrender of policies. Most of them deduct a-half, some a-fourth, and others three-fifths, from the real worth of the policy. It is believed, however, there are two offices in Edinburgh that take off only a-tenth. The London Equitable Society returns the whole value. 2. It is required to find the value of a policy for £100, effected 10 years ago on a life then aged 40: What is the value thereof, immediately before the premium becomes due, interest 3 per cent, Northampton ? By Case XXIX. the annual premium for an assurance of £100 on = 3.398 a life aged 40, And this sum multiplied by an annuity on a life 50, plus unity, = 13.436 Gives 45.656 Which, being subtracted from value of an assurance at 50, - - - - - - - = - 60.866 Leaves 15.210 Or, £15, 4s. 3d. is the answer. If the premium for the 11th year has been just paid, it is only necessary to add it to the value found above. The value of the policy, in terms of the above case, is = 15.210 To which add the renewal premium, - - - Together Or, £18, 12s. 2d. is the value required. = = 3.398 18.608 3. What is the value of the above policy after a period of ten years and four months ? 18.608 The value found above, with a year's premium added, And the value at the end of the 11th year, found by Ex- = ample 2d, - - - - - - = 16.808 Difference = 1.800 One-third of this remainder, equal to .600, being deducted from 18.608, leaves 18.008, or £18, Os. 2d. for the value required. 4. If an insurance has been effected on a life by a single present sum, the value at the time of surrender would be the value of an assurance in one payment at the advanced age. A. person aged 20 effected an assurance for the whole period of his life for £1000, for which he paid down £428.006, and ten years after he wished to dispose of his interest in the policy: What is the value of same, interest 3 per cent, Northampton? The value of an assurance on a life aged 30, by Case XXIX., is equal to 478.009, or £478, Os. 2d.; but from this value an office would make a deduction, as noticed under the 1st Example. 42 VALUE OF BONUSES. 5. Suppose ten years and four months elapsed on the above assurance, the value in this case may be found as follows:From the single premium for an assurance of £1 at the age of - - - - Take the value of do. at 30, - - - 31, - - .483516 - - .478009 Which leaves .005507 And four-twelfths of this difference, or .001836, added to the value at 30, gives .479845, which, multiplied by £1000, produces 479.845, or £479, 16s. 11d. 6. What is the value of a policy for £1000 on two joint lives aged 40 and 30, which has endured 10 years, the annual premium being £50, 8s. 10d ? From the value of an assurance of £1000 on two joint lives, 50 and 40, in a single present payment, - - - 691.530 Take the present value of the annual premium, equal to £50.442, multiplied by the value of an annuity on the two joint lives 50 and 40, plus unity, = 9.590 + 1 = 10.590, 534.191 = - - - - - - Which leaves 157.339 Or, £157, 7s. 2d. is the answer. VALUE OF BONUSES. XXXIX. To FIND THE VALUE OF A BONUS. Find the value of the reversion of £1 at the age of the party when the bonus is to be estimated, and multiply it by the given bonus. 1. What is the present value of a bonus of £300 assigned to a policy effected 12 years ago, on a life then aged 50, interest 3 per cent, Northampton ? By Case XXIX. the present value of an assurance of £1 in a single payment on a life aged 62, Which, multiplied by the bonus, - - - - - - - .- .70275 300 Gives 210.825 Or, £210, 16s. 6d. is the answer. 2. Suppose it were required to find the value of a policy for £1000, together with the bonus as in last Example. The value of a policy for £1000 effected on a life at 50, but now aged 62, is - - - Add value of bonus found above, - - - - - 240.432 - - = 210.825 Together = 451.257 Or, 451, 5s. 2d. is the value of the policy with the bonus. 43 VALUE OF BONUSES. NoTE.---The sum insured in the policy and the declared bonus are equal to £1300, which would be paid to the representatives of the assured at his death; and the present value of both may also be found by the following method:-The annual premium fdr £1300 on a life at 62, by Case XXIX., is equal to 89.518, and the annual premium for the sum insured, that is £1000, the age then 50, is 45.301, and the difference, or 44.217, between these two premiums, multiplied by an annuity, plus unity, for a life at 62, equal to 10.206, will give 451.257, or £451, 5s. 2d. as above. XL. TO FIND WHAT REDUCTION OF THE FUTURE PAYMENTS OF ANNUAL PREMIUM IS EQUIVALENT TO ANY ASSIGNED BONUS, Multiply the annualpremium for an assurance of £1 at the age of the assured when the bonus is to be applied to the reduction of premium by the bonus. A person aged 50 effected an assurance on his life for £1000, at an annual premium of £45, 6s., and at the end of 12 years a bonus of £300 was declared as a vested addition thereto : What equivalent annual deduction from the future premiums should be allowed for commuting the bonus? By Case XXIX. the annual premium for an assurance of £1 on a life aged 62, interest 3 per cent, Northampton, is = .06886 Which, being multiplied by the sum of the bonus, -= 300 Gives 20.658 Or, £20, 13s. 2d. is the value of future deduction. And from the annual premium for an assurance of £1000 on a life = - 45.301 at 50, Case XXIX. Take the value of the commuted bonus, as above, = 20.658 Leaves 24.643 Or, £24, 12s. 10d. for the future annual premium. TABLES OF COMPOUND INTEREST. accumulated at the rates of 3, 32, 4, 42, and 5 per cent. Years.~ 3.2 3 1 2 3 4 5 6 7 8 9 10 1.030,000 1.060,900 1.092,727 1.125,508 1.159, 274 1.194,052 1.229,873 1.266,770 1.304,773 1.343,916 11 12 13 14 15 16 .17 18 19 20 14 1 I- 1 5 1 i 1 1.035,000 1.071,225 1.108,718 1.147,523 1.187,686 1.229,255 1.272,279 1.316,809 1.362,897 1.410,599 1.040,000 1.081,600 1.124,864 1.169,858 1.216,652 1.265,319 1.315,931 1.368,569 1.423,311 1.480,244 1.045,000 1.092,025 1.141,166 1.192,518 1.246,181 1.302,260 1.360,861 1.422,100 1.486,095 1.552,969 1.050,000 1.102,500 1.157,625 1.215,506 1.276,281 1.340,095 1.407,100 1.477,455 1.551,328 1.628,894 1.384,233 1.425,760 1.468,533 1.512,589 1.557,967 1.604,706 1.652,847 1.702,433 1.753,506 1.806,111 1.459,961 1.511,069 1.563,956 1.618,695 1.675,349 1.733,986 1.794,676 1.857,489 1.922,501 1.989,789 1.539,454 1.601,032 1.665,073 1.731,676 1.800,943 1.872,981 1.947,900 2.025,816 2.106,849 2.191,123 1.622,853 1.695,881 1.772,196 1.851,944 1.935,282 2.022,370 2.113,376 2.208,478 2.307,860 2.411,714 1.710,339 1.795,856 1.885,649 1.979,931 2.078,928 2.182,874 2.292,018 2.406,619 2.526,950 2.653,297 21 22 23 24 25 26 27 28 29 30 1.860,294 1.916,103 1.973, 586 2.032,794 2.093,777 2.156,591 2.221, 289 2.287,927 2.356,565 2.427,262 2.059,431 2.131,512. 2.206,112 2.283,328 2.363,245 2.445,959 2.531,567 2.620,172 2.711,878 2.806,794 2.278,768 2.369,918 2.464,715 2.563,304 2.665,836 2.772,469 2.883,368 2.998,703 3.118,651 3.243,397 2.520,241 2.633,652 2.752,166 2.876,013 3.005,434 3.140,679 3.282,009 3.429,699 3.584,036 3.745,318 2.785,962 2.925,260 3.071,523 3.225,099 3.386,354 3.555,672 3.733,456 3.920,129 4.116,135 4.321,942 31 32 33 34 36 37 38 39 40 2.500,080 2.575,082 2.652,335 2.731,905 2.81,62 2.898,278 2.985,226 3.074,783 3.167,026 3.262,037 2.905,031 3.006,708 3.111,942 3.220,860 3.333,590 3.450,266 3.571,025 3.696,011 3.855,372 3.959,259 3.378,133 3.508,058 3.648,381 3.794,316 3.946,088 4.103,932 4.268,089 4.438,813 4.616,365 4.801,020 3.913,857 4.089,981 4.274,030 4.466,361 4.667,347 4.877,378 5.096;860 5.326,219 5.565,899 5.816,364 4.538,039 4.764,941 5.003,188 5.253,347 5.516,015 5.791,816 6.081,406 6.385,477 6.704,751 7.039,988 41 42 43 44 45 46 47 48 49 50 3.359.898 3.460,695 3.564,516 3.671,452 3.781,9 3.895,043 4.011,895 4.132,251 4.256,219 4.383,906 4.097,834 4.241,258 4.389,702 4.543,342 4.702,359 4.866,941 5.037,284 5.213,589 5.396,065 5.584,927 4.993,061 5.192,783 5.400,495 5.616,515 5.841,175 6.074,822 6.317,815 6.570,528 6.833,349 7.106,683 6.078,100 6.351,615 6.637,438 6.936,122 7.248,248 7.574,419 7.915,268 8.271,455 8.643,671 9.032x636 7.391,988 7.761,587 8.149,666 8.557,150 8.985,007 9.434,258 9.905,971 10.401,269 10.921,33 11.467,399 4 TABLES OF COMPOUND INTEREST. 45 3-, II. The present value of £1 payable at the end of any number of years not exceedingfifty, discounting at the rates of 3, 4, 42, and 5 per cent. Years. 3 3 4 25 1 2 3 4 5 6 7 8 9 10 .970,874 .942,596 .915,142 .888,487 .862,609 .837,484 .813,092 .789,409 .766,417 .744,094 .966,184 .933,511 .901,943 871,442 .841,973 .813,501 .785,991 .759,412 .733,731 .708,919 .961,538 .924,556 .888,996 .854,804 .821,927 .790,315 .759,918 .730,690 .702,587 .675,564 .956,938 .915,730 .876,297 .838,561 .802,451 .952,381 .907,029 .863,838 .822,702 .783,526 .767,896 .746,215 .734,828 .703,185 .672,904 .643,928 .710,681 .676,839 .644,609 .613,913 11 12 13 14 15 16 17 18 19 20 .722,421 .701,380 .680,951 .661,118 .641,862.623,167 .605,016 .587,395 .570,286 .553,676 .684,946 .661,783 .639,404 .617,782 .596,891 .576,706 .557,204 .538,361 .520,156 .502,566 .649,581 .624,597 .600,574 .577,475 .555,265 .533,908 .513,373 .493,628 .474,642 .456,387 .616,198 .589,664 .564,271 .539,973 .584,679 .556,837 .530,321 .505,068 .516,720 .481,017 .494,469 .473,176 .452,800 .433,302 .414,643 .458,112 .436,297 .415,521 .395,734 .376,889 21 22 23 24 25 26 27 28 29 30 .537,549 .521,893 .506,692 491,934 .477,606 .463,695 .450,189 .437,077 .424,346 .411,987 .485,571 .469,151 .453,286 .437,957 .423,147 .408,838 .395,012 .381,654 .368,748 .356,278 .438,834 .421,955 .405,726 .390,121 .375,117 .360,689 .346,817 .333,477 .320,651 .308,319 .396,787 .379,701 .363,350 .347,703 .332,731 .318,402 .304,691 .291,571 .279,015 .267,000 .358,942 .341,850 .325,571 .310,068 .295,303 .281,241 .267,848 .255,094 .242,946 .231,377 31 32 33 34 35 36 37 38 .399,987 .388,337 .377,026 .366,045 .355,383 .345,032 .334,983 .325,226 .344,230 .332,590 .321,343 .310,476 .299,977 .289,833 .280,032 .270,562 .296,460 .285,058 .274,094 .263,552 .253,415 .243,669 .234,297 .225,285 .255,502 .244,500 .233,971 .223,896 .214,254 .205,028 .196,199 .187,750 .220,359 .209,866 .199,873 .190,355 .181,290 .172,657 .164,436 .156,605 39 40 41 42 43 44 45 46 47 48 49 50 .31 5,754 .261,413 .216,621 .179,665 .149,148 .306,557 .252,572 .208,289 .171,929 .142,046 .297.628 .288,959 .280,543 .272,372 .264,439 .256,737 .249,259 .241,999 .234,950 .228,107 .244.031 .235,779 .227,806 .220,102 .212,659 205,468 .198,520 .191,806 .185.320 .179,053 .200.278 .192,575 .185,168 .178,046 .171,198 .164,614 .158,283 .152,195 .146,341 .140,713 .164.525 .157,440 .150,661 .144,173 .137,964 .132,023 .126,338 .120,898 .115,692 .110,710 .1.35,282 .128,840 .122,704 .116,861 .111,297 .105,997 .100,949 .096,142 .091, 564 .0817,204 46 TABLES 46 OF COMPOUND INTEREST. III. The amount of £1 per annum for any number of years not exceedingfcfy, accumulated at the rates of 3, 3, 4, 42, and 5 per cent. Years. 3 1 2 3 4 5 6 7 8 9 10 1.000,000 2.030,000 3.090,900 4.183,627 5.309,136 6.468,410 7.662,462 8.892,336 10.159,106 11.463,879 1.000,000 2.035,000 3.106,225 4.214,943 5.362,466 6.550,152 7.779,408 9.051,687 10.368,496 11.731,393 1.000,000 2.040,000 3.121,600 4.246,464 5.416,323 6.632,975 7.898,294 9.214,226 10.582,795 12.006,107 11 12 13 14 15 16 17 18 19 20 12.807,796 14.192,030 15.617,790 17.086.324 18.598,914 20.156,881 21.76,588 23.414,435 25.116,868 26.870,374 13.141,992 14.601,962 16.113,030 17.676.986 19.295,681 20.971,030 22.705,016 24.499,691 26.357,181 28.279,682 21 22 23 24 25. 26 27 28 29 28.676,486 30.536,780 32.452,884 34.426,470 36.459,264 38.553,042 40.709,634 42.930,923 45.218,850 31 32 33 30 34 35 36 37 38 39 40 41 42 43 44 45 46 31 4 41 5 1.000,000 1.000,000 2.045,000 3.137,025 4.278,191 5.470,710 6.716,892 8.019,152 9.380,014 2.050,000 3.152,500 4.310,125 5.525,631 6.801,913 8.142,008 9.549,109 10.802,114 11.026,564 12.288,209 12.577,893 13.486,351 15.025,805 16.626,838 18.291.911 20.023,588 21.824,531 23.697,512 25.645,413 27.671,229 29.778,079 13.841,179 15.464,032 17.159,913 14.206,787 15.917,127 17.712,983 47.575,416 30.269,471 32.328,902 34.460,414 36.666,528 38.949,857 41.313,102 43.759,060 46.290,627 48.910,799 51.622,677 50.002,678 52.502,759 55.077,841 57.730,177 54.429,471 57.334,502 60.341,210 63.453,152 60.462,082 66.674,013 63.275,944 66.174,223 69.159,449 72.234,233 75.401,260 70.007,603 73.457,869 77.028,895 80.724,906 84.550,278 78.663,298 82.023,196 85.483,892 89.048,409 92.719,861 96.501,457 88.509,537 92.607,371 96.848,629 101.238,331 105.781,673 110.484,031 47 100.396,501 115.350,973 48 49 101.408,396 108.540,648 120.388,257 125.601,846 50 112.796,867 130.997,910 18.932,109 19.598,632 20.784,054 22.719,337 24.741,707 26.855,084 29.063,562 31.371,423 21.578,564 23.657,492 25.840,366 28.132,385 30.539,004 33.065,954 31.969,202 34.247,970 36.617,889 39.082,604 41.645,908 44.311,745 47.084,214 49.967,583 52.966,286 56.084,938 33.783,137 36.303,378 38.937,030 41.689,196 44.565,210 47.570,645 50.711,324 53.993,333 57.423,033 61.007,070 35.719,252 38.505,214 41.430,475 44.501,999 47.727,099 51.113,454 54.669,126 58.402,583 62,322,712 66.438,848 59.328,335 62.701,469 66.209,527 69.857,909 64.752,388 68.666,245 72.756,226 77.030,256 70.760,790 75.298,829 80.063,771 85.066,959 73.652,225 81.496,618 90.320,307 77.598,314 81.702,246 85.970,336 90.409,150 95.025,516 86.163,966 91.041,344 96.138,205 101.464,424 107.030,323 95.836,323 101.628,139 107.709,546 114.095,023 120.799,774 99.826,536 104.819,598 110.012,382 115.412,877 121 .0 29,392 126.870,568 112.846,688 118.924,789 125.276,404 131.913,842 138.849,965 146.098,214 127.839,763 135.231,751 142.993,339 151.143,006 159.700,156 168.685,164 153.672,633 178.119, 422 161.587,902 169.859,357 188.025,393 198.426,663 132.945,390 139.263,206 145.833,734 152.667,084 178.503,028 209.347,996 TAB3LES OF COMPOUND INTEREST. 4 47 per IV. The present value of £1 annum, for any number of years not exceeding discounted at the several rates of 3, 32, 4, 42, and 5 per cent. fifty, 3 Years. 3 I 1 2 3 4 5 6 7 8 9 10 .9709 1.9135 2.8286 3.7171 4.5797 5.4171 6.2302 7.0196 7.7861 8.5302 .9662 1.8997 2.8016 3.6731 4.5151 5.3286 6.1145 6.8740 7.6077 8.3166 11 12 13 14 15 16 17 18 19 20 9.2526 9.9540 10.6349 11.2960 11.9379 12.5611 13.1661 13.7535 14.3238 14.8774 21 22 23 24 25 26 27 28 29 30 4 I_42 l- -- _ 5 _ I- .9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 .9569 1.8727 2.7490 3.5875 4.3899 5.1579 5.8927 6.5959 7.2688 7.9127 .9524 1.8594 2.7232 3.5460 4.3295 9.0016 9.6633 10.3027 10.9205 11.5174 12.0941 12.6513 13.1897 13.7098 14.2124 8.7605 9.3851 9.9856 10.5631 11.1184 11.6523 12.1657 12.6593 13.1339 13.5903 8.5289 9.1186 9.6829 10.2228 10,7395 11.2340 11.7072 12.1600 12.5933 13.0079 8.3064 8.8633 9.3936 9.8986 10.3797 10.8378 11.2741 11.6896 12.0853 12.4622 15.4150 15.9369 16.4436 16.9355 17.4131 17.8768 18.3270 18.7641 19.1884 19.6004 14.6979 15.1671 15.6204 16.0584 16.4815 16.8904 17.2854 17.6670 18.0358 18.3920 14.0292 14.4511 14.8568 15.2470 15.6221 15.9828 16.3296 16.6631 16.9837 17.2920 13.4047 13.7844 14.1478 14.4955 14.8282 15.1466 15.4513 15.7429 16.0219 16.2889 12.8212 13.1630 13.4886 13.7986 14.0939 14.3752 14.6430 14.8981 15.1411 15.3725 31 32 33 34 35 36 37 38 39 40 20.0004 20.3888 20.7658 21.1318 21.4872 21.8322 22.1672 22.4924 22.8082 23.1148 18.7363 19.0689 19.3902 19.7007 20.0007 20.2905 20.5705 20.8411 21.1025 21.3551 17.5885 17.8736 18.1476 18.4112 18.6646 18.9083 19.1426 19.3679 19.5845 19.7928 16.5444 16.7889 17.0229 17.2468 17.4610 17.6660 17.8622 18.0500 18.2297 18.4016 15.5928 15.8027 16.0025 16.1929 16.3742 16.5469 16.7113 16.8679 17.0170 17.1591 41 42 43 44 45 46 47 48 49 50 23.4124 23.7014 23.9819 24.2543 24.5187 24.7754 25.024725.2667 25.5017 25.7298 21.5991 21.8349 22.0627 22.2828 22.4955 22.7009 22.8994 23.0912 23.2766 23.4557 19.9931 20.1856 20.3708 20.5488 20.7200 20.8847 21.0429 21.1951 21.3415 21.4822 18.5661 185.7236 18.8742 19.0184 19.1563 19.2884 19.4147 19.5356 19.6512 19.7620 17.2944 17.42 17.5459 17.6628 17.7741 17.8801 17.9810 18.0772 18.1687 18.2559 25.000000 22.000000 _I Pep- _t 33.333 28 571429 5.0 ,57 5.7864 6.4632 '1.1078 7.7217 1 20.000000 48 TABLES OF COMPOUND INTEREST. 48 V. The annuity which £1 will purchase for any number of years not exceeding fifty, at 3, 32, 4, 42, and 5 per cent. 41 5 Years. 3 1 2 3 4 5 6 7 8 9 10 1.0300000 0.5226108 .3535304 .2690270 .2183546 .18415975 .1605064 .14240564 .1284339 .1172305 1.0350000 0.5264005 .3569342 .2722511 .2214814 .1876682 .1635445 .1454767 .1314460 .1202414 1.0400000 0.5301961 .3603485 .2754901 .2246271 .1907619 .1666096 .1485278 .1344929 .1232909 1.0450000 0.5339976 .3637734 .2787437 .2277916 .1938784 .1697015 .1516097 .1375745 .1263788 1.0500000 0.5378049 .3672086 .2820118 .2309748 .1970175 .1728198 .1547218 .1406901 .1295046 11 12 13 14 15 16 17 18 19 20 .1080775 .1004621 .0940295 .0885263 .0837666 .0796109 .0759525 .0727087 .0698139 .0672157 .1110919 .1034839 .0970616 .0915707 .0868251 .0826848 .0790431 .0758168 .0729403 .0703611 .1141490 .1065522 .1001437 .0946689 .0899411 .0858200 .0821985 .0789933 .0761386 .0735818 .1172482 .1096662 .1032754 .0978203 .0931138 .0890154 .0854176 .0822369 .0794073 .0768761 .1203889 .1128254 .1064558 .1010239 .0963423 .0922699 .0886991 .0855462 .0827450 .0802426 21 22 23 24 25 26 27 28 29 30 .0648718 .0627474 .0608139 .0590474 .0574279 .0559383 .0545642 .0532932 .0521147 .0510193 .0680366 .0659321 .0640188 .0622728 .0606740 .0592054 .0578524 .0566027 .0554454 .0543713 .0712801 .0691988 .0673091 .0655868 .0640119 .0625674 .0612385 .0600129 .0588799 .0578301 .0746006 .0725457 .0706825 .0689870 .0674390 .0660214 .0647195 .0635208 .0624146 .0613915 .0779961 .0759705 .0741368 .0724709 .0709525 .0695643 .0682919 .0671225 .0660455 .0650514 31 32 33 34 35 36 37 38 39 40 .0499989 .0490466 .0481561 .0473219 .0465393 .0458038 .0451116 .0444593 .0438439 .0432624 .0533724 .0524415 .0515724 .0507597 .0499984 .0492842 .0486133 .0479821 .0473878 .0468273 .0568554 ".0559486 .0551036 .0543148 .0535773 .0528869 .0522396 .0516319 .0510609 .0505235 .0604435 .0595632 .0641321 .0632804 .0587445 .0624900 .0579819 .0572705 .0566059 .0559840 .0554017 .0548557 .0543432 .0617555 .0610717 .0604345 .0598398 .0592842 .0587646 .0582782 41 42 43 44 45 46 47 48 49 50 .0427124 .0421917 .0416981 .0412299 .0407852 0403625 .0399605 .0395778 .0392131 .0388655 .0462982 .0457983 .0453254 .0448777 .0444534 .0440511 .0436692 .0433065 .0429617 .0426337 .0500174 .0495402 .0490899 .0486645 .0538616 .0534087 .0529824 .0525807 .0522020 .0518447 .0515073 .0511886 .0508872 .0506022 .0578223 .0573947 .0569933 .0566163 .0562618 .0559282 .0556142 .0553184 .0550397 .0547767 I -- I ~-----~- I I 310 22 .0482.625 .0478821 .0475219 .0471807 .0468571 .0465502 4 TABLE OF MORTALITY AT DIFFERENT PLACES. VI. Comparative Rates of the Progressive Decrement of Life. ___YII _ ____ V_ Ag. Age. Northamp- 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35° 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 49 11,650 8650 7283 6781 6446 6249 6065 5925 5815 5735 5675 5623 5573 5523 5473 5423 5373 5320 5262 5199 5132 5060 4985 4910 4835 4760 4685 4610 4535 4460 4385 4310 4235 4160 4085 4010 3935 3860 3785 3710 3635 3559 3182 3404 3326 3248 3170 3092 3014 2936 2857 2776 2694 Carlisle. 10,000 8461 7779 7274 6998 6797 6676 6594 6536 6493 6460 6431 6400 6368 6335 6300 6261 6219 6176 6133 6090 6047 6005 5963 5921 5879 5836 5793 5748 5698 5642 5585 5528 5472 5417 5362 5307 5251 5194 5136 5075 5009 4940 4869 4798 4727 4657 4588 4521 4458 4397 4338 4276 Governrment. MalesF Females 1000 981 963 919 937 927 919 912 906 901 896 891 886 881 876 872 866 860 854 816 837 827 816 804 793 782 771 761 751 742 732 723 714 705 696 687 679 670 662 653 644 636 627 619 610 602 594 586 578 570 561 552 542 1000 981 967 955 945 935 926 019 913 908 903 899 895 892 887 883 876 870 863 856 848 841 834 827 820 813 805 798 791 784 777 A Northamps Ag. ton. 53 54 55 56 2612 2530 2448 2366 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 Crse rie. Government. Males. Fema~e. 4211 4143 4073 4000 531 520 508 495 2284 3924 482 568 2202 2120 2038 1956 1874 3842 3749 3613 3521 3395 468 454 440 426 413 559 549 539 529 519 1793 1712 1632 1552 1472 1392 1312 1232 1152 1072 992 912 832 752 3268 3143 3018 2894 2771 2648 2525 2401 2277 2143 1997 1841 1675 i515 399 385 370 355 339 322 305 288 270 253 235 218 202 185 508 496 484 471 457 443 428. 412 395 377 Z58 339 319 298 171 277 156 141 255 233 77 675 1359 78 79 602 534 1213 1081 80 469 953 125 81 82 83 84 85 86 87 406 346 289 234 186 145 111 837 725 623 529 445 367 296 110 95 81 68 56 44 34 83 232 24 62 46 34 24 16 9 4 181 142 1O5 75 54 40 30 17 11 7 4 3 1 770 763 755 748 740 732 89 724 90 716 91 708 92700 93 693 94 685 95 677 96 669 97 661 98 654 99 646 638 101 631] 1025 623 1033I 616 1041 6.08 88 Human 1 23 18 14 1 1 7, 601 593 585 576 210 189 168 149 132 117 103 89 76 64 52 41 30 21 14 8 5 2 1 50 TABLE OF THlE EXPECTATION OF HUMAN LIFE. VII. Expectation of Life deduced from the preceding Table of Mortality. Ioria tae f " ' 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 ~35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 ri sle. ;_Government ton 25.18 32.74 37.79 39.55 40.58 40.84 41.07 41.03 40.79 40.36 39.78 39.14 38.49 37.83 37.17 36.51 35.85 35.20 34.58 33.99 33.43 32.90 32.39 31.88 31.36 30.85 30.33 29.82 29.30 28.79 28.27 27.76 27.24 26.72 26.20 25.68 25.16 24.64 24.12 23.60 23.08 22.56 22.04 21.54 21.03 20.52 20.02 19.51 19.00 18.49 17.99 17.50 17.02 T\Lr~~ I Maes. 38.72 44.68 47.55 49.82 50.76 51.25 51.17 50.80 50.24 49.57 48.82 48.04 47.27 46.51 45.75 44.27 43.57 42.87 42.17 50.16 50.13 50.04 49.80 49.42 48.93 48.36 47.71 47.02 46.30 45.57 44.83 44.07 43.31 42.53 41.76 41.01 40.29 39.61 38.98 41.46 40.75 40.04 39.31 38.59 37.86 37.14 36.41 35.69 35.00 34.34 33.68 33.03 32.36 31.68 31.00 30.32 29.64 28.96 28.28 38.39 37.83 37.34 36.87 36.39 35.90 35.41 34.86 34.31 33.75 33.17 32.59 32.00 31.40 30.79 30.17 29.54 28.91 28.28 27.65 27.61 26.97 26.34 25.71 25.09 24.46 23.82 23.17 22.50 21.81 21.11 20.39 19.68 27.02 26.39 25.74 25.08 24.42 23.75 23.07 22.38 21.68 20.98 20.30 19.62 18.97 45.00 I Ae. emaes. 55.51 53 55.59 54 55.37 55 55.05 56 54.65 57 54.23 58 53.72 59 53.15 60 52.50 61 51.80 62 51.05 63 50.27 64 49.48 65 48.70 66 47.93 67 47.19 68 46.51 69 45.86 70 45.22 71 44.60 72 43.99 73 43.36 74 42.73 75 42.09 76 41.45 77 40.81 78 40.17 79 3952 80 38.87 81 28.22 82 37.57 83 36.91 84 36.26 85 86 35.61 34.96 87 34.31 88 33.68 89 33.04 90 32.40 91 31.76 92 31.12 93 30.46 94 29.81 95 29.14 96 28.48 97 27.81 98 27.13 99 26.44 100 25.75 101 25.06 102 24.35 103 23.65 104 22.39 Northamp.. ton. 16.54 16.06 15.58 15.10 14.63 14.15 13.68 13.21 12.75 12.28 11.81 11.35 10.88 10.42 9.96 9.50 9.05 8.60 8.17 7.74 7.33 6.92 6.54 6.18 5.83 5.48 5.11 4.75 4.41 4.09 3.80 3.58 3.37 3.19 3.01 2.86 2.66 2.41 2.09 1.75 1.37 1.05 .75 .50 I aris Government. Males. Females. 18.97 18.28 17.58 16.89 16.21 15.55 14.92 14.34 13.82 13.31 12.81 12.30 11.79 11.27 10.75 10.23 9 70 9.18 8.65 8.16 18.34 17.73 17.15 16.57 16.02 15.47 14.93 14.39 13.84 13.28 7.72 7.33 7.01 6.69 6.40 6.12 5.80 5.51 5.21 4.93 4.65 4.39 4.12 3.90 3.71 3.59 3.47 3.28 3.26 3.37 3.48 3.53 3.53 7.96 7.54 7.12 6.69 6.23 5.78 5.35 4.94 4.55 4.18 3.82 3.46 3.12 2.81 2.53 2.31 2.12 1.95 1.83 1.65 3.46 3.28 3.07 2.77 2.28 1.79' 1.30 .83 .50 12.72 12.17 11.63 11.10 10.61 10.14 9.67 9.22 8.79 8.37 1.49 1.34 1.18 .97 .75 .50 22.22 21.50 20.79 20.08 19.38 18.69 18.00 17.32 16.64 15.96 15.30 14.64 14.00 13.37 12.76 12.16 11.57 10.99 10.44 9.92 9.41 8.92 8.46 8.00 7.58 7.19 6.83 6.50 6.20 5.89 5.57 5.22 4.84 4.44 3.62 3.2] 2.83 2.49 2.21 1.97 1.75 1.55 1.32 1.12 .94 .75 .50 5 TABLES OF ANNUITIES. 51 VIII. Value of an Annuity of £1 on a SINGLE LIFE deduced from observations made at Northampton by Dr Price ; and at Carlisle by Dr Heysham, interest 3, 4, and 5 per cent. N0RTIIAMPT0 CARLISLE. Age. 5 8.863 11.563 13.420 14.135 14.613 14.827 15.041 15.166 15.226 15.210 15.139 15.043 14.937 14.826 14.710 14.588 14.460 14.334 14.217 14.108 14.007 13.917 13.833 13.746 13.658 13.567 13.473 13.377 13.278 13.177 13.072 12.965 12.854 12.740 12.623 12.502 12.377 12.249 12.116 11.979 10.327 13.465 15.633 16.462 17.010 17.248 17.482 17.611 17.662 17.625 17.523 17.393 17.251 17.103 16.950 16.791 16.625 16.462 16.309 16.167 16.033 15.912 15.797 15.680 15.560 15.438 15.312 15.184 15.053 14.918 14.781 14.639 14.495 14.347 14.195 14.039 13.880 13.716 13.548 13.375 3 4 11.83711.695 11.551 11.407 11.258 11.105 10.947 10.784 10.616 10.443 10.269 I I~zrrs 13.197 I 13.018 12.838 '12.657 12.472 12.283 12.089 11.890 11.685 11.475 11.264 12.270 16.021 18.599 19.575 20.210 20.473 20.727 20.853 20.885 20.812 20.663 20.480 1 0 1 2 3 4 5 6 7 8 11 20.283 12 20.081 19.872 19.657 19.435 19.218 19.013 18.820 18.638 18.470 18.311 18.148 17.983 17.814 17.642 17.467 17.289 17.107 16.922 16.732 16.540 16.343 16.142 15.938 15.729 15.515 15.298 15.075 14.848 14.620 14.391 14.162 13.929 13.692 13.450 13.203 12.951 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 I I I.zn~ II uu II 4 5 17.320 20.085 21.501 22.683 23.285 23.693 23.846 23.867 23.801 23.677 23.512 23.327 23.143 22.957 22.769 22.582 22.404 22.232 22.058 21.879 21.694 21.504 21.304 21.098 20.885 20.665 20.442 20.212 19.981 19.761 19.556 19.348 19.134 18.910 18.675 18.433 18.183 17.928 17.669 17.405 17.143 16.890 16.640 16.389 16.130 15.863 15.585 15.294 14.986 14.282 16.555 17.726 18.715 19.231 19.592 19.745 19.790 19.764 19.691 19.583 19.459 19.335 19.209 19.082 18.955 18.836 18.721 18.607 18.486 18.362 18.232 18.094 17.950 17.801 17.645 17.486 17.320 17.154 16.997 16.852 16.705 16.552 16.391 16.219. 16.041 15.856 15.666 15.471 15.272 15.074 14.883 14.695 14.505 14.309 14.105 13.889 13.662 13.419 13.153 12.869 12.083 13.995 14.983 15.824 16.271 16.590 16.735 16.790 16.786 16.742 16.669 16.581 16.494 16.406 16.316 16.227 16.144 16.066 15.987 15.904 15.817 15.726 15.628 15.525 15.417 15.303 15.187 15.065 14.942 14.827 14.723 14.617 14.506 14.387 14.260 14.127 13.987 13.843 13.695 13.542 13.390 13.245 13.101 12.957 12.806 12.648 12.480 12.301 12.107 11.892 11.660 52 52 TABLES OF ANNUITIES. VIII. Value of an Annuity of £1 on a CARLISLE. NORTHAMPTON. 5 10.097 9.925 9.748 9.567 9.382 9.193 8.999 8.801 8.599 8.392 8.181 7.966 7.742 7.514 7.276 7.034 6.787 6.536 6.281 6.023 5.764 5.504 5.245 4.990 4.744 4.511 4.277 4.035 3.776 3.515 3.263 3.020 2.797 2.627 2.471 2.328 2.193 2.080 1.924 1.723 1.447 1.153 .816 .524 .238 .000 4 11.057 10.849 10.637 10.421 10.201 9.978 9.749 9.517 9.280 9.040 8.796 8.548 9.291 8.031 7.762 7.488 7.211. 6.930 6.647 6.362 6.076 5.790 5.508 5.230 4.963 4.710 4.457 4.198 3.922 3.644 3.378 3.122 2.887 2.709 2.544 2.393 2.252 2.132 1.968 1.758 1.474 1.171 .827 .530 .240 .000 SINGLE LIFE. Age. 12.183 11.930 11.674 11.414 11.150 10.882 10.612 10.337 10.059 9.777 9.493 9.206 8.910 8.612 8.305 7.994 7.682 7.367 7.051 6.734 6.418 6.104 5.794 5.491 5.199 4.925 4.652 4.373 4.077 3.782 3.499 3.229 2-982 2.794 2.620 2.462 .2.312 2.185. 2.013 1-795 1.501 1.190 .839 .536 .243 .000 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 4 13.932 13.558 13.180 12.798 12.408 12.014 11.614 11.218 10.841 10.491 10.180 9.875 9.567" 9.246 8.917. 8.578 8.228 7.869 7.499 7.123 6.737 6.373 6.044 5.752 5.512 5.277 5.059 4.838 4.592 4.365 4.119 3.898 3.672 3.454 3.229 3.033 2.873 2.776 2.665 2.499 2.481 2.577 2.687 2.736 2.757 2.704 2.559 2.388 2.131 1.683 1.228 .771 .324 5 12.566 12.258 11.945 11.627 11.300 10.966 10.625 10.286 9.963 9.663 9.398 9.137 8.872 8.593 8.307 8.010 7.700 7.380 7.049 6.709 6.358 6.026 5.725 5.458 5.239 5.024 4.825 4.622 4.394 4.183 3.953 3.746 3.534 3.329 3.115 2.928 2.776. 2.683 2.577 2.416 2.398 2.492 2.600 2.650 2.674 2.628 2.492 2.332 2.087 1.653 1.210 .762 .321 11.410 11.154 10.892 10.624 10.347 10.063 9.771 9.478 9.199 8.940 8.712 8.487 8.258 8.016 7.765 7.503 7.227 6.941 6.643 .6.336 6.015 5.711 5.435 5.190 4.989 4.792 4.609 4.422 4.210 4.015 3.799 3.606 3.406 3.211 3.009 2.830 2.685 2.597 2.495 2.339 2.321 2.412 2.518 2.569 2.596 2.555 2.428 2.278 2.045 1.624 1.192 .753 .317 53 TABLES OF ANNUITIES. IX. Yalue of an Annuity of £1 on Two JOINT LIVES deduced from Observations made at Northampton and at Carlisle, interest 3, 4, and 5 per cent. .Difference of Age 0. NORTHAMPTON. 5 14 8.252 11.107 12.325 13.185 13.591 14.005 14.224 14.399 14.396 14.277 14.133 13.966 13.789 13.604 13.411 13.212 13.019 12.841 12.679 12.535 12.409 12.293 12.179 12.062 11.944 11.822 11.699 11.573 11.445 11.313 11.179 11.042 10.902 10.759 10.612 10.462 10.307 10.149 9.986 9.820 9.654 9.491 9.326 9.160 8.990 8.815 8.637 8.453 8.266 8.081 7.900 7.287 9.793 10.862 11.621 11.984 12.358 12.596 12.731 12.744 12.665 12.546 12.411 12.268 12.118 11.960 11.793 11.630 11.483 11.351 11.232 11.131 11.042 10.951 10.858 P-.764 10.667 10.567 10.466 10.362 10.255 10.146 10.034 9.919 9.801 9.680 9.555 9.427 9.294 9.158 9.016 8.876 8.737 8.599 li8.457 8.312 8.162 8.008 7.849 7.686 7.522 7.366 i LV L I I Ages.gCARLISLE. Ages. 3 9.491 12.789 14.196 15.181 15.638 16.099 16.375 16.510 16.483 16.339 16.142 15.926 15.702 15.470 15.229 14.979 14.737 14.516 14.316 14.133 13.974 13.830 13.688 13.534 13.383 13.230 13.074 12.915 12.754 12.589 12.422 12.252 12.079 11.902 11.722 11.539 11.351 11.160 10.964 10.764 10.565 10.369 10.175 9.978 9.776 9.571 9.362 9.149 8.931 8.714 8.507 1& 1 2 2 3 3 4- 4 5 5 6- 6 7- - 7 8 8 9- 9 10 -10 14.079 11.924 10.299 16.155 18.030 19.065 19.815 20.156 20.280 20.261 20.146 13.671 15.260 16.147 16.801 17.112 17.242 17.251 17.179 11.793 13.162 13.932 14.507 14.789 14.917 14.942 14.898 19.963 17.049 14.803 11 19.748 16.891 14.684 19.538 19.327 19.115 18.908 18.719 18.542 16.737 16.582 16.425 16.272 16.134 16.007 14.568 14.450 14.331 14.215 14.112 14.018 - 11 12 12 13 -13 14 - 14 15 - 15 16-16 17 17 18-18 18.365 15.880 13.925 19 -19 18.182 20 - 20 17.993 21 - 21 17.797 17.588 22-22 23 23, 17.372 24 24 17.148 25 - 25 16.916 26. 26 16.681 16.437 27 - 27 15.748 15.610 15.466 13.827 13.724 13.616 28-28 29 - 29 30 - 30 31 -31 32 - 32 33 - 33 34-34 35 35 36 -36 37 -37 38-38 39-39 40-40 41 - 41 42 -42 43-43 44 -44 45 -45 46 -46 47 -47 48 -48 49 -49 50 -50 51 - 51 15.310 13.497 15.148 13.372 14.978 13.240 14.800 14.620 14.431 13.101 12.960 12.811 16.196 14.244 12.663 15.976 15.784 15.591 15.392 15.180 14.954 14.720 14.477 14.231 14.075 13.930 13.784 13.632 13.469 13.294 13.111 12.919 12.724 12.530 12.419 12.308 12.191 12.064 11.926 11.780 11.627 11.470 13.981 13.727 12.525 12.322 11.309 11.144 13.481 12.125 10.984 13.254 13.036 11.945 11.772 10.839 10.701 12.822 11.602 10.566 12.600 12.371 12.128 11.870 11.591 11.426 11.243 11.047 10.837 10.607 10.425 10.278 10.119 9.947 9.756 11.279 10.942 10.345 10.059 9.535 9.291 10.579 9.748 9.023 54 TABLES 54 OF ANNUITIES. IX. Value of an Annuity of £1 on Two JOINT LIVES. Difer'ence of Age 0. CARLISLE. NORTHAMPTON. Ages. 3 5 4__ 7.213 7.056 6.897 6.735 6.571 6.404 6.234 6.062 5.888 5.712 5.533 5.347 5.158 4.960 4.759 4.555 4.348 4.140 3.930 3.719 3.510 3.304 3.105 2.917 2.750 2.583 2.410 2.217 2.018 1.827 1.642 1.472 1.357 1.256 1.171 1.098 1.063 1.001 .909 .748 .576 .361 .199 .059 7.723 7.544 7.362 7.179 6.993 6.805 6.614 6.421 6.226 6.030 5.831 5.626 5.417 5.201 4.982 4.760 4.537 4.312 4.087 3.862 3.639 3.421 3.211 3.015 2.833 2.656 2.470 2.271 2.068 1.869 1.681 1.510 1.387 1.339 1.195 1.124 1.030 1.015 .922 .756 .583 .365 .201 .060 8.304 8.099 7.891 7.681 7.470 7.256 7.041 6.824 6.606 6.387 6.166 5.938 5.709 5.471 5.231 4.990 4.747 4.504 4.261 4.020 3.781 3.548 3.324 3.114 2.920 2.741 2.550 2.338 2.122 1.917 1.719 1.538 1.416 1.309 1.218 1.141 1.103 1.036 .938 .769 .591 .369 .203 .060 I 52 & 52 53 -53 54-54 55-55 56 -- 56 57-57 58 - 58 59 -59 60 -60 61 -61 62-62 63 -63 64 -64 65 -65 66-66 67 -67 68 -68 69 -69 70-70 71 - 71 72 -72 73 -73 74-74 75-75 76 -76 77 -77 78 -78 79-79 80 -80 81 - 81 82 -82 83 -83 84 - 841 85 -85 86-~86 87 -87 88 -88 89 -89 90 - 90 91 -91 92 -92 93-93 94 -94 95 -95 4 5 10.215 9.849 9.480 9.103 8.721 8.334 7.954 7.605 7.295 7.044 6.804 6.563 6.308 6.047 5.774 5.486 5.188 4.877 4.556 4.217 3.904 3.631 3.400 3.231 3.068 2.927 2.784 2.610 2.459 2.283 2.135 1.978 1.825 1.657 1.509 1.389 1.328 1.248 1.088 1.050 1.120 1.226 1.302 1.383 9.434 9.117 8.796 8.465 8.128 7.783 7.444 7.131 6.854 6.630 6.417 6.202 5.974 5.738 5.490 5.228 4.954 4.666 4.367 4.050 3.755 3.497 3.279 3.119 2.966 2.833 2.698 2.533 2.390 2.222 2.079 1.929 1.782 1.619 1.476 1.359 1.301 1.223 1.066 1.028 1.096 1.199 1.273 1.353 8.751 8.474 8.192 7.900 7.600 7.293 6.988 6.705 6456 6.257 6.067 5.875 5.669 5.456 5.230 4.990 4.737 4.471 4.191 3.893 3.615 3.371 3.165 3.015 2.870 2.744 2.617 2.460 2.324 2.163 2.027 1.882 1.741 1.583 1.444 1.331 1.275 1.199 1.045 1.007 1.073 1.173 1.245 1.323 12.331 .Dferenceof Age 5 Years. 16.828 14.269 18.087 15.341 15.300 15.809 1 & 6 7 8 3 9 4. - 19.100 19.584 16.214 16.644 15.974 16.110 5 6 - 10 11 19.874 19.935 16.913 16.989 9.479 10.741 12.347 11.100 12.581 14.461 11.755 12.165 13.319 13.775 13.933 12315 12.447 14.068 2 13.258 14.019 14.402 14.649 14.731 5 TA~BLES OF ANNUITIES. IX. Value of an Annuity of £1 on Two J5 JOINT LIVES. Dirence of Age 5 Years. CARLISLE. NORTHAMPTON. Age. 4 - 5 12.498 12.492 12.421 12.302 12.158 12.009 11.864 11.723 11.585 11.452 11.327 11.209 3 16.137 16.089 15.957 15.762 15.538 15.308 15.086 14.870 14.660 14.457 14.265 14.082 3.908 13.741 13.584 13.433 13.280 13.124 12.966 12.805 12.641 12.474 12.304 12.131 11.955 11.775 11.592 11.404 11.213 11.021 10.828 10.635 10.437 10.236 10.033 9.829 9.624 9.414 9.204 8.997 8.790 8.579 8.366 8.152 7.941 7.730 7.518 7.304 7.088 6.870 6.651 6.427 6.201 14.111 14.089 13.992 13.841 13.664 13.480 13.303 13.130 12.961 12.799 12.646 12.500 12.361 12.229 12.105 11.987 11.866 11.743 11.618 11.489 11.359 11.225 11.088 10.948 10.805 10.659 10.508 10.354 10.196 10.037 9.877 9.716 9.550 9.381 9.210 9.037 8.862 8.683. 8.503 8.326 8.147 7.965 7.780 7.593 7.409 7.225 7.039 6.850 6.659 6.465 6.270 6.070 5.867 11.096 10.989 10.890 10.796 10.699 10.600 10.499 10.396 10.289 10.181 10.069 9.954 9.837 9.716 9.591 9.463 9.331 9.198 9.062 8.927 8.787 8.643 8.497 8.350 8.200 8.046 7.891 7.737 7.582 7.424 7.262 7.098 6.936 6.774 6.609 6.442 6.272 6.100 5.925 5.744 5.561 ' rv v ( TP~L,.3 I vr L 7 & 12 8-13 9-14 10 -15 11-16 12-17 13 -18 14 -19 15 -20 16 - 21 17 -22 18 - 23 19 - 24 20 -25 21 -26 22 -27 23-28 24 -29 25 -30 26-31 27-32 28 -33 29 -34 30-35 31- 36 32-37 33 -38 34 -39 35 - 40 36-_41 37-42 38 -43 39-44 40 -45 41 -46 42-47 43-48 44-49 45 -50 46 -51 47-52 48 -53 49 -54 50-55 51 -56 52 -57 53 -58 54 - 59 55-60 56-61 57 -62 58 -63 59 -64 I 71vI 19.889 19.771 19.606 19.410 19.208 19.014 18.820 18.622 18.423 18.230 18.036 17.838 17.633 17.421 17.204 16.977 16.747 16.524 16.311 16.097 15.875 15.648 15.424 15.209 14.989 14.764 14.531 14.290 14.048 13.812 13.579 13.346 13.107 12.868 12.630 12.389 12.139 11.868 11.580 11.271 10.955 10.628 10.284 9.924 9.550 9.172 8.797 8.439 8.098 7.788 7.480 7.175 6.875 4~ 16.975 16.900 16.785 16.643 16.495 16.354 16.213 16.068 15.922 15.781 15.639 15.493 15.341 15.182 15.019 14.846 14.670 14.500 14.339 14.176 14.006 13.830 13.657 13.491 13.321 13.146 12.964 12.773 12.581 12.394 12.209 12.024 11.833 11.641 11.450. 11.256 11.053 10.830 10.591 10.332 10.065 9.787 9.492 9.181 8.855 8.524 8.194 7.876 7.574 7.299 7.025 6.752 6.482 ~ 5 14.736 14.689 14.606 14.500 14.389 14.284 14.178 14.069 13.959 13.853 13.746 13.636 13.520 13.398 13.272 13.137 13.000 12.867 12.742 12.615 12.482 12.344 12.208 12.078 11.944 11.806 11.661 11.508 11.354 11.204 11.056 10.907 10.753 10.598 10.444 10.287 10.121 9.937 9.737 9.519 9.292 9.054 8.799 8.528 8.242 7.950 7.6577.375 7.106 6.860 6.615 6.370 6.127 56 TABLES OF ANNUITIES. 56 IX. Value of an Annuity' of £1 on Two Diference of Age NORTHAMPTO )N. 5 1.573 1.447 1.329 1.235 1.145 1.038 .892 .734 .547 .369 .175 5.658 5.447 5.285 5.017 4.798 4.573 4.349 4.124 3.901 3.683 3.471 3.270 3.070 2.869 2.659 2.448 2.258 2.077 1.899 1.751 1.608 1.478 1.356 1.259 1.164 1.054 .902 .738 .554 .373 .177 Ages. 3 3 .4 J5 _________________ ___________ _________________ __________ f I ii VI I 5.372 5.180 4.986 4.786 4.585 4.378 4.169 3.960 3.752 3.547 3.347 3.159 2.971 2.780 2.580 2.381 2.195 2.013 1.838 1.750 5 Years. ICARLISLE. - 4 JOINT LIVES. 5.970 5.737 5.503 5.265 5.025 4.783 4.540 4.298 4.059 3.825 3.599 3.386 3.176 2.963 2.743 2.526 2.325 2.131 1.947 1.793 1.645 1.511 1.385 1.284 1.188 1.074 .921 .756 .562 .377 .179 60 & 65 61 - 66 62-67 63-68 64-69 65-70 66-71 67 -72 68-73 69-74 70-75 71 -76 72 -77 73-78 74 -79 75 -80 76 -81 77-82 78 -83 79 -84 80-85 81-86 82-87 83-88 84 -89 85 -90 86-91 87--92 88 -93 89 -94 90-95 6.589 6.323 6.054 5.779 5.490 5.193 4.882 4.580 4.297 4.035 3.804 3.568 3.353 3.152 2.952 2.790 2.618 2.471 2.318 2.155 1.993 1.834 1.704 1.606 1.496 1.335 1.255 1.245 1.272 1.266 1.217 6.225 5.986 5.743 5.493 5.229 4.956 4.667 4.386 4.123 3.878 3.661 3.439 3.237 3.047 2.857 2.704 2.540 2.400 2.255 2.099 1.943 1.790 1.664 1.569 1.464 1.307 1.229 1.218 1.245 1.240 1.191 5.895 5.678 5.458 5.230 4.988 4.737 4.469 4.207 3.961 3.731 3.528 3.319 3.127 2.948 2.767 2.623 2.467 2.333 2.194 2.045 1.895 1.747 1.626 1.535 1.433 1.279 1.203 1.192 1.219 1.214 1.167 14.160 15.095 15.873 16.248 16.494 16.573 16.568 16.505 16.400 16.264 16.112 15.955 15.794 15.628 15.460. 15.298 15.136 14.975 12.275 13.087 13.769 14.106 14.334 14.419 14.432 14.395 14.321 14.221 14.106 13.987 13.864 13.737 13.608 13.483 13.359 13.235 .Djerence of Age 10 Years. 9.544 11.010 11.528 11.850 11.954 12.052 12.083 12.070 12.006 11.906 11.797 11.686 11.570 11.450 11.324 11.193 11.063 10.939 10.782 12.438 13.019 13.374 13.479 13.578 13.599 13.569 13.482 13.355 13.217 13.078 12.934 12.346 14.239 12.630 12.470 12.311 12.158 14.230 12.784 14.895-15.287 15.391 15.486 15.490 15.436 15.316 15.151 14.974 14.795 14.612 14.424 14.030 13.832 13.642 1 & 11 2-12 3-13 4-14 5-15 6-16 7-17 8-18 9-19 10 -20 11-21 12 --22 13-23 14-24 15 -25 16-26 17 -27 118-28 16.623 17.713 18.609 19.027 19.289 19.354 19.319 19.215 19.062 18.873 18.666 18.454 18.238 18.017 17.794 17.578 17.363 17.149 TAB3LES OF ANNUITIES. IX. Value of an Annuity of £1 on Two JOINT LIVES. .Deference of Age 10 Years. I. 1I NORTHAMPTON 5 CARLISLE, i 3 12.013 11.873 11.742 11.615 11.485 11.352 11.217 11.078 10.936 10.791 10.642 10.490 10.336 10.182 10.027 9.869 9.706 9.540 9.370 9.195 9.015 8.834 8.658 8.483 8.308 8.130 7.948 7.763 7.574 7.382 7.186 6.989 6.795 6.600 6.399 6.196 5.986 5.774 5.559 5.341 5.121 4.900 4.679 4.458 4.236 4.019 3.806 3.606 3.405 3.199 2.979 2.757 10.820 10.707 10.600 10.498 10.393 10.285 10.175 10.062 9.946 9.826 9.703 9.576 9.448 9.320 9.190 9.058 8.921 8.781 8.636 8.487 8.333 8.177 8.025 7.875 7.724 7.569 7.411 7.249 7.084 6.915 6.742 6.568 6.395 6.222 6.042 5.860 5.671 5.479 5.283 5.084 4.883 4.680 4.476 4.272 4.066 3.864 3.665 3.477 3.289 3.095 2.88 7 2.675 4 13.461 13.286 13.121 12.961 12.798 12.632 12.463 12.291 12.116 11.937 11.755 11.568 11.382 11.195 11.007 ]10.817 10.622 10.424 10.221 10.014 9.803 9.590 9.383 9.179 8.975 8.767 8.557 8.344 8.127 7.907 7.684 7.461 7.240 7.021 6.795 6.568 6.334 6.098 5.860 5.621 5.380 5.139 4.898 4.659 4.420 4.186 3.958 3.743 3.529 3.310 3.077 2.843 Ages. 4 16.943 16.749 16.551 16.344 16.126 15.897 15.660 15.417 15.168 14.918 14.675 14.449 14.232 14.017 13.798 13.569 13.331 13.082 12.823 12.550 12.257 11.954 11.645 11.338 11.031 10.720 10.400 10.071 9.733 9.392 9.053 8.729 8.429 8.135 7.839 7.53 7.219 6.896 6.562 6.224 5.890 5.565 5.254 4.963 4.699 4.459 4.257 4.055 3.863 3.664 3.442 3.229 19 & 29 20 -30 21- 31 22-32 23 - 33 24 -34 25 - 35 26 -36 27-37 28-38 29-39 30 -40 31 -41 32 -42 33-43 31 -44 35 -45 36 - 46 37 -47 38 -48 ~39 - 49 40 -50 41 -51 42 -52 43 -53 44 -54 45 -55 46 - 56 47 -57 48 -58 49 -59 50 -60 51 -61 52 -62 53 -63 54-64 55-65 56 -66 57 -67 58 -68 59 -69 60-70 61 -71 62 -72 63-73 64-74 65 -75 66 - 76 67-77 68 -78 69-79 70 -801 ., 14.821 13.117 14.677k -13.008 12.896 14,530 14.374 12.776 14.208 12.648 14.032 12.510 13.848 12.365 13.658 12.214 13.462 12.058 13.265 11.900 13.074 11.747 12.897 11.607 12.728 11.474 12.560 11.342 12.389 11.207 12.208 11.063 12.019 10.912 11.819 10.750 11.610 10.579 10.396 11.388 10.195 11.146 10.894 9.984 10.635 9.766 10.378 9.548 10.120 9.329 9.856 9.104 8.870 9.583 8.626 9.301 8.372 9.009 8.711 8.111 8.416 7.851 8.132 7.601 7.370 7.869 7.611 7.142 '6.911 7.350 7.078 6.798 6.508 6.205 5.89~7 5.591 5.293 5.006 4.737 4.492 4.269 4.082 3.895 3.716 3.531 3.322 3.121 6.418 6.156 5.881 5.600 5.319 5.044 4.779 4.529 4.302 4.094 3.921 3.746 3.580 3.407 3.210 3.020 58 -58 IX. TABLES OF ANNUITIES. Value of an Annuity of £1 on Two JOINT LIVES. Defference of Age 10 Year&. NORTHAMPTON. CARLISLE. 5 4 3 2.470 2.271 2.085 1.941 1.811 1.699 1.597 1.514 1.400 1.255 1.061 .852 .606 .398 .185 2.542 2.334 2.141 1.991 1.856 1.739 1.633 1.546 1.427 1.278 1.078 .864 .614 .403 187 2.618 2.401 2.199 2.043 1.903 1.781 1.670 1.580 1.456 1.302 1.096 .877 .622 .408 .189 Ages. 3 i' 71 & 81 72-82 73 -83 74-84 2.781 2.577 2.391 75 -85 2.217 76-86 77-87 10.406 11.981 12.531 12.876 12.993 13.121 13.178 13.168 13.112 12.998 12.861 12.715 12.564 12.408 12.246 12.078 11.911 11.750 11.595 11.445 11.302 11.163 11.020 10.874 10.725 10.574 10.423 10.272 10.117 9.959 9.797 9.631 9.461 11.864 13.659 14.277 14.657 14.776 14.904 14.950 14.929 14.834 14.683 14.508 14.323 14.132 13.936 13.734 13.527 13.320 13.121 12.930 12.744 12.567 12.394 12.218 12.038 11.854 11.670 11.486 11.302 11.114 10.923 10.728 10.530 10.327 2.062 1.935 78 -88 79 -89 1.849 1.739 81-91 82-92 1.589 1.520. 1.531 84 -94 1.537 80-90, 83 -93 85-95 Diference of Age 9.243 10.642 11.134 11.447 11.561 11.685 11.748 11.761 11.715 11.627 11.519 11.402 11.280 11.153 11.021 10.883 10.746 10.613 10.486 10.363 10.246 10.132 10.015 9.895 9.771 9.647 9.522 9.396 9.267 9.135 8.998 8.858 8.714 2.992 1 15 &16 2 -17 3--18 4 -19 5--20 6.-21 7 -22 8 -23 9 -24 10 -25 11 -- 26 12 -27 13 -28 14 -29 15 -30 16-31 17 -32 18 -33 19 -34 20 -35 21 -36 22 -37 23 -38 24 -29 25 -40 26 -41 27-42 28 - 43 29 -44 30 -45 31--46 32-47 33-48 1.549 1.509 2.897 2.696 2.501 2.323 2.157 2.007 1.885 1.803 1.697 1.551 1.484 1.495 1.513 1.502 1.475 2.807 2.616 2.430 2.260 2.100 1.956 1.838 1.759 1.657 1.515 1.450 1.460 1.479 1.468 1.443 Years. 16.119 17.180 18.056 18.467 18.722 18.773 18.714 18.583 18.404 18.189 17.958 17.724 17.491 17.269 17.063 16.865 16.669 16.466 16.252 16.031 15.802 15.565 15.322 15.073 14.824 14.584 14.344 14.107 13.875 13.650 13.416 13.171 12.908 13.802 14.718 15.483 15.855 16.097 16.166 16.141 16.055 15.927 15.768 15.594 15.417 15.240 15.072 14.918 14.771 14.625 14.473 14.311 14.142 13.966 13.782 13.593 13.398 13.202 13.014 12.825 12.638 12.455 12.278 12.093 11.897 11.685 12.013 12.812 13.487 13.823 14.049 14.126 14.122 14.065 13.971 13.850 13.716 13.579 13.442 13.312 13.195 13.083 12.973 12.857 12.733 12.602 12.464 12.319 12.169 12.013 11.856 11.706 11.556 11.407 11.261 11.121 10.974 10.817 10.644 5 TABLES OF ANNUITIES. 59 IX. Value of an Annuity of £1 on Two JOINT LIVEs. Dirence of Age 15 Years. II I CARLISLE. NORTHAMPTON. 5 8.565 8.415 8.267 8.119 7.966 7.810 7.651 7.489 7.326 7.162 6.994 6.822 6.648 6.469 6.283 6.093 5.897 5.701 5.504 5.303 5.100 4.893 4.685 4.477 4.269 4.064 3.866 3.679 3.492 3.297 3.088 2.873 2.664 2.461 2.272 2.126 1.991 1.867 1.753 1.660 1.538 1.387 1.180 .955 .688 .448 .206 Age. 4J3 9.286 9.110 8.937 8.763 8.586 8.406 8.221 8.035 7.848 7.660 7.469 7.274 7.076 6.875 6.667 6.454 6.236 6.019 5.801 5.580 5.357 5.132 4.905 4.679 4.455 4.234 4.021 3.821 3.621 3.414 3.192 2.965 2.746 2.533 2.336 2.183 2.042 1.914 1.794 1.697 1.570 1.413 1.200 .970 .697 .453 .208 4 =3_10.120 9.912 9.707 9.503 9.296 9.085 8.870 8.655 8.439 8.222 8.003 7.781 7.556 7.328 7.093 6.854 6.611 6.369 6.127 5.884 5.638 5.391 5.145 4.899 4.656 4.418 4.189 3.974 3.760 3.538 3.303 3.063 2.833 2.610 2.403 2.244 2.097 1.963 1.838 1.736 1.603 1.440 1.221 .985 .706 .458 .210 12.620 34&49 12.314 35-50 11.989 36-51 11.661 37-52 11.330 38-53 10.995 39-54 10.658 40-55 10.325 41-56 9.992 42-57 9.665 43-58 9.353 44-59 9.063 45-60 8.803 46-61 8.545 47-62 8.279 48-63 7.992 49-64 7.691 50-65 7.374 51-66 52-67 7.047 6.713 53-68 6.370 54-69 6.019 55-70 5.656 56-71 5.310 57-72 4.995 58-73 4.719 59-74 4.498 60-75 4.299 61-76 4.120 62-77 63-78 3.939 64-79 3.733 65-80 3.542 66-81 3.332 67-82 3.138 68-83 2.937 69-84 2.736 2.523 70-85 2.322 71-86 72-87' 2.151 2.033 73-88 1.911 74-891 1.758 75-90 76-91 1.707 1.744 77-92 78-93 1.796 1.802 79-941 80-95 1.806 I 5 11.449 11.196 10.924 10.649 10.369 10.449 10.238 10.009 9.776 9.538 10.084 9.294 9.796 9.510 9.223 8.940 8.669 8.417 8.193 7.970 7.739 7.487 7.221 6.939 6.646 6.344 9.046 8.799 8.549 8.302 8.066 7.846 7.652 7.458 7.256 7.034 6.799 6.546 6.282 6.009 6.033 5.725 5.712 5.378 5.058 4.765 4.509 4.304 4.120 3.954 3.786 3.594 3.416 3.218 3.035 2.844 2.653 2.449 2.257 2.092 1.979 1.862 1.712 1.663 1.699 1.750 1.756 1.762 5.431 5.123 4.826 4.553 4.315 4.125 3.954 3.800 3.644 3.464 3.297 3.111 2.938 2.757 2.575 2.380 2.195 2.037 1.928 1.815 1.669 1.621 1.656 1.706 1.713 1.720 60 TABLES OF ANNUITIES. IX. Value of an Annuity of £1 on Two JOINT LIVES. Difference of Age 20 Years. NORTHAMPTON. CARLISLE. 5 8.961 10.34-1 10.843 11.163 11.281 11.400 11.452 11.455 11.401 11.304 11.188 11.062 10.932 10.796 10.655 10.507 10.358 10.214 10.074 9.937 9.809 9.685 9.562 9.435 9.304 9.170 9.032 8.890 Age. 10.053 11.605 12.161 12.511 12.633 12.754 12.798 12.786 12.710 12.586 12.441 12.286 12.125 11.959 11.787 11.609 11.430 11.257 11.089 10.924 10.768 10.619 10.470 10.317 10.160 10.000 9.836 9.667 11.413 13.172 13.794 14.178 14.301 14.420 14.451 14.417 14.310 14.150 13.965 13.770 13.570 13.363 13.151 12.932 12.714 12.502 12.297 12.096 11.906 11.723 11.540 11.354 11.164 10.970 10.773 10.572 1 &21 15.623 13.455 22 16.625 14.326 3 23 4-24 5 25 ' 17.441 17.805 18.016 15.046 15.380 15.586 2 6-26 7-27 8 28 9 29 10-30 11-31 12-32 13-33 14-34 15-35 16-36 17-37 18-38 19-39 20-40 21 -41 22-42 23 43 24-44 25-45 26-46 27-47 28-48 11.766 12.531 13.170 13.476 13.672 18.032 17.944 15.625 15.574 13.723 13.697 17.792 17.609 17.411 17.198 16.983 16.760 16.529 16.295 16.063 15.469 15.336 15.190 15.031 14.870 14.702 14.526 14.347 14.169 13.623 13.525 13.416 13.295 13.172 13.042 12.905 12.765 12.626 15.834 13.993 12.489 15.603 13.815 12.350 15.367 13.632 12.206 15.131 14.903 13.449 13.272 12.062 11.923 14.673 13.094 11.783 14.442 14.202 13.954 13.696 13.425 12.914 12.726 12.530 12.325 12.107 11.641 11.492 11.335 11.170 10.993 13.143 12.849 10.805 10.607 10.404 10.186 9.495 9.321 9.151 10.160 9.957 12.551' 131-51 12.237 8.157 8.980 8.806 11.878 11.638 11.393 11.132 9.756 9.550 32-52 133-53 11.919 11.594 10.866 10.593 8.005 9.962 9.730 8.629 9.342 11.261 7.849 7.690 7.527 7.360 10.311 8.448 8.264 8.076 7.884 9.490 9.131 8.916 8.698 8.477 35-55 36-56 37-57 38-58 10.919 10.570 10.216 9.865 10.020 9.721 9.416 9.111 9.240 8.981 8.716 8.449 7.189 7.689 8.253. 39- 59 9.531 7.015 6.838 7.490 7.290 8.025 7.796 40-60 41-61 9.224 8.960 8.553 8.325 6.660 7.961 7.763 7.088 7.567 6.477 6.289 6.094 5.894 8.705 6.881 6.671 6.453 6.230 8.104 7.571 7.332 7.095 6.850 6.602 8.450 8.183 7.910 7.624 7.884 7.651 7.411 7.159 7.379 7.175 6.964 6.740 5.690 5.481 6.004 5.774 6.351 6.096 7.325 7.012 5.268 6.893 6.612 5.541 6.503 6.251 5.839 49-69 6.682 6.314 5.980 5.054 4.841 5.306 5.074 5.582 5.328 50-70 51-71 6.338 5.977 6.001 5.671 5.695 5.391 8.744 8.596 8.451 8.306 10.366 29-49 30-50 134-54 42-62 43-63 44-64 45-65 46-66 47-67 48-68 8.820- 8.194 6 TABLES OF. ANNUITIES. IX. Yas Value of an Annuity of Ag 1 20 Two JOINT £ on LIVES.Difrneo NORTHIAMPTC)N. 5 4 4.630 4.417 4.208 4.006 3.815 3.623 3.424 3.210 2.992 2.782 2.578 2.387 2.242 2.107 1.984 1.870 1.777 1.650 1.486 1.259 1.012 .723 .469 .215 4.845 4.614 4.389 4.171 3.966 3.761 3.549 3.322 3.092 2.870 2.656 2.457 2.305 2.163 2.035 1.915 1.817 1.685 1.515 1.280 1.028 .733 .474 .217 CARLISLE. 3 5.077 4.828 4.585 4.350 4.129 3.908 3.682 3.440 3.197 2.964 2.739 2.530 2.371 2.223 2.089 1.963 1.860 1.722 1.545 1.303 1.044 .743 .480 .219 Ages. 52 & 72 53--73 54-74 55-75 56-76 57-77 58-78 59-79 60-80 61--81 62-82 63-83 64-84 65-85 66-86 67-87 68-88 69-89 70-90 71-91 72-92 73-93 74-94 75-95 Difference of Age 25 8.742 10.080 10.555 10.855 10.959 11.062 11.100 11.090 11.024 10.916 10.788 10.651 10.509 10.360 10.205 10.046 9.889 9.739 9.592 9.448 9.310 9.173 9.031 8.886 8.739 8.595 61 9.770 11.264 11.790 12.116 12.220 12.322 12.350 12.323 12.234 12.098 11.941 11.773 11.600 11.42011.234 11.044 10.856 10.677 10.502 10.330 10.165 10.001 9:833 9'.661 9.488 9.318 11.037, 12.722 13.307 13.661 13.762 13.859 13.871 13.820 13.698 13.525 13.328 13.120 12.906 12.686 12.459 12.229 12.002 11.785 11.574 11.367 11.167 10.969 10.768 10.562 10.356 10.154 3 4 5 5.636 5.357 5.326 5.071 5.048 4.813 4.815 4.598 4.581 4.384 4.362 4.181 4.141 3.905 3.695 3.484 3.297 3.105 2.916 2.719 2.541 2.389 3.976 3.755 3.558 3.359 3.183 3.002 2.823' 2.635 2.465 2.319 2.285 2.220 2.163 1.987 1.919 1.940 1.977 1.983 2.103 1.932 1.866 1.886 1.924 1.930 1.993 1.941 5.102 4.837 4.600 4.400 4.201 4.013 3.821 3.614 3.430 3.242 3.076 2.905 2.735 2.555 2.393 2.253 2.159 2.047 1.880 1.816 1.836 1.873 1.880 1.893 Years. 1&26 14.994 13.001 6-31 15.923 16.677 17.011 17.219 13.816 14.486 14.797 15.001 2-27 3-28 4-29 5-30 17.241 15.046 7-32 8-33 9-34 10-35 11-36 12-37 13-38 14-39 17.164 17.018 16.824 16.596 16.349 16.102 15.851 15.597 15.006 14.906 14.763 14.590 14.400 14.209 14.015 13.817 15.348 13.623 16-41 17-42 18-43 19-44 20-45 21-46 22-47 23-48 24-49 25-50 26-51 15.116 14.894 14.673 14.444 14.207 13.959 13.696 13.417 13.114 12.793 12.454 13.444 13.273 13.103 12.926 12.741 12.545 12.336 12.111 11.864 11.599 11.317 15-40 11.426 12.146 12.746 13.033 13.229 13.287 13.271 13.202 13.096 12.963 12.814 12.664 12.511 12.354 12.201 12.061 11.928 11.796 11.657 11.511 11.355 11.187 11.004 10.801 10.581 10.344 6~2 TABLES OF ANNUITIES. 62 IX. Value of an Annuity of £1 on Two JOINT LIVES. Deference of Age 25 Years. ICARLISLE. NORTHAMPTON. 1---1 ____K 9.148 8.975 8.799 8.619 8.436 8.250 8.060 7.866 7.669 7.469 7.265 7.053 6.838 6.614 6.388 6.159 5.929 5.696 5.460 5.222 4.746 4.511 4.285 4.074 3.864 3.648 3.416 3.180 2.953 2.733 2.530 2.376 2.234 2.105 1.985 1.886 1.751 1.575 1.330 1.067 .760 .491 .224 9.952 9.748 9.540 9,329 9.115 8.897 8.677 8.454 8.227 7.997 7.765 7.525 7.281 7.029 6.776 6.522 6.266 6.008 5.749 5.488 5.228 4.970 4.716 4.472 4.245 4.019 3.787 3.540 3.291 3.051 2.820 2.608 2.446 2.297 2.162 2.036 1.932 1.790 1.606 1.354 1.083 .770 .497 .227 __- 11 I - 8.451 8.304 8.153 7.999 7.841 7.680 7.515 7.346 7.174 6.998 6.819 6.631 6.440 6.240 6.037 5.831 5.622. 5.411 5.195 4.978 4.758 4.539 4.322 4.112 3.916 3.720 3.518 3.299 3.076 2.861 2.651 2.457 2.310 2.174 2.051 1.937 1.843 1.714 1.544 1.307 1.050 .750 .485 .222 5 Ages.4 3 27 &52 28-53 29-54 30-55 31-56 32-57 33-58 34-59 35-60 36-61 37-62 38-63 39-64 40-65 41-66 42-67 43-68 44-69 45-70 46-71 47-72 48-73 49-74 50-75 51-76 52-77 53 -78 54-79 55-80 56-81 57-82 58-83 59-84 60-85 61-86 62-87 63-88 64-89 65-90 66-91 67-92 68-93 69-94 70-95 i ' 3 I f 12.110 11.765 11.425 11.089 10.749 10.402 10.055 9.721 9.410 9.132 8.859 8.584 8.296 8.006 7.713 7.413 7.106 6.790 6.465 6.127 5.806 5.513 5.247 5.022 4.797 4.587 4.375 4.140 3.920 3.681 3.462 3.238 3.025 2.812 2.634 2.488 2.397 2.290 2.131 2.096 2.156 2.228 2.249 2.248 11.029 10.738 10.450 10.164 9.873 9.575 9.275 8.986 8.716 8.476 8.239 8.000 7.748 7.493 7.234 6.967 6.692 6.407 6.113 5.804 5.510 5.241 4.996 4.790 4.583 4.390 4.194 3.975 3.770 3.545 3.339 3.127 2.925 2.722 2.552 2.412 2.325 2.223 2.069 2.034 2:093 2.164 2.186 2.187 10.100 9.853 9.608 9.364 9.114 8.855 8.594 8.341 8.105 7.897 7.691 7.481 7.260 7.034 6.804 6.565 6.319 6.061 5.793 5.510 5.240 4.992 4.766 4.577 4.385 4.208 4.026 3.821 3.630 3.418 3.224 3.024 2.832 2.637 2.474 2.341 2.258 2.159 2.009 1.976 2.033 2.103 2.126 2.130 12.514 13.301 13.945 14.228 14.391 14.396 11.064 11.766 12.347 12.613 12.775 12.798 Difference of Age 30 Years. 8.483 9.767 10.213 10.488 10.572 10.656 9.438 10.865 11.355 11.651 11.732 11.812 10.605 12.203 12.743 13.061 13.136 13.207 1 &31 2-32 3-33 4-34 5-35 6-36 14.328 15.217 15.933 16.231 16.389 16.365 63 TABLES OF ANNUITIES. IX. Value of an Annuity of £1 on Two JOINT LIvEs. Diffrence of Age 30 Years. NORTHAMPTON.]CARLISLE. 3 10.676 10.648 10.565 10.442 10.302 10.156 10.007 9.852 9.690 9.522 9.353 9.186 9.021 8.861 8.712 8.568 8.421 8.270 8.116 7.958 7.797 7.632 7.464 7.292 7.116 6.937 6.750 6.559 6.360 6.156 5.948 5.735. 5.518 5.298 5.076 4.854 4.634 4.417 4.206 4.006 3805 3.596 3.369 3.140 2.920 2.707 2.510 2.360 2.222 2.097 1.980 1.883 1.750 11.819 11.772 11.665 11.513 11.342 11.165 10.985 10.799 10.607 10.408 10.208 10.011 9.818 9.630 9.454 9.284 9.111 8.934 8.754 8.570 8.383 8.193 7.999 7.802 7.601 7.397 7.186 6.971 6.747 6.520 6.288 6.052 5.813 5.571 5.329 5.087 4.848 4.613 4.386 4.171 3.954 3.731 3.490 3.247 3.015 2.792 2.585 2.428 2.284 2.153 2.030 1.928 1.788 13.195 13.122 12.981 12.791 12.580 12.363 12.144 11.918 11.687 Ages. 3 4 5 7&37 8-38 9-39 16.248 14.320 12.750 16.069 15.849 14.190 14.023 12.654 12.526 10-40 15.605 11-41 12-42 13-43 14-44 15.358 15.117 14.877 14.631 15-45 11.448 16-46 11.210 17-47 10.975 18-48 10.746 19-49 10.523 20-50 10.313 21-51 10.111 22-52 9.905 23-53 9.696 ti 24-54 9:484 25-55 9.269 26-56 9.051 27-57 8.830 28-58 8.605 29-59 8.378 30-60 8.147 31-61 7.914 32-62 7.673 33-63 7.429 34-64 7.177 35-65 6.922 36-66 6.663 37-67 6.401 38-68 6.137 39-69 5.871 40-70 5.605 41-71 5.341 42-72 5.081 43-73 4.826 44-74 4.580 45-75 4.348 46-76 4.115 47-77 3.875 48-78 3.619 49-79 3.362 50-80 3.117 51-81 2.882 52-82 2.665 53-83 2.501 54-84 2.349 55-85 2.211 56-86 2.082 57-87 58-88 1.975 1.828 59-89 13.835 13.644 12.378 13.458 13.272 13.080 12.228 12.082 11.936 11.785 14.381 12.884 11.630 14.129 13.872 13.601 13.307 12.995 12.663 12.325 11.981 11.632 11.274 10.911 10.541 12.685 12.481 12.264 12.025 11.769 11.494 11.212 10.924 10.629 10.325 10.015 9.696 11.472 11.309 11.134 10.939 10.727 10.498 10.261 10.017 9.766 9.505 9.237 8.960 10.176 9.380 8.684 9.836 9.529 9.259 8.993 9.085 8.820 8.587 8.358 8.427 8.196 7.995 7.796 8.721 8.122 7.591 8.434 8.140 7.834 7.517 7.191 6.856 6.515 6.169 5.846 5.556 5,299 5.089 4.883 4.691 4.493 4.267 4.054 3.819 3.607 3.390 3.180 2.961 2.765 2.600 2.489 2.268 7.872 7.614 7.343 7.061 6.769 6.466 6.157 5.841 5.544 5.278 5.042 4.850 4.660 4.484 4.303 4.092 3.894 3.674 3.475 3.271 3.072 2.863 2.677 2.518 2.413 2.296 7.372 7.143 6.903 6.651 6.388 6.113 5.832 5.542 5.269 5.023 4.806 4.630 4.456 4.294 4.126 3.930 3.746 3.539 3.352 3.159 2.971 2.772 2.594 2.442 2.341 2.229 64 TABLES.OF ANNUITIES. IX. Value of an Annuity of £1 on Two JOINT LIVES. Difference of Age 30. NORTHAMPTON.-CARLISLE. Ages. 1.577 1.334 1.071 .764 .494 .226 1.608 1.358 1.088 .774 .500 .228 1.641 1.382 1.105 .785 .506 60 61 62 63 64 .230 65 Difference 8.173 9.390 9.800 10.043 10.102 10.163 10.165 10.124 10.031 9.900 9.774 9.592 9.425 9.252 9.076 8.899 8.724 8.552 8.383 8.216 8.053 7.891 9.047 10.392 10.838 11.097 11.150 11.203 11.190 11.130 11.012 10.851 10.697 10.481 10.284 10.080 9.872 9.665 9.461 9.260 9.063 10.104 11.600 12.087 12.362 12.405 12.446 .12.412 12.325 12.174 11.976 11.756 11.525 11.288 11.045 10.799 10.554 10.313 10.076 9.845 8.869 9.617 8.679 8.491 9.394 9.174 7.725 8.299 8.951 7.556 8.104 8.725 7.383 7.207 7.906 7.704 8.495 8.263 7.027 6.839 7.499 7.286 8.028 7.785 6.648 7.069 7.539 6.447 6.844 7.286 6.243 6.033 5.820 6.615 6.382 6.146 7.028 6.768 6.504 5.603 5.906 6.239 5.382 5.663 5.971 5.159 4.934 5.419 5.174 5.703 5.435 4.710 4.930 5.169 4.488 4.272 4.069 4.690 4.457 4.238 4.908 4.656 4.420 3.865 4.019 4.183 3.655 3.428 3.794 3.552 3.942 3.685 & 90 -91 -92 -93 -94 2.199 2.169 2.244 2.335 2.376 2.132 2.103 2.176 2.265 2.306 2.070 2.041 2.111 2.199 2.240 2.398 2.330 2.266 13.597 14.395 15.030 11.973 12.688 13.266 10.656 11.299 11.827 15.273 13.503 12.054 15.391 13.632 12.188 6 -41 15.353 13.624 12.201 7 --42 8 9 -44 10-45 11-46 12-47 13-48 14-49 15-50 16 - 51 17 18-53 19-54 20 21 22 - 57 15.234 13.546 12.152 15.061 13.420 12.060 14.847 14.601 14.334 13.257 13.066 12.855 11.935 11.785 11.617 14.059 13.769 13.457 12.636 12.403 12.150 11.441 11.252 11.044 13.131 12.794 11.882 11.603 10.822 10.589 12.459 11.325 10.356 12.122 11.780 11.043 10.755 10.119 9.875 11.429 11.072 10.458 10.154 9.621 9.359 10.706 9.840 9.087 10.342 9.526 8.814 9.994 9.225 8.551 9.669 9.380 8.943 8.694 8.306 8.090 9.094 8.807 8.447 8.198 7.875 7.658 8.515 7.943 7.434 8.224 7.688 7.210 7.924 7.612 7.288 7.423 7.146 6.857 6.975 6.728 6.468 6.952 6.554 6.1941 6.608 6.242 5.910 6.251 5.914 5.916 5.607 5.611 5.327 5.609 5.326 5.068 5.337 5.115 4.901 5.076 4.872 4.676 4.838 4.650 4.470 4.706. 4.497 4.305 4.510 4.290 4.317 4.112 4.138 3.947 -95 of Age 35 1 2 3 4 5 & 36 -37 --- 38 -3940 -43 -52 -55 -56 23-58 24 -59 25-60 26-61 27 - 62 28 -63 29-64 30 -65 31-66 32-67 33-68 34 -69 35-70 36 -71 37 - 72 38-73 39 -74 40 - 75 41 - 76 42 -77 43 - 78 44 - 79 Years. 6 TAB3LES OF ANNUITIES. 65 IX. Value of an Annuity of £1 on Two JOINT LIVES. D ff rence of Age 35 Years. NORTHAMPTON. CARLISLE. 3 4K 5 Ages. 5 3.197 2.973 2.756 2.5542.400 2.258 2.131 2.012 1.914 1.778 1.601 1.353 1.085 .773 .499 .228 4 3.308 3,072 2.843 2.632 2.470 2.322 2.188 2.063 1.960 1.817 1.633 1.377 1.102 .784 .505 .230 3 3.426 3.176 2.936 2.714 2.544 2.388 2.248 2.117 2.008 1.858 1.666 1.402 1.120 .794 .511 .233 45 &80 46-81 47-82 48-83 49-84 50-85 51-86 52-87 53-88 54-89 55-90 56-91 57-92 58-93 59-94 60--95 Diference of Age 40 7.800 8.942 9.315 9.531 9.571 9.609 9.589 9.524 9.409 9.260 9.100 8.934 8.763 8.586 8.403 8.214 8.024 7.835 7.648 7.463 7.281 7.100 6.910 6.717 6.515 6.309 6.098 5.883 5.664 5.442 5.218 4.992 4.766 8.585 94 839 10.242 10.468 10.500 10.528 10.491 10.404 10.263 10.085 9.894 9.698 9.497 9.290 9.077 8.858 8.639 8.422 8.207 7.995 7.787 7.580 7.365 7.147 6.920 6.689 6.454 6.215 5.973 5.729 5.483 5.236 4.991 9.523 10.907 11.342 11.578 11.597 11.610 11.550 11.435 11.260 11.044 10.816 10.582 10.344 10.100 9.851 9.595 9.340 9.089 8.841 8.597. 8.357 8.119 7.874 7.626 7.370 7.110 6.847 6.581 6.313 6.043 5.772 5.502 5.235 1&41 2-42 3-43 4-44 5-45 6-46 7-47 8-48 9-49 10-50 11-51 12-52 13-53 14-54 15-55 16-56 17-57 18-58 19-59 20-60 21-61 22-62 23-63 24-64 25-65 26-66 27-67 28-68 29-69 30-70 31-71 32-72 33-73 4.087 3.865 3.665 3.459 3.255 3.040 2.849 2.691 2.591 2.476 2.307 2.272 2.340 2.419 2.447 2.458 3.924 3.716 3.529 3.334 3.142 2.938 2.755 2.604 2.509 2.400 2.236 2.202 2.268 2.345 2.375 2.389 3.772 3.577 3.402 3.218 3.036 2.842 2.668 2.523 2.432 2.327 2.168 2.135 2.199 2.276 2.306 2.322 11.331 11.996 12.536 12.752 12.859 12.820 12.702 12.525 12.298 12.034 11.743 11.450 11.153 10.851 10.543 10.234 9.923 9.614 9.318 9.043 8.800 8.558 10.160 10.765 11.264 11.476 11.592 11.578 11.493 11.355 11.171 10.953 10.710 10.464 10.213 9.956 9.692 9.427 9.158 8.890 8.633 8.394 8.184 8.311 7.760 7.532 7.295 7.047 6.785 6.514 6.236 5.954 5.660 5.379 5.123 Years. 12.753 13.487 14.073 14.290 14.382 14.309 14.146 13.917 13.633 13.310 12.958 12.606 12.251 11.892 11.528 11.166 10.803 10.444 10.101 9.782 9.499 9.218 8.933' 8.635 8.329 8.012 7.683 7.345 7.004 6.662 6.309 5.976 5.673 8.051 7.783 7.503 7.210 6.908 6.600 6.291 5.969 5.664 5.386 7.975 66 TABLES OF ANNUITIES. 66 IX. Value of an Annuity of £1 on Two JOINT LrvEs. Difference of Age 40. CARLISLE. NORTHAMPTON. 4 4.543 4.327 4.123 3.916 3.702 3.471 3.236 3.009 2.789 2.587 2.433 2.291 2.162 2.041 1.941 1.800 1.619 1.367 1.095 .780 .503 .230 4.749 4.516 4.295 4.073 3.844 3.598 3.349 3.109 2.878 2.666 2.505 2.356 2.221 2.093 1.987 1.840 1.651 1.391 1.113 .790 .509 .232 Ages. 4.973 4.720 4.481 4.242 3.996 3.734 3.469 3.216 2.973 2.750 2.581 2.424 2.282 2.148 2.036 1.882 1.685 1.417 1.130 .801 .515 .234 34 & 74 35-75 36-76 37-77 39-79 40-80 41-81 42-82 43-83 44-84 45-85 46-86 47-87 48--88 49-89 50-90 51-91 52-92 53-93 54-94 55-95 Diference of Age 7.379 8.435 8.759 8.932 8.941 8.956 8.919 8.841 8.718 8.560 8.386 8.203 8.015 7.821 7.622 7.416 7.208 6.998 6.789 6.576 6.364 6.151 5.934 5.713 5.489 8.071 9.221 9.566 9.744 9.742 9.745 9.690 9.591 9.442 9.256 9.052 8.839 8.622 8.399 8.170 7.935 7.700 7.462 7.226 6.986 6.749 6.512 6.271 6.027 5.780 4 3 8.888 10.147 10.515 10.696 10.679 10.664 10.586 10.458 10.276 10.055 9.814 9.566 9.312 9.053 8.790 8.521 8.252 7.714 7.444 7.177 6.911 6.643 6.372 6.0991 45 1 &46 2-47 3-48 4-49 5-50 6-51 7-52 8-53 9-54 10-55 11-56 12-57 13-58 14-59 15-60 16-61 17-62 18-63 19-64 20-65 21-66 22-67 23-68 24-69 25-70 5.403 5.179 4.959 4.755 4.547 4.315 4.102 3.874 3.670 3.464 3.264 3.056 2.874 2.726 2.635 2.528 2.365 2.339 2.422 2.518 2.559 2.575 5 5.137 4.933 4.730 4.543 4.351 4.135 3.937 3.723 3.533 3.338 3.149 2.952 2.779 2.637 2.551 2.448 2.290 2.265 2.345 2.440 2.482 2.501 4.894 4.706 4.520 4.348 4.171 3.969 3.784 3.584 3.405 3.221 3.042 2.854 2.689 2.553 2.471 2.373 2.220 2.195 2.273 2.366 2.408 2.430 10.666 11.247 11.694 11.820 11.832 11.699 11.497 11.249 10.970 10.664 10.344 10.019 9.696 9.388 9.103 8.857 8.617 8.375 8.120 7.856 7.581 7.292 6.992 6.680 6.358 9.644 10.180 10.600 10.732 10.763 10.663 10.500 10.295 10.060 9.799 9.524 9.243 8.962 8.694 8.446 8.233 8.026 7.816 7.593 7.361 7.118 6.860 6.591 6.309 6.017 Years. 11.888 12.518 12.993 13.107 13.092 12.916 12.664 12.363 12.029 11.667 11.292 10.913 10.538 10.181 9.852 9.565 9.287 9.006 8.712 8.411 8.099 7.773 7.438 7.091 6.736 TABLES OF ANNUITIES. IX. Value of an Annuity of £1 on Two JOINT LIVES. Difference of Age 45 Years. NORTHAMPTON. ~ 5.263 5.035 4.808 4.583 4.365 4.160 3.952 3.737 3.505 3.268 3.040 2.818 2.613 2.457 2.313 2.182 2.060 1.959 1.818 1.635 1.380 1.105 .786 .507 .231 5.532 5.283 5.036 4.792 4.557 4.335 4.111 3.881 3.633 3.383 3.142 2.909 2.694 2.530 2.379 2.241 2.113 2.006 1.859 1.668 1.405 1.122 .797 .512 .233 CARLISLE. 3~~~~Ages. 5.826 5.554 5.284 5.019 4.764 4.523 4.282 4.035 3.771 3.506 3.251 3.005 2.779 2.607 2.448 2.304 2.168 2.055 1.901 1.702 1.431 1.140 .808 .519 .235 _ 26 &71 27-72 28-73 29-74 30-75 31-76 32-77 33-78 34-79 35-80 36-81 37-82 38-83 39-84 40-85 41-86 42-87 43-88 44-89 45-90 46-91 47-92 48 -93 49-94 50-95 Difference of Age &51 7.479 8.520 8.171 9.300 1 8.815 8.957 8.931 8.902 8.817 9.611. 9.751 9.707 9.659 9.549 3-53 4-54 5-55 6-56 7-57 7.557 7.357 7.147 6.931 6.705 6.472 6.236 6.001 5.766 5.532 5.300 5.070 4.841 4.615 8.691 9395 8.519 8.314 9.191 8.952 8.092 7.863 8.696 8.433 7.625 7.381 7.127 6.866 6.604 6.343 8.161 7.883 7.597 7.304 7.012 6.721 6.084 5.826 6.434 6.149 5.572 5.870 5.321 5.595 5.072 5.323 4,827 5.056 6.369 6.022 5.709 5.434 5.213 4.997 4.797 4.592 4.361 4.148 3.915 3.705 3.490 3.281 3.065 2.879 2.728 2.637 2.532 2.375 2.358 2.451 2.558 2.607 2.630 6.024 5:706 5.418 5.166 4.964 4.766 4.582 4.394 4.179 3.981 3.763 3.566 3.363 3.165 2.961 2.783 2.638 2.552 2.452 2.299 2.282 2.372 2.477 2.527 2.552 5.710 5.418 5.153 4.920 4.735 4.553 4.384 4.210 4.011 3.826 3.621 3.436 3.245 3.058 2.863 2.693 2.554 2.472 2.376 2.227 2.210 2.298 2.401 2.451 2.479 9.741 10.179 10.496 10.533 10.472 10.291 10.046 9.766 9.478 9.196 8.940 8.690 8.436 8.169 7.897 7.618 7.331 7.034 6.725 6.407 6.076 5.762 5.475 5.221 8.893 9.304 9.609 9.659 9.621 9.473 9.265 9.024 8.774 8.530 8.308 8.091 7.870 7.637 7.398 7.151 6.894 6.628 6.350 6.061 5.758 5.469 5.206 4.971 50 Years. 6.885 7.848 8.128 8.269 8.256 8.241 8.176 8.073 7.927 7.750 6 67 2-52 10.743 11.210 8-58 10.621 9-59 10-60 11-61 12-62 13-63 14-64 15-65 16-66 17-67 18-68 19-69 20-70 21-71 22-72 23-73 24-74 11.538 11.556 11.465 11.242 10.950 10.285 9.957 9.659 9.368 9.074 8.769 8.458 8.142 7.817 7.485 7.141 6.790 6.427 6.083 5.771 5.493 68 68 TABLES OF ANNUITIES. IX. Value of an Annuity of £1 on Two JOINT LiVES. Diference of Age NORTHAMPTON. 5_ 50 Years. ,I, CARLISLE. Ages. 4 u i 4.396 4.188 3.979 3.762 3.528 3.290 3.060 2.838 2.632 2.476 2.331 2.200 2.077 1.974 1.832 1.646 1.388 1.111 .790 .509 .232 4.589 4.365 4.140 3.908 3.659 3.406 3.164 2.929 2.713 2.549 2.398 2.260 2.130 2.022 1.872 1.679 1.413 1.128 .800 .515 .234 5 4.799 4.556 4.313 4.064 3.798 3.530 3.274 3.027 2.800 2.627 2.468 2.323 2.187 2.072 1.915 1.713 1.439 1.146 .811 .521 .236 25 &75 26-76 27--77 28-78 29-79 30-80 31-81 32-82 33-83 34-84 35-85 36-86 37-87 38-88 39-89 40-90 41-91 42-92 43-93 44-94 45-95 5.263 5.038 4.828 4.615 4.380 4.168 3.938 3.731 3.518 3.311 3.096 2.906 2.751 2.655 2.544 2.380 2.360 2.450 2.556 2.607 2.633 5.010 4.804 4.610 4.414 4.196 3.999 3.784 3.590 3.390 3.194 2.989 2.809 2.660 2.569 2.463 2.304 2.284 2.371 2.475 2.526 2.556 4.778 4.588 4.410 4.229 4.026 3.843 3.641 3.459 3.270 3.085 2.890 2.718 2.576 2.488 2.387 2.233 2.212 2.297 2.399 2.451 2.482 TABLES OF ANNUITIES. X. Value of an Annuity on THREE JOINT LIVES, Northampton, Interest 4 and 5 per cent. Differences of Age 5 and 10 Years. Ages. 4 Ages. 5 - 5,10,15 6,11,16 7,12,17 8,13,18 9,14,19 10,1520 11,16,21 12,17,22 13,18,23 14,19,24 15,20,25 16,21,26 17,22,27 18,23,28 19,24,29 20,25,30 21,26,31 22,27,32 23,28,33 24,29,34 25,30,35 26,31,36 27,32,37 28,33,38 29,34,39 30,35,40 31,36,41 11.518 10.381 11.573 10.440 11.555 10.435 11.492 10.389 11.378 10.297 11.226 10.171 11.062 10.003 9.897 10.900 9.763 10.742 10.587 9.633 10.435 9.504 10.287 9.379 10.146 9.260 10.010 9.146 9.880 9.037 8.931 9.754 9.635 8.831 9.520 8.735 9.403 8.637 9.283 8.536 9.161 8.433 9.036 8.328 8.908 8.220 8.778 8.109 8.644 7.995 8.507 7.877 8.369 7.758 4 5 Ages. 32,37,42 33,38,43 34,39,44 35,40,45 36,41,46 3'7,42,47 38,43,48 39,44,49 40,45,50 41,46,51 42,47,52 43,48,53 44,49,54 45,50,55 46,51,56 47,52,57 48,53,58 49,54,59 50,55,60 51,56,61 52,57,62 53,58,63 54,59,64 55,60,65 56,61,66 57,62,67 58,63,68 8.230 8.090 7.947 7.800 7.651 7.500 7.348 7.192 7.033 6.878 6.724 6.569 6.411 6.252 6.094 5.936 5.775 5.612 5.448 5.286 5.125 4.960 4.794 4.623 4.451 4.277 4.100 7.638 7.517 7.393 59,64,69 60,65,70 61,66,71 62,67,72 63,68,73 64,69,74 65,70,75 66,71,76 67,72,77 68,73,78 69,74,79 70,75,80 71,76,81 72,77,82 73,78,83 74,79,84 75,80,85 76,81,86 77,82,87 78,83,88 79,84,89 80,85,90 81,86,91 82,87,92 83,88,93 84,89,94 85,90,95 iI. 7.135 7.003 6.869 6.731 6.591 6.454 6.318 6.180 6.039 5.896 5.755 5.613 5.468 5.320 5.172 5.025 4.879 4.728 4.576 4.419 4.260 4.099 3.935 4 5i 3.921 3.739 3.556 3.373 3.191 3.011 2.834 2.668 2.503 2.336 2.161 1.987 1.825 1.667 1.516 1.388 1.267 1.160 1.061 0.981 0.902 0.812 0.694 0.569 0.421 0.287 0.138 3.769 3.599 3.428 3.257 3.085 2.915 2.748 2.590 2.433 2.273 2.106 1.940 1.784 1.631 1.484 1.360 1.242 1.139 1.042 0.964 0.888 0.684 0.561 0.416 0.284 0.137 Differences of Age 10 and 20 Years. 5,15,25 6,16,26 7,17,27 8,18,28 9,19,29 10,20,30 11,21,31 12,22,32 13,23,33 14,24,34 15,25,35 16,26,36 17,27,37 18,28,38 19;29,39 20,30,40 21,31,41 22,32,42 23,33,43 24,34,44 25,35,45 26,36,46 10.655 10.708 10.700 10.654 10.562 10.438 10.305 10.170 10.031 9.887 9.738 9.584 9.429 9.278 9.131 8.986 8.850 8.718 8.586 8.451 8.313 8.171 9.659 9.716 9.719 9.687 9.615 9.512 9.402 9.290 9.174 9.053 8.927 8.795 8.663 8.534 8.408 8.284 8.167 8.055 7.942 7.8267.707 7.585 27,37,47 28,38,48 29,39,49 30,40,50 31,41,51 32,42,52 33,43,53 34,44,54 35,45,55 36,46,56 37,47,57 38,48,58 39,49,59 40,50,60 41,51,61 42,52,62 43,53,63 44,54,64 45,55,65 46,56,66 47,57,67 48,58,68 8.027 7.878 7.725 7.571 7.420 7.272 7.123 6.971 6.816 6.658 6.497 6.332 6.164 5.994 5.827 5.662 5.494 5.322 5.145 4.965 4.782 4.597 4.408 4.219 4.221 4.046 56,66,76 3.128 57,67,77 2.959 31025 58,68,78 59,69,79 2:785 2.598 60,70,80 61,71,81 62,72,82 63,73,83 64,74,84 65,75,85 66,76,86 67,77,87 68,78,88 69,79,89 2.408 2.224 2.044 1.875 1.743 1.623 1.519 1.425 1.350 1.248 7.459 7.330 7.196 7.061 6.929 6.799 6.668 49,59,69 50,60,70 6.534 6.397 6.257 6.113 5.970 5.820 5.667 5.516 5.366 5.213 5.058 4.8971 4.734 4.566 4.395 51,61,71 4.032 3.872 52,62,72 3.847 3.699 53,63,73 3.660 3.525 54,64,74 3.477 3.353 55,65,75 '3.298 3.184 70,80,901 1.122 2.865 2.701 2.523 2.342 2.165 1.992 1.830 1.703 1.586 1.486 1.395 1.323 1.225 1.103 70 TABLES OF ANNUITIES. 70 XI. Logarithm of the present value of £1 due at the end of any number of years not exceeding fifty, interest 3, 32, 4, 42, and 5 per cent. Years. 3 _ 4 3 i 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 39 40 41 42 43 44 45 46 47 48 49 50 1.9871628 .9743256 .9614884 .948651.2 .9358139 .9229767 .9101395 .8973023 .8844650 .8716278 .8587906 .8459534 .8331161 .8202789 .8074417 .7946045 .7817672 .7689300 .7560928 .7432556 .7304183 .7175811 .7047439 .6919067 .6790694 .6662322 .6533950 .6405578 .6277205 .6148833 .6020461 .5892089 .5763716 .5635344 .5506972 .5378600 .5250227 .5121855 .4993483 .4865111 .4736738 .4608366 .4479994 .4351622 .4223249 .4094877 .3966505 .3838133 .3709760 .3581388 1.9850596 .9701193 .9551789 .9402386 .9252983 .9103579 .8954176 .8804772 .8655369 .8505965 .8356562 .8207158 .8057755 .7908351 .7758948 .7609544 .7460141 .7310737 .7161334 .7011930 .6862527 .6713123 .6563720 .6414316 .6264913.6115509 .5966106 .5816702 .5667299 .5517895 .5368492 .5219088 .5069685 .4920281 .4770878 .4621474 .4472071 .4322667 .4173264 .4023860 .3874457 .3725053 .3575650 .3426246 .3276843 .3127439 .2978036 .2828632 .2679229 .2529825 4 2 I 5 i 1.9829667 .9659333 .9489000 .9318666 .9148333 .8978000 .8807666 .8637333 .8467000 .8296667 .8126333 .7956000 .7785667 .7615333 .7445000 .7274667 .7104333 .6934000 .6763667 .6593333 .6422999 .6252666 .6082332 .5911999 .5741666 .5571333 .5401000 .5230667 .5060333 .4890000 .4719667 .4549333 .4379000 .4208667 .4038333 .3868000 .3697667 .3527333 .3357000 .3186667 .3016333 .2846000 .2675667 .2505333 .2335000 .2164667 .1994333 .1824000 .1653667 .1483333 1.9808837 .9617674 .9426511 .9235348 .9044185 .8853022 .8661859 .8470696 .8279533 .8088371 .7897208 .7706045 .7514882 .7323719 .7132556 .6941393 .6750230 .6559067 .6367904 .6176742 .5985579 .5794416 .5603253 .5412090 .5220927 .5029764 .4838601 .4647438 .4456275 .4265113 .4073950 .3882787 .3691624 .3500461 .3309298 .3118135 .2926972 .2735809 .2544646 .2353484 .2162321 .1971158 .1779995 .1588832 .1397669 .1206506 .1015343 .0824180 .0633017 .0441855 1.9788107 .9576214 .9364321 .9152428 .89-10535 .8728642 .8516749 .8304856 .8092963 .7881070 .7669177 .7457284 .7245391 .7033498 .68321605 .6609712 .6397819 .6185926 .5974033 .5762140 .5550247 .5338354 .5126461 .4914568 .4702675 .4490782 .4278889 .4066996 .3855103 .3643210 .3431317 .3219424 .3007531 .2795638 .2583745 .2371852 .2159959 .1948066 .1736173 .1524280 .1312387 .1100495 .0888602 .0676709 .0464816 .0252923 .0041030 2.9829137 .9617244 .9405352 7 TABLES OF ANNUITIES. 71 XII. The Logarithm, and its Arithmetical Complement, of the number who complete each year of Age, according to the Northampton Table of Mortality. Age. 0 1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 I Log. 4.0663259 3.9370161 .8623103 .8312937 .8092903 .7958105 .7828308 .7726883 .7645497 .7585334 .7539659 .7499681 .7460890 .7421750 .7382254 .7342396 .7302168 .7259116 .7211508 .7159198 .7102866 .7041505 .6976652 .6910815 .6843965 .6776070 .6707096 .6637009 .6565773 .6493349 .6419696 .6344773 .6268534 .6190933 .6111921 .6031444 .5949447 .5865873 .5780659 .5693739 .5605044 .5513280 .5418288 .5319896 .5219222 .5116160 .5010593 .4902395 L Comp. irij 5.9336741 .0629839 .1376897 .1687063 .1907097 .2041895 .2171692 .2273117 .2354503 .2414666 .2460341 .2500319 .2539110 .2578250 .2617746 .2657604 .2697832 .2740884 .2788492 .2840802 .2897134 .2958495 .3023348 .3089185 .3156035 .3223930 .3292904 .3362991 .3434227 .3506651 .3580304 .3655227 .3731466 .3809067 .3888079 .3968556 .4050553 .4134127 .4219341 .4306261 Age. Log. Comp. 48 49 50 51 52 53 54 55 3.4791432 .4677561 .4559102 .4434195 .4303976 .4169732 .4031205 .3888114 .3740147 .3586961 .3428173 4.5208568 .5322439 .5440898 .5565805 .5696024 .5830268 .5968795 .6111886 .6259853 .6413039 .6571827 .6736641 .6907958 .7086311 .7272304 .7464197 .7664962 .7872798 .8091083 .8320922 .8563608 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 .4394956 78 79 80 81 82 83 84 85 86 87 88 .3263359 .3092042 .2913689 .2727696 .2535803 .2335038 .2127202 .1908917 .1679078 .1436392 .1179338 .0906107 .0614525 .0301948 2.9965117 .9599948 .9201233 .8762178 .8293038 .7795965 .7275413 .6711728 .6085260 .5390761 .4608978 .3692159 .2695129 .1613680 .0453230 1.9190781 .8820662 .9093893 .9385475 .9698052 3.0034883 .0400052 .0798767 .1237822 .1706962 .2204035 .2724587 .3288272 .3914740 .4609239 .5391022 .6307841 .7304871 .8386320 .9546770 2.0809219 .4486720 .4581712. .4680104 .4780778 .4883840 .4989407 .5097605 89 90 91 92 93 94 95 .7923917 .6627578 .5314789 .3802112 .2041200 0.9542425 .6020600 .2076083 .3372422 .4685211 .6197888 .7958800 1.0457575 .3979400 77 TABLES OF ANNUITIES. 72 XIII. The Logarithm and its Arithmetical Complement of the Number who complete each Year of Age, according to the Carlisle Table of Mortality. Age. o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42, 43 44 45 46 47 48 49 50 51 I %LI Age. L fog.Comp. 4.0000000 3.9274217 .8909238 .8617733 .8449739 .8323173 .8245163 .8191489 .8153120 .8124454 .8102325 .8082785 .8061800 .8040030 .8017466 .7993405 .7966437 .7937206 .7907073 .7876730 .7846173 .7815400 .7785130 .7754648 .7723951 .7693035 .7661153 .7629035 .7595168 .7557224 .7514331 .7470232 .7425680 .7381461 .7337588 .7293268 .7248491 .7202420 .7155019 .7106250 .7054360 .6997510 .6937269 .6874398 .6810602 .6745856 .6681062 .6616234 .6552345 .6491401 .6431565 .6372895 I ~lnnlzzL~ 44.0000000 I .0725783 .1090762 .1382267 .1550261 .1676827 .1754837 .1808511 .1846880 .1875546 .1897675 .1917215 .1938200 .1959970 .1982534 .2006595 .2033563 .2062794 .2092927 .2123270 .2153827 .2184600 .2214870 .2245352 .2276049 .2306965 .2338847 .2370965 .2404832 .2442776 .2485669 .2529768 .2574320 .2618539 .2662412 .2706732 .2751509 .2797580 .2844981 .2893750 .2945640 .3002490 .3062731 .3125602 ".3189398 .3254144 .3318938 .3383766 .3447655 .3508599 .3568435 .3627105 Log. 52 53 54 55 56 57 3.6310377 .6243852 .6173149 .6909144 .6020600 .5937290 .5845574 .5739154 .5614592 .5466660 .5308398 .5142820 .4973444 .4797192 .4614985 .4426365 .4229180 .4022614 .3803922 .3573630 .3310222 .3003781 .2650538 .2240148 .1804126 .1332195 .0838608 .03,8258 2.9790929 .9227255 .8603380 .7944880 .7234557 .6483600 .5646661 .4712917 .3654880 .2576786 .1522883 .0211893 1.8750613 .7323938 .6020600 .4771213 .3617278 .2552725 .1461280 .0413927 0.9542425 .8450980 .6989700 .4771213 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 - Comp. 4.3689623 .3756148 .3826851 .3900856 .3979400 .4062710 .4154426 .4260846 .4385408 .4533340 .4691602 .4857180 .5026556 .5202808 .5385015 .5573635 .5770820 .5977386 .6196078 .6426370 .6689778 .6996219 .7349462 .7759852 .8195874 .8667805 .9161392 .9661743 3.0209071 .0772745 .1399620 .2055120 .2765443 "3516400 .4353339 .5287083 .6345120 .7423214 .8477117 .9788107 2.1249387 .2676062 .3979400 .5228787 .6382722 .7447275 .8538720 _.9586073 1.0457575 .1549020 .3010300 .5228787 7 TABLES OF ANNUITIES. 73 XIV. Preparatory Table for finding the Value of Annuities, Assurances, &c.--Nor'thampton 3 per cent. Age. D N 0 11650.000 142947.351 1 8398.058 134549.293 2 6864.926 127684.367 3 6205.576 121478.791 4 5727.188 115751.604 5 5390.442 110361.161 6 5079.342 105281.819 7 4817.567 100464.252 8 4590.415 95873.837 9 4395.400 91478.437 10 4222.733 87255.705 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 4062.175 3908.790 3760.894 3618.298 3480.817 3348.276 3218.688 3090.870 2964.917 2841.464 2719.999 2601.634 2487.856 2378.500 2273.402 2172.410 2075.372 1982.143 1892.585 1806.562 1723.945 1644.607 1568.429 1495.293 1425.087 1357.703 1293.034 1230.981 1171.446 1114.334 1059.258 1006.156 954.968 905.908 858.897 813.855 770.708 729.384 83193.530 79284.740 75523.846 71905.548 68424.731 65076.455 61857.767 58766.897 55801.980 52960.516 50240.516 47638.882 45151.026 42772.526 40499.124 38326.714 36251.343 34269.199 32376.615 30570.053 28846.108 27201.501 25633.072 24137.779 22712.691 21354.988 20061.954 18830.973 17659.528 16545.194 15485.936 14479.780 13524.811 12618.903 11760.007 10946.152 10175.444 9446.059 M 7147.166 4234.544 2946.015 2486.614 2188.971 2019.037 1864.940 1751.107 1664.272 1602.958 1558.313 15.0.747 1485.678 1451.630 1418.574 1386.481 1355.323 1323.257 1289.188 1253.260 1216.164 1177.460 1138.318 1100.317 1063.422 1027.601 992.8241 959.0599 926.2791 894.4531 863.5541 833.5551 804.4298 776.1528 748.6994 722.0456 696.1682 671.0445 646.6525 622.9710 599.9792 577.3595 555.1096 533.2273 511.9823 491.3561 471.3307 451.8885 433.0126 lAge. D 49 689.814 50 651.702 51 614.782 52 579.244 53 545.256 54 512.756 55 481.686 56 451.991 57 423.618 58 396.514 59 370.629 60 345.916 61 322.328 62 299.821 63 278.506 64 258.179 65 238.946 66 220.615 67 203149 68 186.512 69 170.673 70 155.598 71 141.257 72.127.619 731114.655 74 102.339 75 90.6425 76:79.5406 77 69.3167 78 '60.0196 79 51.6893 80 44.0751 81 37,0434 82 30.6495 83 24.8547 84 19.5384 85 15.0781 86 11.4121 87 8.4817 88 6.1574 89 4.4655 90 3.2166 91 2.3083 92 1.5819 93 1.0238 94 .5591 95 .2413 96 .0585 N M 8756.245 414.6865 8104.543,396.6660 7489.762 378.7275 6910.517 361.0965 6365.262 343.9790 5852.506 327.3600 5370.820 311.2251 4918.829 295.5601 4495.211 4098.697 3728.068 3382.152 3059.824 2760.004 2481.497 23.17 1984.371 1763.756 1560.608 1374.095 1047.824 906.5667 778.9479 280.3512 265.5855 251.2498 237.3317 223.8190 210.6998 198.1180 185.9027 174.1896 162.8177 151.7770 141.0579 130.6510 120.5472 110.7377 101.2139 664.2927 91.9675 561.9540 471.3115 391.7710 322.4543 262.4347 210.7454 166.6703 129.6269 98.9774 74.1227 54.5843 39.5062 28.0941 19.6124 13.4550 8.9895 5.7729 3.4846 1.8827 .8589 .2998 .0585 .0000 82.9904 74.2748 65.8130 57.9058 50.6277 44.0455 37.9370 32.1889 26.8740 21.9718 17.3795 13.4883 10.2614 7.66344 5.58622 4.07368 2.95484 2.14015 1.48101 .969059 .534150 .232548 .056858 1203.422 74 TABLES OF ANNUITIES. 74 XV. Preparatory Table for finding the Value of Annuities, &c.-Northcunpton 4 .per cent. Assurances, Age. D N M Age. M D - 131970.4425 0 11650.0000 120320.4425 6674.1061 49 429.6574 1 8317.3076 112003,1349 3789.6061 50 402.0159 2 6733.5429 105269.5920 2525.6779 51 375.5944 3 6028.2843 99241.3077 2079.4501 52 350.4804 4 5510.0677 93731.2400 1793.0928 53 326.7429 5 5136.2225 88595.0175 1631.1792 54 304.3128 83801.7599 1485.7640 55 283.1246 6 4793.2576 79299.2469 1379.3780 56 263.1162 7 4502.5130 8 4248.9636 75050.2833 1299.0010 57 244.2281 9 4029.3349 71020.9484 1142.7930 58 226.4038 67187.1217 1102.2510 59 209.5891 10 3833.8267 11 3652.5935 63534.5282 1068.4718 60 193.7331 12 3480.8794 60053.6488 1037.2418 61 178.7866 56736.6781 1007.2168 62 164.7033 13 3316.9707 53576.1570 978.3418 63 151.5234 14 3160.5211 950.5786 64 139.1137 50564.9576 15 3011.1994 923.8832 65 127.5126 16 2868.6886 47696.2690 896.6744 66 116.5980 17 2731.1458 44965.1232 106.3345 868.0440 18 2597.4711 42367.6521 96.6878 19 2467.6659 39899.9862 838.1415 68 87.6261 20 2342.1779 37557.8083. 807.5636 69 775.9676 70 79.1183 21 2220.4980 35337.3103 744.3209 71 71.1353 22 2103.4476 33233.8627 713.8914 72 63.6494 23 1992.1163 31241.7464 56.6341 24 1886.2372 29355.5092 684.6323 73 25 1785.5560 27569.9532 656.4985 74 50.0642 629.4468 75 43.9160 26 1689.8289 25880.1243 38.1667 603.4355 76 27 1598.8244 24281.2999 578.4247 77 32.9410 22768.9796 28 151220 554.3758 78 28.2485 29 1430.1053 21338.8743 30 1351.9773 19986.8970 531.2519 79 24.0939 509.0174 80 20.3472 31 1277.7437 18709.1533 16.9366 487.6380 81 32 1207.2204 17501.9329 467.0809 82 13.8785 33 1140.2317 16361.7012 11.1463 15285.0908 447.3145 83 34 1076.6104 14268.8947 428.3083 84 8.67791 35 1016.1961 410.0331 85 6.63253 36 958.8363 13310.0584 4.9 7166 392.4608 86 37 904.3858 12405.6726 87 3.65951 11552.9673 375.5644 2.63114 10749.3049 359.3179 88 343.6962 89 1.88984 9992.1743 40 757.1306 328.4751 90 1.34821 9279.3852 41 712.7891 .958175 8608.8394 313.6468 91 42 670.5458 .650345 7978.5269 299.2037 92 43 630.3125 285.3161 93 .416888 7386.3448 44 592.1821 271.9626 94 .225480 6830.2925 45 556.0523 259.1227 95 .096359 6308.4666 46 521.8259 .023163 5819.0569 246.7767 96 47 489.4097 234.9055 5360.3419 48 458.7150 IV~V.VY;L~ UVVV1 VYV -VVV B ~ ) I U~YVI 67 4930.6845 4528.6686 4153.0742 3802.5938 3475.8509 3171.5381 2888.4135 2625.2973 2381.0692 2154.6654 1945.0763 1751.3432 1572.5566 1407.8533 1256.3299 1117.2162 989.7036 873.1056 766.7711 670.0833 582.4572 503.3389 432.2036 368.5543 311.9202 261.8559 217.9399 179.7733 146.8323 118.5837 94.48981 74.14256 57.20599 43.32749 32.18120 23.50329 16.87076 11.89910 8.23960 5.60846 3.71862 2.37041 1.41223 .761890 .345003 .119522 .023163 .000000 223.4909 212.3746 201.4153 190.7474 180.4898 170.6267 161.1429 152.0239 143.2556 134.8246 126.7178 118.9228 111.4276 104.2207 97.3755 90.7936 84.5430 78.5328 72.7537 67.1969 61.8538 56.7162 51.7762 47.0262 42.4589 38.0673 33.8446 29.7843 26.0266 22.6011 19.5330 16.7130 14.0849 11.6782 9.4798 7.4401 5.7285 4.3227 3.20184 2.31423 1.67412 1.20518 .86700 .59602 .38758 .21221 .09176 .022272 75 TABLES OF ANNUITIES. XVI. Preparatory Table for Assurances, Age. D) 7 t 10000.000 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 8214.563 7332.454 6656.740 6217.632 5863.152 5591.045 5361.525 5159.579 4976.344 4806.847 4645.891 4488.831 4336.298 4188.181 4043.730 3901.648 3762.597 3627.749 3497.564 3371.885 3250.560 3133.964 3021.403 2912.740 2807.843 2706.122 2607.945 2512.317 2417.926 2324.429 37 38 39 40 41 42 43 44 45 2233.928 2146.727 2063.088 1982.865 1905.566 1831.087 1758.995 1689.225 1621.710 1555.776 1490.819 1427.459 1365.964 1306.840 1250.001 46 1195.622 47 48 49 50 51 52 1144.599 1093.077 1047.408 1002.987 36 960.7073 919.3947 N M 173198.234 4664.129 164983.671 3169.954 157651.218 2527.104 150994.477.2064.957 144776.845 1819.735 138913.693 1646.351 133322.648 1545.015 127961.123 1478.341 122801.544 1432.556 117825.200 1399.600 113018.353 1375.015 108372.462 103883.631 99547.333 95359.152 91315.421 87413.773 83651.176 80023.427 76525.862 73153.977 69903.417 66769.452 63748.049 60835.310 58027.467 55321.344 52713.399 50201.082 47783.156 45458.727 43224.799 41078.072 39014.984 37032.119 35126.553 33295.466 31536.470 29847246 28225.536 26669.760 25178.941 23751.482 22385.519 21078.679 19828.678 18633.056 17488.457 16395.380 15347.972 14344.985 13384.277 12464.883 finding the Values of Annuities, &c.-Carlisle3 per 1354.095 1332.352 1310.561 1288.744 1266.279 1241.976 1216.565 1191.307 1166.785 1142.977 1119.862 1097.943 1076.662 1056.000 1035.741 1016.002 996.6439 976.9755 955.7581 932.6869 909.8876 887.7524 866.6389 846.5065 826.9604 807.9836 789.2245 770.6867 752.3729. 733.6730 714.0295 694.0913 674.1728 654.8344 636.0593 Age. ; 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 618.0877 600.8888 100 584.6749 101 569.8371 102 555.9585 103 542.8922 104 529.5614 a I cent. jD 879.0475 839.6626 801.4327 764.1444 727.7919 691.8283 655.4193 618.3376 580.2235 543.1651 507.6178 473.9822 441.8752 411.3786 382.4216 354.8025 328.4679 303.2400 279.2030 255.1185 230.8132 M 11585.8,135 10746.1' .73 9944.7-'400 9180.5;;956 >038 8452.81 7760.9'755 7105.5 562 6487.2 186 5906.9 951 5363.8 300 4856.2 121 4382.2 300 3940.3 548 3528.9 762 3146.5 5546 2791.7 521 2463.2 2160.0)442 412 1880.1. 7227 1394.0)095 1188.E3243 206.5852 5411 182.4832 845.' 5965 160.2447 139.5575 706.( )390 120.9365 585.1[025 480. 1656 104.6369 3. )054 89.56018 314. 5376 76.36780 250.' 3153 64.22226 196.17359 53.57947 152. 5657 44.17014 116. 4916 36.07413 87.460711 28.88449 98917 22.61795 47."77792 17.21124 34. 74128 13.03664 81154 24.E 9.92746 17. 68298 7.128560 73946 4.943523 9.'28379 3.455667 6.' .79859 2.485197 4. .98898 1.809610 64202 3.1 1.346959 2.'.61858 1.023438 1.84576 .772823 1..25623 .589532 787934 .468296 434312 .353621 189083 .245230 046231 .142852 1005. 515.9926 502.2111 488.4374 474.4917 460.3959 455.6301 429.3714 411.3797 391.2754 371.1167 351.3898 332.5391 314.2374 296.6110 279.6359 263.1553 247.1547 2842 231.4938 216.2891 200.3367 183.4621 165.9567 147.8718 130.9483 114.9285 100.3722 87.5951 75.5660 64.9822 55.0610 46.2887 38.4400 31.6305 25.4915 20.0663 15.3184 11.6450 8.91786 6.40589 4.42849 3.08461 2.21480 1.61159 1.20165 .9173~60 .696554 .535772 .431706 .330672 .232580 .137345 .044884 76 TABLES OF ANNUITIES. 76 XVII. Preparatory Table for finding the value of Annuities, Assurances, Carlisle, 4 per cent. Ft77e Lh78TT i ca v" - &c.-. innaao Age. 0 10000.0000 142816,43354122.4446 1 8135.5769 134680.85662642.6369 2 7192.1228 127488.7339 2012.0895 3 6466.5595 121022.1744 1563.1464 4 5981.9197 115040.2547 1327.2204 5 5586.6386 109453.6161 1162.0131 6 5276.1398 104177.4763 1066.3850 7 5010.8980 99166.5782 1004.0718 8 4775.7912 94390.7871 961.6917 9 4561.8957 89828.8914 931.4805 10 4364.1445 85464.7469 909.1869 11 4177.4550 81287.2919 890.3490 12 3997.4211 77289.8708 870.9865 13 3824.4558 73465.4150 851.7682 14 3658.3046 69807.1103 832.7115 15 3498.1664 66308.9440 813.2772 16 3342.7991 62966.1449 792.4548 17 3192.6682 59773.4766 770.8931 18 3048.6473 56724.8294 749.6671 19 2910.9820 53813.8474 7292575 20 2779.3965 51034.4509 709.6329 21 2653.6268 48380.8241 690.7630 22 25338421 45846.9820 673.0409 23 2419.3461 43427.6359 656.0004 24 2309.9092 41117.7267 639.6153 25 22053117 38912.4150 623.8604 26 2104.9823: 36807.4327 608.3507 27 2009.1084 34798.3243 593.4376 28 1916.8285 32881.4958 578.4311 29 1827.0717 31054.4240 562.3986 30 1739.5339: 29314.8901 545.1327 31 1655.7306 27659.1596, 528.2345 32 1575.80031 26083.3593 511.9862 33 1499.84331 24583.5160 496.6369 34 1427.6617 23155.8543 482.1415 35 1358.8137 21797.0406, 468.2037 36 1293.1499 20503.89071 454.8019 ( 37 1230.2928 19273.5979 441.6813 38 1170.1325 18103.4654' 428.8400 39 1112.5635 16990.9019 416.2760 40 1057.0669 15933.8350 403.5704 41 1003.1921 14930.6430 390.3520 42 951.3202 13979.3228 377.0644 43 901.5840 13077.7388 363.9174 44 854.2664 12223.4724 351.2761 45 809.2549 11414.2176 339.1211 46 766.6067 10647.6108 327.5981 47 726.2004 9921.4104 316.6766 48 9233.3379 306.4795 688.0725 652.3887 8580.9492 297.2600 49 50 51 D. i 618.7134 686.9340 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 82 83 84 85 86 87 88 89 90 91 {_ N. 556.2936 16 819.0083 526.7666 62292.2417 498.3272 57 793.9145 471.0649 53322.8496 444.8289 48 878.0207 44 458.4273 419.5934 395.0242 40063.4031 370.6367 36 92.7664 346.3050 33346.4614 321.8343 30024.6271 298.3821 27 726.2451 24 450.0718 276.1733 255.3940 2] 194.6778 1°958.8732 235.8046 17 217.4193 741.4540 1 541.2822 200.1717 183.9293 1f357.3530 168.6402 11 188.7128 154.1908 1(034.5220 893.9186 E 140.6034 127.2395 766.6792 652.6688 1140103 101.0617 551.6071 463.1945 88.4126 386.3028 76.8916 319.9817 66.3212 56.9194 z 263.0623 214.2878 48.7744 41.34527 172.9426 138.02654 108.94588 29.08066 84.91770 24.02818 65.29968 19.61802 49.43154 15.86814 36.84812 12.58342 27.08943 9.75868 19.73492 7.35452 14.21781 5.51711 10.05595 4.16186 7.09688 2.95907 92 93 94 95 96 97 98 99 100 101 7962.2358 288.6766 102 7375.3019: 280.6938 I '103 I I 2.0323291 1.406997~ 1.002135: .722693, .532755 .400902 .299820 .226512 .178200 .133270 .091531 .052806 M~. 272.6278 264.4968 256.3176 248.2218 240.1036 231.9770 223.5459 214.3517 204.2753 193.1240 182.0500 171.3174 161.1602 151.3936 142.0778 133.1925 124.6489 116.4340 108.4708 100.8139 92.8577 84.5224 75.9588 67.1967 59.0762 51.4631 44.6121 38.6563 33.1031 28.26413 23.77167 19.83768 16.35168 13.35635 10.68194 8.34118 6.31235 4.75780 3.61475 2.57203 5.06454'7 1.75910 3.65755 0 1.21194 2.655411 .861190 6 .6202921 1.93272'2 1.39996'7 .458149 .346787 .99906,5 .261124 .6992415 .4727333 .199618, .29453' 1600181 .121941 33 .16126, .0853291 .0697331 .0501241 .01692Z5 32 77 CONSTRUCTION OF TABLES XIV., &c. THE number in column D opposite any age, is the product obtained by multiplying the number living opposite to that age in Table VI., by the present value of £1, due as many years hence as are equal to that age. Thus, at the age of 30, the number living, Table VI., Carlisle, is 5642, and the present value of £1 due 30 years hence, interest 4 per cent, Table IL, is .308319; the product of these two numbers is equal to 1739.5339, which is the number in Table XVII. opposite to the age 30. The numbers in column D being thus found for all ages from birth to the extremity of life, those in column N are found by beginning at the oldest age, and taking the successive sums of the numbers in column D, the number in column N at any age being the sum of the numbers in column D at all the ages above the given one. Column M is formed by multiplying the decrements at each age, in Table Vt., by the present value of £1 due as many years hence as are equal to that age, increased by unity, and taking the successive sums from the extremity of life, as in the formation of N from the numbers in D. The following formula is a modification of that of Mr George Barrett, Sussex, who first pointed out the principle of making these and other tables, which greatly abridge the labour of calculating laborious questions in life contingencies. FORMULA, &c., according to BARRETT's Notation improved. Din, Nm, Mm, denote the numbers opposite to any age m in the respective columns of these names. Dmi_, N,1, Mm-1, represent the numbers opposite to an age one year younger than m. Dm+t, Nm+t, Mm+t, ditto t years older than m. D(m-1)+t, N(m-l)+t, M(m-1)+t, ditto t years older than a life one year younger than m. 1. VALUE of an ANNUITY on a single life. Nm Dm Required the present value of an annuity of £1, payable at the end of each year from the time of purchase, during the life of a person aged 45, Carlisle 3 per cent. Nm = N4~ = 19828.68 = log. 4.29732 3.09691 Dm = D45 = 1250.00 = £15.864 = 1.20041 2. A TEMPORARY ANNUITY for n years payable at the end of each year on a life aged m. Dm 78 DEFERRED 78 ANNUITIES. 3. A TEMPORARY ANNUITY for n years, payable at the beginning of each year. N i Nm~n-1 Dm Required the present value of an annuity of £1 to continue 15 years, payable at the end of each year to a person aged 30, the annuity to drop should the life fail during that term-Carlisle 3 per cent. Nm = N30 = 45458.73 Nm+n = N4 = 19828.68 5 2324.43 = log. 4.40875 3.36631 £11.025 = 1.04244 25630.05 Dm 4. A = D30 = DEFERRED ANNUITY. Nm+n Dm Required the value of an annuity of £1, to be entered on at tbe expiration of 25 years, and thereafter to continue during the life of a person now aged 30-Carlisle 3 per cent. N? _Hj, = N30 25 = 9944.74 = log. 3.99760 + = 2324.43-= 3.36631 £4.279= = D30 Dm 0.63129 3. The annualpremium payable for ditto in advance. Nm+ni Nm-1- Nm~nThe numerator as above log. 3.99760 Nm i = N29 = 47783.16 = -Nm+n- 1 = N5 4 =10746.17 37036.99 = £0.2685 6. A 4.36864 1.42896 DEFERRED TEMPORARY ANNUITY. Nm+d -Nm+d~n Dm Required the present value in a single payment of a temporary deferred annuity of £1, to commence at the end of 10 years from the time of purchase, and thereafter to continue 15 years on a life now aged 25 interest 3 per cent Carlisle. 35126.33 Nnmt{d = N 25 +10 -Nm-{+n = N 2 5+10+15 = 14344.99 =D2 = 20781.36 = log. 4.31769 Dm 2807.84 = 3.44837 £7.402 = 0.86932 7 E~NDOWMENT S. 79 7. The annual premium for ditto, payable at the beginning of each year during the period deferred:Nm+dNm+d+n Nm-1 -N m+d-1 Numerator as above = log. 4.31769 = N24 = 60835.31 Nm+d-1= N3 4 = 37032.12 Nmi1 -- 23803.19 4.17663 1.14106 £.1383 = 8. ENDOWMENTS. Dm+n Dm Required the present value of £100, in a single payment, to be paid to a child now aged 10, provided he attain the age of 21-Carlisle 3 per cent. log. 3.51196 Dmn = D1o+11= 3250.56 Dm = D 10 = 4806.85 = 3.68187 1.83009 = .67623 x 100 = 67.623 = £67, 12s. 5d. 9. The annual premiumc for ditto:-- Dm+lz Nm-1'-Nm~n-1 Numerator as above Nmi1= Ns = 117825.20 -Nm+,n_= N 20 = 73153.98 44671.22= .07277 X log. 3.51196 4.65003 2.86193= 100 = 7.277 = £7, 5s. 6d. 10. ENDOWMENT ASSURANCE.' The value of £1, to be received at the end of the year in which a life aged m shall die, provided that event shall happen within n years, or to be received at the end of n years, if the life survive that time. This consists of two cases 1st. An endowment payable on the life surviving n years; Dm+n Dm 2d. A temporary assurance on the given life for n years ; Mm-Mm+n The sum of these gives the value in a single payment. Dmrnn + MmnM~n~n 80 ASSURANCES. 80 Required the value of an assurance-of £100 to be paid to a person aged 30, on his attaining the age of 65, or to his heirs, &c., should lie die within that time--Northampton 3 per cent. +35= 238.95 D30 Dm+n + Mm = M 30 = 863.55 --- 1V 2n = 1 6 5 D~2 = D30 1102.50 = 174.19 928.31= log. 2.96769 = 1806.6 = 3.25686 .51385 X 100 = 51.385 1.71083 = £51, 7s. 8d. 11. And the annualpremiums payable in advance. Dm n+ Mm nMm+n Nm v"1'Nm+n-1 Numerator as above = log. 2.96769 Nm_1 = N 29 = 32376.62 N64 = 2223.32 .Nm+n1= 30153.30= 4.47934 2.48835= .03078 x 100 = 3.078 = £3, 12. is. 7d. ASSURANCE of £1 on a life m. Mm Dm Required the present value in a single payment, of £100 payable one year after the death of a person now aged 40-Northampton 3 per cent. Mm= M40 = 599.98 = log. 2.77808 Dm= D 40 = 1114.3 3.04689 = 1.73119= .53842 X 100 = 53.842= £53, 16s. l0d. 13. And the annualpremium for same, payable in advance. Mm Nmi1 Numerator as above= log. 2.77808 Nm--i = N 39 = 17659 = 4.24697 2.53111 = .03397 X 100 = 3.397 = £3, 7s. lid. i4.AssURANCE of Li on a life m, the annualpremium to drop after t payments. Mm 8 ASSURANCES. 81 Required the value of the above assurance in seven premiums. Numerator as above = log. 2.77808 = N 39 = 17659 Nm+ 1z 1= N46 = 10946 6713 = .08937 definite annual 3.82692 2.95116 = x 100=8.937=f8, 18s. 9d. 15. TEMPORARY AsSURANCE of 1 should the life fail within t years. Mm..Mm+2z Dm What is the value, in a single payment, of a temporary assurance of £100 on a life aged 35, for 10 years--Northampton, 3 per cent. Mm = M35 = 722.05 Mm+n = M45 = 491.36 23.69=log. 2.36305 Dm =D 35 =1425.08= 3.15381 1.20924-= .16190 100 = 16.190 = 16, 3s. 9d. x 16. And the annual premium for same, payable in advance. Mm -- Mm+n Nm-1- Nm+n-I Numerator as above log. 2.36305 Nmi -- N = =N 34 =24137 ,hn N44=12618 11519 = 4.06145 2.30160 = .02004 17. DEFERRED X 100-= 2.004= £2, Os. id. ASSURANCE of £1 to be entered on at the expiration of n years. Dm Required present value, in a ceived after the years-Northampton single payment, of £100 to be re3 per cent. 10 happen on the death of a person now aged 20, provided that event Mm~n=M 3 0 Dm = D 20 = 863.55=log. 2.93631 =2841-46= 3.45347 1.48284 = .30398 x 100 = 30.398 = £30, 7s. lid. 82 VALUE OF POLICIES. 82r 18. And the Annual Premium is, 1st. If assurance is deferred. paid during the term the Mm+n Nm-1-Nm+n. 2d, If paid during the whole term of life. Mm+n Nmi1 Required the annual premium payable in advance during the period deferred. Numerator as above = log. 2.93631 Nrni = N 19 = 55801 -- Nm+n-1= N 29 = 32376 23425 = 4.36968 2.56663= .03687 X 100 = 3.687 = £3, 13s. 9d. Required the annual premium payable in advance during the continuance of the life. N Numerator as above = log. 2.93631 = N 19 55801 = 4.74664 = r-1 2.18967 = .01548 x 100 = 1.548 = £1, l0s. lid. of 19. VALUE OF A POLICY of assurance £1 on any life at the end of t years, from the time it was effected, the annual premium being just due, but not paid. - Drn'Nrn+n-1 Dm~n' m1 Required the value of a policy opened 10 years ago for £100 on a life then aged 35, and the value to be computed at the same rate of interest and mortality used by the office, that is, Dm =D3 Nm+n- 1 = N4 4 = 1425.08 = 12618.9..= Northampton ,3 per cent. log. 3.15381 4.10106 7.25487 Dm+n = D 45 NmiN 34 = = 858.8 = log. 2.93389 24137.8 = 4.38274 - 7.31663 .86745 -1.93824 1-.86745 = And the difference between .86745 and unity is X 100 =' 13.255, or £13, 5s. I d. is the value of the policy. .13255 INCREASING AND DECREASING PREMIUMS. 83 20. And the value of the same policy when the annual premium has been just paid. Dm " Nm+n. v- Nm-1 Dm+n v being equal to the present value of £1 for one year, Required the value of the above policy, the renewal premium for the next year having been just paid. Dm - D35 = 1425.08 = log. 3.15381 4.07041 Nm+ = N 45 = 11760.01 = 7.22422 7.31663 Denominator as above = .80824 = 1.90759 And the difference between .97087, the present value of £1 discounted for one year, and .80824 is .16263 X 100 = 16.263, or £16, 5s. 3d. is the value of the policy in this case. INCREASING AND DECREASING PREMIUMS. Let x be the age of the party; and n denote the number of years which elapse between the increase or decrease of the premiums. To find the value of the first premium on the supposition that the increase or decrease is to be a given fraction k of the first premium:1. When the premium increases, this first premium is, the assurance being LA. AM, N-s+I k ((Nx+n- 1 + Nxs-2n-1 ... There being as many terms within the double brackets as there are epochs at which the premium is to increase. 2 When the premium decreases, the first premium is AMx Ne_k (Nx+ -- 1 + Nx+ 2 n--1 +" ') 3. If the increase or decrease of the premium is to be a given sum g, and A the sum assured, the first premium should be, ) Premiums 1_AMx -g (Nx+,,_i + Nx+2n-1 + increasing,J N_ Premiums ) AM, +g (Nx+n-1 + Nx+2n- 1 + decreasing, f Nx-1 Lastly, suppose the first premium, P, to be given, and the sum to be required by which the premium ought to increase or decrease; If AMx be greater than PNx_ 1 it ought to increase by AMx-PNXi Nx+n _ + N+2n-1 + 84 INCREASING AND DECREASING PREMIUMS. If AM, be less than PN,_1 + it ought to diminish by PN, i--AM, A, N 1 Nx+ + Nx+27-1 + * I. To find the premium for an assurance of £100 upon a life aged 30, on an ascending scale, during two successive periods of 7 years, and afterwards for the remainder of life; In this case seven premiums are the same; the next seven premiums are each greater than the first seven, but equal to one another; and all that come after are again greater than the preceding, and also equal to one another. Here = 30; n = 7; number of changes 2. 1st. Let the increase be the fraction k of the first premium. v That first premium is N129 100 Mao k (N N43) 2d, Let the increase be given = g"; S100 Mao-g (Na6 + N 43) N 29 The first premium is 3d. Let the first premium be P; 100 Ma0-PN The increase is N3 3-N 43 29 f 100 M30 N PN 29 II. To find the value of the policy after nine years' endurance, there will then be, if the premium be just due, (being the tenth,) five premiums as first increased, with all after the second increase, as possible payments. Let P be the premium of the first seven years, P-+g of the next seven, and P + 2 g" for the remainder of life; The present value of all the premiums will then be (P g)N th 38 + 3 party's age being 39. The present value of the assurance will be 100 M39 Da39 The value of the policy will be 100 M 9-{ 3 P-g N38s+g N 43 Da 39 To find the value after the premium is paid, add P +g to the preceding. III. To find the premium for an assurance of £100 on a life 35 on the descending scale, for three periods of five years, and afterwards for the remainder of life. ASCENDING 8 PREMIUMS. 85 = Here x 35; n = 5; number of changes 3; 1st. Let the decrease be the fraction Ikof the first premium. That first premium is 100 M35 N 34 -- /£ (N39 + N44 + 2d. Let the decrease be given =g; The first premium is 100 Mss g N49) N34 3d. Let the first premium be P; PN 34 -100 M3 if PN 34 i 100 M35 N 39 + N44 + N49 IV. To find the value of the policy when 12 years have elapsed, and a premium, the thirteenth, is just due, there will be (if P be the premium of the first five years, P -g, of the next, and P-2g of the next) three premiums P--=2g, together with premiums for the remainder of life, as possible payments; the age of the party being 47, the present value of all the premiums will be, The decrease is P-3g (P-2 g) N4 6 g N4 9 D47 D47 The present value of the assurance will be, 100 M4 7 D47 Hence the present value of the policy will be, 100 M 47 P-2 g N4 6 --g N49 1 D 47 And the addition of P - 2 will give the value of the policy immediately after the payment just due has been made. Numerical example of each separate process, on the supposition that the diminution or increase is 10 per cent of the. first premium. g Ic 1. = ASCENDING SCALE, Carlisle 3 per cent. 10 the rest as in the preceding formula :- Mao = 932.6869 100 M30 = 93268.69 100 M30 = 93269= log. 4.96974 4.72714 53551 = 0.24260 = N 36 = 33295.466 N43 22385.519 10) 55680.985 5568.099 N 29 = 47783.156 53351.255 1.7482 .1748 1.9230 .1748 2.0978 86 DESCENDING 86 PREMIUMS, The 1st seven years' annual premium, 2d seven years' ditto, And for remainder of life, - - - - &c. = £11 14 1.14 18 64 1.748 = = 1.923 2.098 2 1 111 2. For the value of the policy at the end of nine years, supr 'g the preceding premium to be charged P=1.7482 ; g .1748 ; P + g 1.9230. 1.9230 = log. 0.28398 P + g M39 = 752.3729 100 M39 = 75237.29 N3 29847 4.47490 g = .1748 = 1.24254 57396= 4.75888 N43 = 22386 = 4.34997 3913 l ... 3.59257 = 61309 M39 75237 13928 log. 4.14389 13928 = 100 M 39 D39 = 1621.73.20997P{ gN g Val. of Policy £8.580 = 0.93392P = = = = - DESCENDING SCALE. 3. Suppose the diminution of the Premium to be £1 at the end of each period of five years, we have then g = 1, and the calculation is as follows 100 M35 = 82696.04 N39 = 28225.54 N 44 = 21078.68 N 49 15347.97 147348.23 log. 5.16835 4.56857 N34 = 37032.12= 3.9791 = 0.59978 = For 1st five years' annual premium,-- For the next five years,-------= And for remainder of life, - - 4. The value of the policy after due. - 2 N46 1.9791 = 18633 = = 36877 = 3.979 2.979 1.979 = = 38560 7 2 19 1 19 7 7 P--2g=19791. log. 0.29647 4.27028 N 49 = 15347 g = 1 4.56675 15348 = 15348 100 M47 = 60089 £3 19 12 years, the 13th premium being just P 3.9791;g= 1; P -- = = D7= 71144.6 = log. 4.58614 3.05866 1.52748. 33.698= £33, 13s. lid., value of the policy. LIFE ASSURANCE OFFICES. 87 A DIGEST Of the DISTINCTIVE FEATURE S &c. of all the LIFE ASSURANCE Offices in Great Britain. ABERDEEN-Established 1825-Capital £1,000,000.-The whole profits resulting from the participation scale of premiums, will be divided among the policy-holders of this class, except a small proportion which the directors will apply for the expense of management. It will be optional for the assured to have the bonus added to their policies, or an equivalent reduction in their annual premium. The premiums may be paid yearly, half-yearly, or quarterly. The first period for division is not stated in the prospectus; and as the company adopted the participation plan only in 1840, it may, therefore, be at least seven years before any division of profits is declared. ACTIVE-London, 1839-£500,000.-A sum equal to three-fourths of the ascertained profits as declared by the directors, and sanctioned by the auditors, will be divided amongst the assured for the The first division whole term of life in the sum of £100 and upwards. will be made at the expiration of five years, (after 1839,) and subsequently at the end of every three years, to all such as shall have paid three whole years' premiums. The assured to have the option of, 1st, taking the sum awarded to him in a present money payment; or, 2d, of having its equivalent value added to the amount of his policy; or, 3d, to allow it to go in reduction of annual premium; or, 4th, to its total extinction at a future time. Endowments secured to children upon a most advantageous principle, whereby the whole premiums paid are returnable by the company in the event of the death of the child occurring before the given time; or such return will be made, and the agreement cancelled, at any time that may be desired by the partymaking the payments. ALLIANCE-London, 1824-£5,000,000.-The profits appropriated to the assured will be applied either to the reduction of the rate of the future premium to be paid on the policy, or to the sum assured on the life, as shall be most agreeable to the assured: the party to make his choice at the time the proposition for assurance is made. ALBION--London, 1805-£1,000,000.-A fine will be chargeable in cases wherein the persons insured do not appear; but it is undertaken that such fine shall be returned, provided the party or parties insured shall appear before the second payment shall become due on such insurances, and it shall be found that the state of health of such parties be unobjectionable. It often happens that persons who have made insurance on lives have occasion to transfer their policies, as collateral securities for the advance of money, or for other purposes. In such cases, the disclosure of the transfer, by an entry into the officebooks, as heretofore required, may be injurious to the credit of the party transferring; or may, in other respects, be inconvenient. It will be early enough to state a change of interest when a loss shall have taken 88 LIFE ASSURANCE OFFICES. place. The company will not require the registering of any such transfer; nor will it desire any communication on the subject until a claim be made. All losses are paid in thirty days after sufficient proof of death. ALFRED-London, 1838.-To those who may proceed to distant countries, the directors are prepared to make a very considerable abatement in the rates usually required for such risks, in some amounting to exemption from all extra premium whatever-for example, all Europe, the present British possessions in Australia, at the Cape of Good Hope, in North America, and the Republic of La Plata and Chili in South America; but in others, where they would not be justified in making such material reductions, they are empowered to offer to the party proposing to assure, the option of an arrangement whereby his policy may continue in full force, without payment of any additional premium, upon an understanding that in the event of his death in certain countries, or in his voyage to, or from them, a deduction commensurate with the risk will be made from the sum, which under ordinary circumstances, would become payable upon his policy. To such persons as may not find it convenient to pay a large increased premium during their absence abroad, this alternative must be peculiarly acceptable. Four-fifths of the profits will be divided amongst the assured for the whole term of life everyfjve years. The directors have determined to offer to annuitants a periodical participation in the profits. In order to do this, they propose to make the granting of annuities an entirely separate branch of their business. By keeping the funds of the two establishments quite distinct, those of the annuitants will be available for investment in such purchases and securities as are peculiarly suited to their objects. On the 31st December, 1842, and afterwards every three years, four-fifths of the profits of such investments will be returned to the annuitants in the form of a bonus. AMICABLE-London, 1706-Mutual Assurance.-The general outline of the plan of distribution finally adopted by this society, may be described as follows:-1. The respective interests of the members and contributors are represented by shares in the joint stock of the corporation, each share being guaranteed to produce £200 at the least on the death of the assured.-2. A valuation is made at the end of every year of all the premiums payable, and of all the sums assured; and an exact account taken of all the assets and liabilities of the society, for the purpose of ascertaining the profit or loss of the year.-3. The amount of the bonus, or addition to the guarantee, which is paid on every share becoming a claim in any year, is determined partly by the amount of the reserved capital of the society in reference to its liabilities, and partly by the amount of the average profits of the seven preceding years, according to a plan definitely laid down in the last Charter. The plan adopted by this corporation is the equal distribution ofprojqits, share for share, among the representatives or nominees of the deceased members, without reference to the length of time during which the assurance may have continued. By the last charter, a bonus of £50 per share, or 25 per cent. on the sum assured, was guaranteed to every claim arising by the death of a member during the five years commencing with the 5th LIFE ASSURANCE OFFICES. 89 day of April 1836. The minimum dividend during those five years is therefore £250 per share. Assurances on single lives for the whole of life are only effected for shares, with participation in the profits. Assurances for limited periods of time, or on joint lives and survivorships, are effected either for specified sums, without participation in the profits, or for shares with participation, at the option of the parties. AnGus-London, 1834-£C300,000-The age may in every case be admitted in the policy, and all difficulty or dispute after death will be thus avoided; and in case of unintentional misstatements as to age, the policy will not become forfeited, but an equitable proportion will be deducted from the sum assured. AsYLM--London, 1824-£240,000.-Parties having a fixed or variable interest in the lives of others, may have a general admission of interest on the policy. Persons of advanced age, infirm health, peculiar form, or suffering from chronic disease, are insurable with this company. Many, when they effect insurances on their lives, do not contemplate the possibility of being obliged to go beyond the limits of Europe; yet business or delicate health may render such a voyage absolutely necessary. On any such occasion the assured is obliged to ash leave to depart of the office in which he has opened his policy, and is altogether in the power of the director as to the rate of premium to be demanded as the price of permission. A consideration of still greater importance has hitherto escaped observation. Men who advance money on policies on the lives of others have no control over them after the transaction has been completed; and if the limits of the policy be exceeded, the assured cannot redeem himself by claiming, as a right, the continuance of the insurance on payment of an extra premium. In the ASYLUM, the terms may be agreed on at the commencement, and the party have a positive right to go beyond the limits of Europe, whenever he shall think fit to do so, without further trouble or delay. ATLAs-London, 1808- £1,200,000-Persons assuring for the whole term of life for £100 and upwards, will be entitled at the end of every seventh year to participate in the surplus premiums to be then ascertained by actual valuation, after deduction of a moderate sum for the expense of management and compensation for the guarantee capital. The amount of such surplus premiums, when so ascertained, may be applied at the option of the persons assured, 1st, In adding to the sum assured by the policy; 2d, In reducing the future annual premiums; 3d, In rendering the parties assured free from all payment of premiums after a fixed number of years. The total additions made to policies for £1000, which had been in force for nearly one year ending Christmas 1837 were, according to the age of the party, from £338 to £789. The next valuation will be at Christmas 1844. The Company holds itself liable for Policies of five years' standing, though assured on his own life by a person afterwards committing suicide. AUSTRALASIAN-London, 1839-£200,000-One-half of the pro- fits will be divided among the assured and annuitants; but in the first instance one-fifth of the whole will be retained to form an extra pre- 90 LIFE ASSURANCE OFFICES. cautionary fund. Two directors and one auditor may be chosen from the assured. For the profits to which the assured may become entitled at each quinquennial rest and division, a separate policy will be issued, which, being unencumbered by the payment of premium, will be an absolute reversion, payable at the death of the assured, and increasing, without cost, in value every year, and therefore readily available for private sale or deposit; and which the society will always purchase on equitable terms, or receive in commutation of future premiums on the original policy. Two directors and one auditor may be chosen from the annuitants, thereby giving them cognizance of, and control over the disposal of the funds. The benefited members of the company will consist of the first 1000 policy-holders for the time being, for the whole of life for £500 or upwards, in one or more policies, and of the first 1000 annuitants for the time being, who have paid £500 or upwards for their annuities; every vacancy in the 1000 benefited policy-holders to be filled up by the next oldest policy of assurance, on the plan of the Equitable Society of London; and, in like manner, every vacancy in the 1000 benefited annuitants, by the next oldest deed of annuity. The assured and annuitants, however, will only succeed to the vacancies in their respective class. BRITISH COMMERCIAL-London, 1820-£1,000,000.-When proof of age is given at the time the insurance is effected, the age will be admitted on the policy. For the convenience of insurers for the whole period of life, who may wish to pay a smaller premium in the first instance, this company offers the advantage of allowing one-third of the annual premiums to remain unpaid for seven years at interest, the loan to be paid off at any time that may suit the wishes of the insurers or to be deducted from the amount insured when the loan is paid, and the interest on the loan to be paid with the premium at the beginning of every year. At the first septennial division of the profits in December 1835, a bonus was declared, amounting to £26, 7s. 10d. per cent on the premiums paid. The future division of profits will be made at the end of every succeeding seven years. BRITANNIA-London, 1837-£1,000,000.-No proof of birth is required at the time the claim is made: the age of the assured being in every case admitted in the policy, cannot, under any circumstances, be afterwards called in question. Policies having become forfeited in consequence of the non-payment of the renewal premiums, may be revived without the exaction of a fine at any time within twelve calendar months, on the production of satisfactory evidence relative to the state of the health of the assured, and the payment of interest on the premiums due. All claims payable within one month after proof of death. BRITISH AUSTRALIAN-London, 1839-9£1,000,000.-This company engage to re-purchase policies effected for the whole duration of life after three years' premiums have been paid, at ONE-HALF the amount of the premiums so paid. Policies will be granted as low as £20, thereby affording the humbler classes an opportunity of participating in the benefit of life assurance. The society will also grant small loans, especially to parties emigrating to Australia, on giving satisfactory LIFE ASSURANCE OFFICES. 91 guarantees for the repayment, and assuring their lives with the company. No division of profits will be made until 10th March 1843, being three years after the commencement of business. CALEDONIAN-Edinburgh, 1833--£150,000.-A tthe expiry of the first ten years, from 21st March 1833, and afterwards of every seventh year, the profits shall be ascertained by a careful investigation, and that four-sixths thereof shall be apportioned to each policy of five years' standing and upwards, entitled to participate; and that according to the capital sum assured, and the number of years such policy has existed. One-sixth shall be set aside as a guarantee fund for the life policy holders, and eventually, at periodical investigations, apportioned among those entitled to participate. One-sixth shall be allotted for the proprietors of the company, as a consideration for their having pledged their subscribed and accumulated capital in addition to the profits of the life department, as a farther guarantee to the life policy holders. The company undertake to give appearance in any of the courts in England or Ireland, in the event of a disputed claim, by service of the proper writ on the company's agent, where the insurance was effected. It is imperative on the directors and parties making the assurance to submit any subject of dispute to arbitration. CHURCH OF ENGLAND-London, 1840-l£1,000,000.- One-tenth ofthe entire profits of this institution will be applied to the relief of distressed and aged clergymen, and the widows and orphans of clergymen who may be recommended by the bishops, or by the clergy of their respective localities. Persons insuring upon the participation rates of premium will be entitled to share in the profits of that branch of business to the extent of four-fifths. The bonus will be declared at the end of seven years, in which all those insured for the whole period of life, who have paid five annual premiums, will participate; and the amount may either be added to the policy or applied to the reduction of the annual premiums, at the option of the assured. Clergymen and others may insure against sickness. Age admitted in the policy, and in no case to be disputed afterwards. Unopposed probates of the diocesan courts may be held sufficient to entitle claimants to receive or recover the amount of policies without the expense and delay of a prerogative probate. A person effecting a policy for the term of life for £1000, will be entitled to vote on the election of auditors. Policies forfeited for non-payment of premium renewable, within twelve months, upon proof of the same state of health, and the payment of the premium in arrear, with interest thereon. CITY OF GLASGOw-1838-£750,000-In redeemable annuity and similar transactions, and on redemption, a policy of assurance will be delivered at the rate of premium applicable to the age of the party at the date when the transaction was entered into. Two-thirds of the profits allotted to the assured, and the principles and periods of division of those profits will be fixed upon the most favourable system for the assured. CLERICAL, MEDICAL, AND GENERAL-London, 1825-£500,000.- The balance-sheet of the auditors for the year ending June 30, 1839, 92 LIFE ASSURANCE OFFICES. showed the following result :--lst, That the profit realized from forfeited, lapsed, and purchased policies during the past year amounted to £11,042, 18s. 2d. 2d, That the sum received for premiums on new policies issued during the same period was £10,040, 11s. ld. 3d, That the income of the Society now exceeds £86,600 per annum. 4th, That, after defraying the claims on account of death, and all other expenses, £52,004 have been carried, as a clear saving, to the consolidated fund during the twelve months embraced in the report. By the deed of settlement, not more than one-sixth part of the profits can be appropriated to the shareholders, nor more than 5 per cent interest be paid on their instalments. A second division of profits was declared in January 1837, and the bonuses on policies, entitled at the two divisions, have amounted on an average to £22 per cent on the premium paid. The future bonuses will be declared at the end of every succeeding term of five years. CoMMERCIAL-Glasgow, 1839-£1,000,000.-This company allot it is not stated five-sixths of profits to the assured;tobut made, how the in the prospectus when the periodical additions are be profits are to be struck, or how they may be applied. The premiums may be paid halfyearly, quarterly, monthly, or weekly ; and the company will assure sums so low as £10. CRowN-London, 1824--£1,500,000.-Two-thirds of such profits as shall be septennially declared divisible, will be apportioned among assurers for that whole term of life, and may be applied to the reduction of the future annual premiums, or to the increase of the sum assured, as may be desired. The first division of profits took place in 1832, when from 18s. to £2, 12s. per cent per annum on the sums assured, varying with the age, being equivalent on the average to 261 per cent on the premium paid; and on the second division, in 1839, upwards of £1 to upwards of £3 per cent per annum on the sums assured, or on the average 33 per cent on the premiums paid for the preceding seven years. The premium is not subject to any charge for interest to proprietors. Policies may be assigned by a separate deed, of which forms may be had at the office, without making any indorsement on the policy or giving notice to the office. EAGLE-London, 1807-£1,000,000.-At the end of every seven years a strict investigation is made into the funds, the full value of each existing claim determined, its amount retained, and the surplus apportioned. Four-fifths of the profits of the periodical divisions are then allotted to the assured, and may, at the option of the party, either be added to the policy or applied in reduction of the future annual premiums. The superior value of female life having been fully demonstrated by the important tables published in 1825, by order of the House of Commons, the country became entitled to the benefit of its experience; and, accordingly, the directors ordered new rates to be calculated, which should distinguish at every age the price of insurance for the two sexes. When the ordinary certificates cannot be procured, and the fact is stated, in the first instance, to the company, the age may be agreed on at the commencement of the assurance, and can never become the LIFE ASSURANCE OFFICES. 93 subject of future enquiry. The first investigation will be in June 1840, when considerable additions to policies may be made. EcoNOMIc-One-fourth of the present profits is only appropriated to the shareholders, the remaining three-fourths to the assured, at the expiration of every fifth year. When a profit of £200,000 shall have been realized, the shareholders will be paid off, and thenceforth the entire profits of the Society will be divided among the policy holders. Every person assured for the whole term of life, at an equal rate of premium, will be entitled, after five annual payments, to participate in the profits; and every such person, if assured to the extent of £500, will, after four years, be entitled to attend and vote at all general meetings, the members of which have absolute control over the affairs of the Society. A bonus was declared in 1834, which amounted on an average to £16 per cent on the premium then paid; and on 23d March 1839, a second bonus was declared, amounting to £31 per cent on the premiums paid during the last five years. Bonuses are applied at the option of assurers, either to increase the sum assured or in reductions of future premiums for the remainder of life, or for five years only. EDINBURGH, 1823-£500,000.-At the first periodical investigation in 1835, a bonus was added to the policies which had been in existence for five years, varying in amount from 20 to 38 per cent on the premiums paid, according to the particular circumstance of each individual insurance. The proportion of profits allotted to the assured at that investigation was, in terms of the original prospectus of the company, twothirds; but from the prosperous state of the company's affairs, it has been determined to allot, in future, four-ffths of the profits to the assured. EDINBURGH AND GLASGOW-The thirds of the profits arising from their may be paid half-yearly or quarterly. upon the assured attaining the age of previously. ENGLISH AND ScoTTISH LAw assured will be entitled to twoown class of policies. Premiums Policies will be issued, payable 60 years, or on occasion of death AssocIATION-London, 1839- £1,000,000.-Part of the funds of this association will be invested in Scotland, and the deed of settlement so framed as to give the assured in Scotland all the facilities afforded by the Scotch offices. By thus blending the English and Scotch system applicable to insurance transactions into the constitution of this association, all the difficulties will be removed which may hitherto have been experienced by parties in Scotland effecting insurances with offices exclusively English. Assurances may be effected for £20 and upwards. The profits will be divided septennially; two-thirds to the assured, and one-third to the proprietors. Assurances may be effected upon payment of a portion of the usual premiums, by the parties paying interest upon the balance reserved. LIFE ASSURANCE OFFICES. EQUITABLE-London, 1762-Mutual Assurance. Accumulated Surplus, Twelve Millions Sterling! Total additions made on each sum of £100, assured by the Equitable Society from 1782 to January 1830, are as follows Year. Sum. 1791 479 446 1793 = = 1782 1783 1784 1785 £496 = 1779 1780 Year. __ 1776* 1777 430 397 1786 = 1787 1788 1789 1790 = = = = Sum. Year. Sum. £267 1801 = 253 240 1795 = 229 218 1796 1797 1798 = = = 207 197 187 1807 1808 1809$ 1809§ 1810 177 167 157 149 141 1792 = 1794 382 367 363 337 323 309 295 281 = = = - .1800 1799 1801t 1802 1803 = = = = £133 1805 = 125 1806 = = = 117 = = = 109 101 93 90 85 1811 = 79 1812 = 74 1813 = 68 184 1815 1816 = = = 63 57 52 In 1816 a new bye-law was made, in which it was declared to the effect, that whenever any addition shall be made to claims or policies, the first Jive thousand policies on the list shall alone participate in the profits of the Society; and that each of the remaining policies shall be considered as having been opened on the day on which it was first declared to be within the limit of those five thousand. No. of Policies. 1817, 1818, -1819, 1820, 1820, 1821, 1822, 1823 and 1824, Date of Assurance. Bonns. -1Ito 164 From 1st Jan. 1817 to 24th April 181 Admitted Dec 31, 1831 20 0 0 165 to 660 - 24th April 1817 to 16thApril1819 to con- Dec. 31, 1832 1710 0 661 to 1019 - 18th April 1818 to 4th Feb. 1819 the Dec. 31,1833 15 0 0 1021to 1413 - 5th April 1819 to 3rd Jan. 1820 numberofjDec.31,1834 12100 1415 to 1856 -- 7th Jan. 1820 to2ld JDec. 1820 5000 old- Dec. 31, 1831 10 0 0 1857 to 2245 -- 23d Dec. 1820 to 30th Nov. 1821 estaisur-jDec. 31, 1836 710 0 2247 to 2699 -- 1st Dec. 1821 to 7th Mar. 1823 ances. Dec. 31, 1837 5 0 0 2700 to 3082 -- 7th Mar. 1823 to 24th May 1824 ,Dec. 31, 1838 2 plete 100 The precise number of policies existing in the Equitable at 31st December 1816, when the excluding bye-law came into operation, was - - - - - - - - - - 9423 Of which were cancelled by death or otherwise before the close of 1831, - - - - - - - - Leaving at the close of 1831 the limited number of - 4423 5000 At the close of 1831, therefore, being just fifteen years after the byelaw came into operation, the insurances opened in 1817 began to enter the privileged class of 5000 ; but it will be observed, that they were *If the policy is dated before 1st May in each year. 1- If the policy is dated on or after the list of May, the whole additions will be £2 less than is stated above. t Policy dated before 8th December. § Policy dated on or after 8th December. 95 LIFE ASSURANCE OFFICES. entitled to count as privileged policies only in reference to the premiums actually paid subsequent to their admission into the privileged class, all the previous payment going in this respect for nothing. The admission into the privileged class of 5000, after the door was thus opened in 1831, has gone on, and continues to go on, slowly and gradually as the members in this class die off. At 1st January 1838, the number of existing policies was - - - - - - - - - 7558 So that before any party assuring in the Equitable, in the commencement of the present year, can come within the privileged class, there must die off, or at least be vacated, policies to the number of - - - - - - - - 2558 So as to reduce the number to the limited amount of 5000 Whatever may be the period of time which it will take to effect this reduction, it operates, during the whole of that time, as a total and irrecoverable exclusion from the profits of the Society. It may perhaps enable the present position of the Equitable Society to be better understood, to give the following extracts from an official document lately prepared and published by their manager : " The assurers may, at the present time, be divided into three classes :- " 1st Class consists of the members assured before the restrictions made by a bye-law in 1816. The number of assurances of this class, on the 31st December 1836, was " This class is entitled, on a division of profits, to an addition to the sums assured by their several policies, computed by way of per centage thereon, in respect of each premium paid by the assurers from the time of their entrance into the Society. " 2d Class (increasing as the first class decreases) consists of members who assured after the restrictions made in 1816, but since included in the limited number of 5000-the number of assurances in this class, on the 31st December 1836, was " This class is entitled, on a division of profits, to a like addition with the first class, but in respect only of every premium paid by them since they became part of the 3837 1163 limited number of 5000. " 3d Class consists of members who assured after the restrictions made in 1816, and who are not included in the limited number of 5000, and therefore not become entitled to any share of profits. Some members of the third class are yearly transferred to the second class to supply vacancies. The number of assurances in the third class, on the 31st December 1836, was "Every new assurer will, on his admission, be a member of this class. Total number of assurances at 31st December 1836, " On every periodical division of profits, one-third part thereof is reserved. 2683 7683 96 LIFE ASSURANCE OFFICES. " In May 1800, the number of assurances being 5124, the amount of the surplus reserved, was 1809, 1819, 1829, - - - - - I of - 9650, 8842, £225,108 - 7320, 640,715 1,090,000 1,790,000 1839, the number expected to be under 8000, the amount of of surplus expected to exceed 1,250,000 " As the first class decreases, and their places are supplied by those who are entitled to an addition, for such payments only as shall have become due on their respective policies after they formed part of the 5000 oldest assurances, the average number of payments on which the additions are to be computed must in consequence of such restriction be less, and the per centage or sum to be added for each payment greater, in proportion to the amount to be divided, than at present. " The operation of the bye-law of 1816 is, in one respect, well illustrated by the events of 1837. " The number of assurances of the first class on the 31st December 1836, as has been already stated, was - - - - - - - - 3837 " Of which there have been cancelled by death, in - Surrendered, - - - - - - - the year 1837, " - - - - - 201 9 ---- Leaving, - - 210 - 3627 " The number of the second class at the same period was - - - - - - - 1163 " Of which there have been cancelled by death, ,, by surrenders, 26 4 - 30 1133 240 " Number to be transferred from the third class, - 1373 5000 " The number of the third class, 31st December 1836, " Cancelled by death, " , by surrender, 2683 - - - - 48 - - - - - 20 - 68 2615 240 " Deduct number to be transferred to second class, 2375 " Add new assurances effected in the course of the year 1837, - - - - - - - 183 Total-January 1, 1838, - 2558 7558" 97 LIFE ASSURANCE OFFICES. The only point requiring explanation in the preceding extracts from Mr Morgan's statement, is, how a declining surplus can be consistent with an increased per centage of addition? Thus it is stated in the foregoing extracts that the reserved surplus, which at 31st December 1829 was £1,790,000, is expected at 31st December 1839 to be only £1,250,000-showing a decrease in the reserved surplus of £540,000. The reason why this may be nevertheless consistent with the expectation of an increased per centage is, that as the policies in the old or first class drop off, in which every payment of premium from the very commencement of the policy must be computed, and are replaced by policies which, after their period of entire exclusion has terminated, only count, in reference to the additions, according to the number of payments made, not from the date of their policies, but from the date of their admission to the privileged class-so it is perfectly consistent to suppose, that a smaller amount of surplus may enable a larger addition to be declared, just because the total participating amount of payments to which the additions will apply, is itself restricted in a greater ratio than the divisible surplus. Thus, supposing a policy for £5000 opened in 1805, to emerge in 1839, to be replaced by a policy of £5000 opened in 1824, or whatever may be the year, whose policies are now in course of admission to the privileged list, while for the first policy an addition must have been provided equal to cover thirty-fve annual payments, there must for the second or substituted policy, although of fifteen years' standing, be provided an addition corresponding only to one annual pay ment; or, taking the addition at 3 per cent, while for the first policy an addition of £520 must be provided for, there would require for the second or substituted policy an addition of only £150. It is this consideration that appears to justify the assumption, that although, with a greatly diminished surplus, the rate of addition by the Equitable at the ensuing decennial division in 1839, may not only be as large, but even larger, than it was in 1829. The plan of excluding all the assured from any participation of profits until they come within the 5000 oldest subscribers, is not a trifling feature; one must live, on an average of chances, at least fifteen years before he reaches admission into that enviable number; and in the next fifteen, should he survive, he might perhaps get the profits of one decennial period, which, after deducting the premium and simple interest upon them, will give him at the end of thirty years at the most about £150. But if the young obtain only so small a pittance, an insurance made at an advanced age is ruinous. Take an example of one supposed to be made in the year 1820 for £1000, the age 55, premium £53. In fifteen years, that is in 1835, he might hope to get within the envied pale; but the division of profits being in 1839, he will then have assigned to him, payable at his death, 3 per cent for the remaining four or five years, say £150. At this time, that is, in nineteen years, he will have paid in - - £1331 Will be entitled, when policy becomes a claim, to - 150 - £1181 premium, with interest at 3 per cent, Balance of money advanced with interest, - - - He is now in his 75th year, and enters into a fresh decennial period, which, if he should survive-and it is ten to one 98 LIFE ASSURANCE OFFICES. against him-he will have paid a further sum of His share of profits will now be about There remains a loss of Add former loss, - - - £607 - - - - 300 - - - - - £307 1181 - - - £1488 Deduct original sum assured, 1000 The actual loss to the assured and gain to the office, £488 How different would the result have been under the old regulations ! In this case the representatives of the assured would have received £1610 in addition to the £1000, instead of sustaining the above loss :for we have the actuary's own statement, put forth somewhat triumphantly, that the Equitable, up to the year 1820, had added to a policy of twenty years' standing 76 per cent; to one of thirty years 161 per cent; to one of forty years 280 per cent, and to one of fifty years 401 per cent! And yet, knowing well what the result of the charge must inevitably be, he actually triumphed in the loss which the assured must incur in the certainty of the great benefit which the office would receive from the device of his own ingenuity. EUROPEAN--London, 1819-£1,000,000.-Policy holders will partake equally with the proprietors, in proportion to their respective assurances, in the accumulated profit realized at the end of every seven years. At those periods the assured for the whole term of life will have an addition allotted to the sums assured by their respective policies, calculated on the amount of premiums paid thereon, and such additions will form part of the amount to be paid on each policy when it becomes a claim. Holders of annuities will be entitled to partake every seven years in the accumulated profits of the company. Endowments to children will also have such proportion of the profits of the company as may, during the existence of such policy, be added thereto. FARMERs.-All claims will be settled within one month-none shall be vitiated save by positive fraud. No policy will be declared forfeited until three months after the period when payment ought to have been made; and life policies may be renewed or revived after twelve months have elapsed, on proof of the same state of health of the assured, at half the diference between the terms of the year of renewal and the original year of commencement. FREEMASONS and GENERAL-London, 1838.-The business of this company consists of two branches, one called the " Modern Mutual," the other the "Proprietary." The Modern Mutual branch differs from other mutual assurance companies, in having a guarantee fund, the capital being subscribed by the proprietary body. Thus, those of the assured who prefer the Modern Mutual, will divide the whole of the profits made in their department, after the expenses of the establishment and their part of the charity is deducted, whilst the assured in the other branch, although not participating at all, will have the advantage of pay- LIFE ASSURANCE OFFICES. 99 ing much lower premiums. The subscribers will receive 5 per cent per annum on the paid-up capital, and divide the whole of the profits remaining after the deduction of their portion of the charity, arising from the proprietary branch of the establishment. The amount of profits arisinig from the modern-mutual branch of the establishment, will be ascertained on the 1st of July 1843: and the whole, deducting as above the expenses and charity, will then be divided among the assured, according to the present value of each respective policy; such profits will either be added, at the option of the assured, to his policy, or will be applied in diminution of future premiums, or in their total extinguishment at a certain age. The same system of equal division will be repeated on the same day, at the termination of every subsequent three years. The assured, although dividing the whole of the profits amongst themselves, will be indemnified from the debts of the company, by the subscribed capital. Parties assured to the amount of £1000, will have one vote at the election of auditors to be chosen by the general body of the modern-mutual assured, to examine and report on the accounts o2 the company. In cases of error, either as to age, or in the form of the policy, or in the answers of referees, such errors, if not fraudulent, will not be deemed to vitiate the policy; but the directors will pay such sums upon the amount of the policy, as from the nature of the case may be just and reasonable. When a party effects a policy upon the life of another, it is often difficult to say how far the person so assuring is interested; or even when ascertained, such interest may cease or be modifled by circumstances; the company will not inquire into these facts, but will be satisfied if the party assuring had at the time a bona Jide interest in the life of the assured, so as to defeat all gambling and fraudulent speculations. GLASGow-1839.-Two distinct plans are offered by this company to assurers. By the first plan persons may insure for the whole term of life, and participate in the company's profits to the extent of two-thirds. By the second plan, persons may effect every kind of assurance at a reduced rate of premium, without participating in the profits of the company. GUARDIAN-London, 1821-£2,000,000.---The share of the profits to be allowed to the assured may be applied either by adding to the amount of their respective policies such reversionary sums as are equivalent to such profit, or in reduction of the premiums thereafter to be payable on such policies, provided such option be declared in writing within three calendar months after the division shall have been declared; but if such option be not so declared, such share of profits will be added to the amount of the policies. The first division of profit to the assured was made to Christmas 1828, and a second division of profit was made to Christmas 1835. At each period the reversionary bonus, added to the several policies, averaged rather more than 28 per cent on the amounts of premiums paid thereon during the preceding seven years. If any person assured with this company for seven years, or for life, should die within thirty days after the premiums shall become due, such 100 LIFE ASSURANCE OFFICES. assurance is to be valid in case the premium be paid within such thirty days. HAND-IN-HAND-London, 1836.-No distribution of profits will take place until June 1842, when an account will be taken of the engagements and property of the society, and a large proportion of the profits Will then be applied to the reduction of the premium of those members who shall have made five complete payments: but if preferred, the shares of such profits will be applied in making equivalent reversionary additions to the sums insured. The proportion of profits not then divided, will be carried forward for the benefit of the members, and included in future valuations. In each subsequent year a similar account will be taken, and as large a proportion of the profits as security will admit of, will be annually distributed amongst those members who shall have been insured for five years at the least, in manner above specifiedthe advantage upon each assurance being in proportion to the amount of profit realized. All members' policies become annually due on the 24th day of June, and the first premium where an assurance is effected after the 24th day of June, is computed accordingly; charging of course only for the short period; and every policy issued by the society for more than one year, on which the premium shall remain unpaid above thirty days after the period of its annual expiration, will be void; but it may be renewed within thirty-seven days after the period of its annual expiration, upon payment of a fine of 2s. 6d. per cent on the sum mentioned in the policy; withinforty-four days, 5s. per cent; within fiftyone days, 7s. 6d. per cent; and after that time, and within three calendar months, 10s. per cent; and in each case giving sufficient proof that the party assured is then in good health. HoPE-London, 1807.-Those who effect an assurance with this company, whether on their own life, or on the life of another, for the whole term of life, are entitled to participate in the profits of the life assurance fund; bonuses of two-thirds of the profits being declared septennially, which will be divided amongst such assured, whether proprietors or not, in proportion to the sum assured, and the duration of the policy. The assured may have such bonuses applied in reduction of the annual payments upon their policy, by giving notice in writing to the company, within six calendar months after the bonus is declared; and if such notice be not given, the bonus will be added to and payable at the same time with the sum assured by the policy. IMPERIAL-London, 1820--£750,000.-Persons assured for the whole term of life will participate periodically in two-thirds of all profits made by the company; and additions will be made to all policies becoming claims afterfive annualpremiums have been paid thereon, although the On assured may not live till the next general appropriation of profits. 22d June 1831, a bonus, or addition of £1 10s. per cent per annum on the sums assured, was declared on all policies for the whole term of life then in force, effected on or before the 31st January 1827. The present value of the above additions may, if desired, be received by the insured, or applied in reduction of their future premiums, at the option 101 LIFE ASSURANCE OFFICES. of the parties; or, upon the whole policy being surrendered, a new insurance for a less sum may be obtained, without any further premium being required by the company. A few examples are here given, as follows :- Age Sum when insured. insurednsure. Addition made to Policies Value of Ten Years Addition if in force on surrendered. the 31st of Jan. 1831 Annual Premium. Premium 20 30 40 £. 1000 1000 1000 £ 21 26 33 s. d. £. 15 10 150 14 2. 150 19 21 150 50 1000 45 6 8 150 60 1000 63 13 4 150 £. s. d. 47 17 7 58 0 10 71 10 11 Reduction in Premium. For Ten Years only. For the whole term of Life. £. s. d.£. s. d. 5 18 7 2 14 1 7 15 6 3 12 9 9 53 5 5 2 New Policy without any Premium £. 333 365 400 4 911 15 3 7 160 438 102 17 815 14 012 120 513 86 Policies which may become claims, before the next decennial appropriation of profits, will have additions made to the sums insured, provided five annualpremiums shall have been paid thereon, agreeably to the following resolution passed at a special court of directors, held on the 27th of January 1836, namely,-" That every policy effected for the whole continuance of a single life, upon the terms of participating in the profits of the company, which shall become a claim after the 31st of January 1836, and after five annual premiums, at least, shall have become due, and been paid thereon, shall have an addition made to the sum insured, and that the addition to be made to such policies as may become claims on or before the 31st January 1841, shall be at the rate of £1 per cent per annum, that is to say:-To policies effected on or before the 31st of January 1827, on addition of £1 per cent on the sums insured, for every premium becoming due, and paid after the 31st of January 1831 :-And to policies effected after the 31st of January 1827, an addition of £1 per cent on the sums insured for every year such policies may have been in force." LAw LIFE-London, 1823.-Four-fifths of the profits made by this society will be appropriated to the persons assured for the whole term of life. On the 31st day of December 1840, and at the end of every seven years from that period, the profits divisible amongst the assured will be apportioned amongst such of the assured for the whole term of life, as shall have been so assured for the space of three years or upwards, previously to those periods respectively, subject only to the reservation of such a sum of money as the directors shall deem necessary, to be carried forward to the period of the next septennial division for the benefit of the assured. For the amounts which shall be so apportioned, equivalent reversionary sums will be added to the policies respectively of those entitled. The subjoined is a specimen table of bonuses, in even pounds, added to policies of £1000 each, which had been in force during the first ten years of the existence of the society, 102 LIFE ASSURANCE OFFICES. and declared up to the 31st December 1833, compared with the amounts of premiums that had been received and improved at interest. Age at Commencement. Amount of Premium. Bonus. 25 35 45 £284 353 460 £177 188 216 55 65 628 925 263 351 Persons who shall have been assured for the space of two years, in £1000 or upwards, for the whole continuance of life, have the power of electing either from among the proprietors or from among themselves, two of the four auditors of the society. LEGAL AND GENERAL-London, 1836.-At Christmas 1846, being a period of ten years from the institution of this society, and at the end of every seven years from that period, four-fifths of the divisible profits will be apportioned amongst such of the assured for their whole term of life, participating in the profits, as shall have been assured for the space of two years or upwards previous to such respective periods. In this periodical division, a share of the profits will be allotted in respect of policies effected on the lives of persons who have died between the periods of distribution, in case two years' premium shall have been paid upon such policies-such share to be paid at the period of distribution to the persons entitled to the benefit of those policies. The amount of profits apportioned in respect of subsisting policies, may, at the option of the assured, be added to their policies, or applied in reduction of future premiums, or in'extinguishment of the premium altogether at a certain age, or be received in a sum of money payable immediately. Persons assured for the space of two years in £1000 and upwards for the whole period of life, will have the power of electing, either from among the proprietors or the assured, two of the four auditors of the society. LICENSED VICTUALLERS-London.-The profits will be divided every five years in the proportion of one-third to the proprietors, and two-thirds to share-members who are assured for life. Every member assured for the whole term of life, whose policy shall have existed three years, will be entitled to a proportional share of the quinquennial profits, which may be applied either by additions to their respective policies, or in reduction of the premiums thereafter to become payable. The proprietors of this company, in addition to their proportion of profits, receive four per cent interest per annum on the amount of their subscribed capital. Every proprietor must insure his own life, or procure a nominee to the amount of the shares standing in his name. Nonassurers pay a yearly fine of one shilling per share. LONDON, EDINBURGH, and DuBLIN-London, 1839.-If parties find it inconvenient to continue paying the same rate of premium, the Comn- LIFE ASSURANCE OFFICES. 103 pany will then reduce the policy according as may be desired, and consider such to have been the amount of the original assurance; the overplus of premium which the assured will thus have been paying, will be considered as so much paid in advance upon the new reduced policy; so that the assured will in any event reap the full benefit of the premiums which they have paid. Endowments will be granted to children or adults contingent on their attaining a given age; and these endowments may be contracted for, so that in the event of death before attaining that age, the whole of the premiums which have been paid will be returned, the Company retaining merely the accumulated interest. A party having an interest in the life of the assured shall not lose the benefit of the policy, although his interest shall have terminated before the death of the assured. The policies granted by this company will be indefeasible and indisputable upon any ground of inadvertency, mistake, or error, either in the preparation of the policies or in the declaration of the parties applying for assurances, or in the certificates of the medical advisers. No error, unless fraudulently committed, shall be held to vitiate the contracts of assurance, and this will be the case whether the policy remain with the original assurer or shall have been transferred to others. Assurances will be granted for sums from £20 to £5000, and annuities or premiums from £10 to £500 per annum. LONDON LIFE ASSOCIATION-1806.-This society adopts two plans of assurance. Those who assure their lives at the higher scale of premium participate in the whole profits, and are mutual assurers to each other. The original regulation of the society was, that the premium, besides the fractional part payable on entering, should be paid in full for five years, and should be reduced on the sixth and after payments as much as the annual accounts might warrant. But, on the 1st January 1830, the surplus capital reserved to supply the future abatements to the then members had been found so considerable, as to require seven entire annualpayments from new members, in order to their being placed on a footing with the existing members, and to entitle them, after making such payments, to participate equally in the existing fund, and the accruing advantages. All premiums on policies of members become annually due on the 1st day of July. No member is entitled to attend or vote at any general court, unless he has been assured, prior to the 15th January 1817, in the sum of £500; or between that date and the 1st January 1830, in the sum of £1500, for five whole years; or subsequently to the 1st January 1830, in the same sum, for seven whole years. Parties not assuring as members have the immediate benefit of a reduced rate of premium. LONDON AND WESTMINSTER-Mutual Assurance.--This society will assure for the whole life, or for a limited term, any sum from £20 to £5000, on a single life, joint lives, or survivorships. Amongst other forms of life assurance, policies will be granted for the amount assured, to be received at the end of a term of years, although the party assured may be alive; but the assurance to be determined, nevertheless, by his death, though it should take place before the expiration of the term; so that a person may himself enjoy the fruits of his prudence, and secure comfortable competency for advanced life. In order to make life assu- 104 LIFE ASSURANCE OFFICES. rance available to the industrious classes, the premiums may be payable quarterly, half-yearly, or annually. In addition to the unlimited liberty of residing in any part of Europe, this society will, under certain regulations, allow persons to visit and reside in those colonies, beyond the confines of Europe, where the climate is not decidedly unhealthy, without charging any extra premium. An ample temporary capital stock has been raised to guarantee the immediate engagements of the society, bearing interest at £5 per cent per annum, which capital may be discontinued at the end of five years, or any time after that period when the directors shall consider the income and accumulated fund of the society are of such amount as to render its continuance unnecessary. One-fifth of the divisible profits of the society will be set aside, and distributed as a bonus to the shareholders, whenever the subscribed capital is discontinued. The profits of the society, at the expiration of the first five years, and every succeeding year, to be estimated, and the average profits of one year to be annually distributed by a reduction of the future premiums, or by a bonus added to the policy, at the option of the assured, to those members who shall have paid premiums for five entire years; thus always leaving in the hands of the society, as a guarantee fund, the average profits of four years. The year may commence on 1st January, 1st April, 1st July, or 1st October, according to the time when the assurance is effected. The society will at all times be prepared to treat on the most equitable terms for the purchase of its policies, whenever the assured may desire to dispose of them. All members who have paid five entire annual premiums may, with the consent of the directors, reside in any part of North America (the British settlements included) not south of Virginia; and all members who have paid ten entire annual premiums may, with the consent of the directors, reside in any part of Australia, Van Diemen's Land, Cape of Good Hope, or Island of Saint Helena; and also in time of peace may, with the consent of the board of directors, proceed direct from England to any of the aforesaid places, and return, in like manner, direct to England once during the continuance of their respective policies, without the payment of any additional pre- mium. effecting LONDON ASSURANCE-Birchin Lane, 1721.-Persons life assurances with this corporation have the choice of two plans:--The one entitling them to an annual abatement of premium after five years' The payment:-The other at a lower fixed rate without abatement. leading features which distinguish the first of these plans are, that the business is carried on by the corporation without any charge for management being deducted from the profits. The abatement of premium for the year 1837, on policies of five years' standing, under the first of the above plans was £86, 13s. 3d. per cent. The future annual abatement must vary according to the success of this branch of the corporation's business. the deed of settlement, MANCHESTE---1824-£2,000,OOO.-By the amount of the profits of " The Life Assurance Fund" are to be ascertained up to the 25th day of March 1839, and every succeeding ten years after that period. A bonus will be declared out of the profits of that fund on the 1st day of October following; and every person assured 105 LIFE ASSURANCE OFFICES. for the whole period of life, by any policy of four years' standing, will be entitled to participatein two-thirds of the bonus when the sum assured by his policy becomes payable. Ten or more persons assured by the Company, not being proprietors, may appoint any number of persons, not exceeding three, on their behalf, to inspect, within the first three calendar months after the holding of every Annual General Court, on certain days to be appointed by the Board of Directors, by notice in the London Gazette, and any two of the Manchester newspapers, during the office hours, at the Office of the Company, the Reports produced at the last preceding Annual General Court, and to examine the accounts of the Company for the preceding year. Thirty or more persons assured by the Company, and entitled to participate in the bonus, not being proprietors, may appoint a person, on the behalf of themselves and the other persons assured, to assist in making the calculation of the profits out of which the bonus is for the time being to be appropriated. At any time after a bonus has been declared out of the profits of " The Life Assurance Fund," any assured entitled to participate in such bonus, may in lieu of his share thereof, on giving notice at the office, claim a reduction of his premium upon the terms mentioned in the deed. METROPOLITAN - London, 1835 - £200,000.-The subjoined table is for an increasing policy upon the following plan: viz. Upon payment of an annual premium, the sum assured to be increased at any required rate per cent for every premium paid after the first year. Upon this plan, the assured has but to determine, in the first instance, what annual rate of addition he may require to the sum first assured, in order to be entitled to such addition, so long as the annual premium be paid; and should the assured, at any time, wish to discontinue the payment of the premium, the policy may either be surrendered for an immediate payment, or he may stand assured for a fixed amount payable at his decease, which amount will-be regulated by the premiums paid. This mode of assuring life appears to the directors to be calculated to meet the views of those who may wish to make a gradual addition to the policy, and may be illustrated as follows :-Suppose an assurance to be granted to a person, in his twenty-fifth year, for £500, subject to an increase of 10 per cent, the annual premium for which will be £6, 16s. 6d. per cent ;-should the life drop in the first year, the society engages to pay - - - If in the second, If in the third, If in the fourth, - - - - - - - - - - - - £500 550 600 650, increasing in the same ratio for each premium paid, until the life be extinct; so that, should the person whose life is assured die in his sixtieth year, and have paid the premium for that year, he will have secured the sum of £2250, for an annual premium of £34, 2s. 6d. only; and if in his eightieth year, the same annual premium will have secured a sum of £3250. MINERVA-London, 1836.-A general statement of the affairs of the company will be submitted every five years; and, of the profits ascertained to have accrued after payment of interest and the necessary expenses, four-fifths will be apportioned among the assured for the whole 106 LIFE ASSURANCE OFFICES. term of life, of one or more years standing, in proportion to the amount of premiums paid by each; and appropriated (at the option of the assured) either as a reversionary bonus, payable when the policy becomes a claim, or its value applied to the reduction of subsequent premiums, in such manner as the directors shall think just and equitable to the assured. Should a person assured by this company die within one month after a renewable premium becomes due, the company will be liable for the payment of the claim, provided the premium be paid within the time specified. MUTUAL ACCUMULATION SOCIETY-Edinburgh, 1839.-The plan of this society is as follows :-A fund is raised by the mutual contributions of members, each of whom, by a payment graduated for all ages, as seen in the society's tables, and which is received either by annual instalments, or by the advance of a single payment in the option of the contributor, purchases a larger or smaller interest (expressed by shares) in this fund, either on his own life or on that of a nominee in whom he has an interest. The time allowed for joining the fund is one year, at the end of which it is closed, whereby the number of shares of which it consists, and number of members among whom these shares are distributed, are finally fixed. In order accurately to ascertain the interest of each member in the fund, the rates of contribution have been calculated for shares of £100 each. The fund or scheme, so far as regards entrants, is thus completed, no more being thereafter admitted into it; and a future term having been previously fixed, at expiry of which it is to be divided among the members, or nominees of members, who have survived that term, it is till that time improved and accumulated for their behoof and advantage solely. On the arrival of the periodfixedfor division, for instance, at the expiry of 15 years, it is ascertained what the accumulated fund amounts to, and what the number of members then alive and of their shares is, and immediately thereupon the whole fund is divided among them according to the number of shares held by each, without any deduction whatever, except a share of the expense of management, which is proportionally borne by all the schemes which the society is simultaneously carrying on. Such is a statement of the society's plans. To meet the views of persons having different objects in making a provision for themselves or others, it is offered under five schemes or classes, all separately managed as explained above; the periods, at expiry of which each of these classes is to have its own fund divided, being respectively 10, 15, 20, 25, and 30 years. Thus, for instance, during the currency of the year 1840, books are opened, containing five schemes :- The first for contributors to a fund which is to be divided in the year 1850 The second do. do. do. do. 1855 The third do. do. do. do. 1860 The fourth do. do. do. do. 1865 The fifth do. do. do. do. 1870 And it is in the power of any individual, during the currency of the year, upon giving proof simply of age, to secure for himself, or for others in whom he has an interest, as many shares as he deems proper in the fund of any of these schemes, or in more than one of them, at his option. At the end of the year, each scheme is closed, as before explained; and LIFE ASSURANCE OFFICES. 107 for the entrants of the next year, 1841, the same number of schemes is again opened for division of the fund in the years 1851, 1856, 1861, 1866, and 1871; and so on annually, each scheme for each year being quite distinct and independent, and its fund managed solely for the interests of the survivors of those who joined it in the year of its formation. Tables are adapted for male and female lives, showing the annual sum which entitles a party, at any age, to an interest of one share in the whole accumulated fund of that class which he enters, to be paid, if the party on whose life the benefit depends be alive at expiry of the period there fixed; and in illustration of these, the following examples may be given :-A young man at the age of twenty-five, by joining the fifth scheme, and paying annually the sum of £16, Os. 10d., may secure an interest of ten shares in the whole accumulated fund of that scheme; in other words, on a division he receives first the original value of his ten shares, being £1000, as do the other members alive, and then he gets added to this the proportional share in the whole remainder of the fund which belongs to his £1000. The period here fixed for division will arrive when he has attained the age of fifty-five; or, if he prefer to make this provision on attaining the age of forty-five, he is enabled to do so by joining the third scheme, in the whole accumulated fund of which he will secure a like interest of ten shares, as above explained, by paying the annual sum of £32, 7s. 6d. NATIONAL.-London, 1830-£500,000.--The profits of the society are ascertained at the end of every year, and one-fifth of the whole appropriated in manner following :-Two-thirds of this one-fifth are divided amongst the assured for the whole term of life, who have been so assured for the full period of five years; and the remaining one-third to the proprietors of the subscribed capital. Thus, an amount equal to one year's average of profit will be annually divided, and a fund equal to fobur years' average of profit will always be in reserve to meet contingencies. This division of profit among the assured for the whole term of life, to be continued until the number of policies entitled to par. ticipate shall amount to one thousand, when no more participators shall be admitted, except as policies fall in, when the next policy in rotation is to succeed. The society, however, is at liberty to extend from time to time the number of policies entitled to participate. NATIONAL LOAN FUND-London, 1837.-The assured will have the option of converting his policy, at any time, into the following uses : viz. 1st, into an immediate payment of its present value; 2d, into a new policy, without any further premium, payable at his death, equal in present value to his original policy; 3d, into an annuity of equivalent value; 4th, into a security on which he may borrow equal to two-thirds of his payments; 5th, in the event of negligence or inability to continue the annual premium, by which his policy would become forfeited, his representatives will, nevertheless, receive from the Society at his death, in addition to any bonus assigned during the continuance of the payments, two-thirds of all payments made after the first five years.-The assured may at any time act upon the Loan Fund to the extent of two-thirds of his payments as a cash credit, upon notice to the office or agent at each branch of the Society. The sum borrowed may be for a permanent or 108 LIFE ASSURANCE OFFICES. temporary period; but irregularity in the payment of interest subjects the loan to be recalled. NOTE.-Any person assured on the scale of profits who may have the bonuses added to his policy, will in the course of a few years be entitled not only to borrow two-thirds of his payments, but to receive as a right full value of the Bonuses so added; and in the majority of cases the sum thus at his command, will considerably exceed the full amount of his entire payments. Two-thirds of the profits, estimated ANNUALLY after the first three or five years, will be divided amongst those assured for life, on a participating scale of the Society, and the profits of the Guarantee Fund, invested in reversionary and other interests, will be estimated in each division. Each bonus, at the option of the assured, will be paid in money, or applied to the reduction of the future premiums, or an equivalent added to the policy. This Society submits a plan of deferred annuities on a new principle, which will not only afford a more ample provision for old age, and protection against sickness and misfortune-but in addition, the means, at all times, of putting his energies in motion, and, in the event of premature death, a better protection to his family. The plan proposed will embody several essential objects :-1. To secure an increased provision for old age out of a given saving, by applying it exclusively to the purchase of a deferred annuity; 2. To render the purchase of a protection in sickness unnecessary, by enabling the purchaser of a deferred annuity to withdraw or borrow two-thirds of his previous payments; 3. By the use of two-thirds of all his payments when required, to limit misfortune and want of employment, and extend the power of productiveness by an increasing command, in each year, of capital, so that, while providing for old age, each successive contribution renders him more secure against present misfortune; 4. To afford, at the age at which the deferred annuity would commence, without reference to his then state of health, the option of receiving, instead of his annuity, its value in money, according to the value fixed on the contract, or a larger sum payable at his death; 5. In the event of death before the age at which he would be entitled to his deferred annuity, to return two-thirds of his payment to his family, or such life assurance as may be settled on the contract; 6. In all such cases where the power of productiveness fails, either from disease or accident, to enable the assured on equal terms to convert his deferred annuity into a present annuity. NORTH BRITisH-Edinburgh, 1823-£1,000,000.-The profits are equitably divided, each policy drawing exactly in proportion to the sum assured, and the number of annual premiums paid, during the septennial period. Previous bonuses being reckoned as additions to the sum assured, and as such entitled to participate. The additions by way of bonus, at 31st December 1837, were as follows :On a policy opened in 1823 for £1000, the bonus was Ditto 1839 for £1000, - £174 10 109 5 0 0 The bonus being annually at the rate of £10, 17s. 6d, and at 1837, being the last investigation back to 1830, at the rate of £12, 10s. Policies assigned to third parties, for onerous causes, are placed on the same favourable footing as if the assurance had been originally effected by the assignee. LIFE ASSURANCE OFFICES. 1.09 NORTH OF ScoTLAND.--Aberdeen, 1836-£1,000,000.-The assured who participate in the profits of the company, receive nine-tenths of the profit to be divided every seventh year, which may be applied either in reduction of the future premiums, or added to the amount assured. Premiums may be paid quarterly, half-yearly, or yearly. NORWICH UNIoN-1808-Mutual Assurance.-Three septennial bonuses have been declared, amounting respectively to £20, £24, and £25 per cent on the amount of premiums deposited-the calculation, in each case, being made upon the whole premiums paid from the date of the policy. In this manner, the larger the amount of premiums paid, the greater, in every case, will be the ultimate claim upon the society. The next division of profits will be in 1843, when important additions may be confidently anticipated. This society demands no entrance money. PALLADIUM-London, 1824-£2,000,000.-The assured participated in four-fifths, or 80 per cent of the estimated profits, which are added every seventh year, as bonus, to policies effected for the whole term of life, on lives not exceeding the age of 50 when assured. Or the additions may be applied in reduction of future annual premiums, at the option of the assured. Lives above 50 when assured, do not participate in profits, but they may be assured at reduced premiums. Every holder of a policy of £1000 or upwards, entitled to profit, may (after two annual payments) attend and vote at all general meetings with the proprietors of shares in the capital stock of the society. Relative proportions of premiums paid, and sums added, on a policy of £5000; being, on an average of all ages from eight to fifty, forty-three per cent on the premiums paid during the fourteen years. Persons assuring their lives at any period before the next distribution of profits in 1845, will have sums appropriated to their policies, in proportion to the profits then declared. PELICAN-London, 1797.-The directors insure, on equitable terms, the lives of persons resident abroad, or about to proceed to foreign climates; and in this department, the Pelican Office presents great advantages to officers of the army and navy, as no extra charge is made for home service. The moderate addition required from such individuals for change of climate may be covered by an average rate, or the proposed destination be made the matter of special agreement on taking out the policy; the insurer paying only the home premium until the contingency contemplated shall happen. An important extension of this plan, rendering a policy, at the option of the possessor, perfectly secure from the forfeiture which the negligence of the assured, or his departure beyond the limits of Europe, might occasion, offers to solicitors, agents, and others, a mode of indemnification peculiarly desirable. PROMOTER-London, 1826.-A division of profits will take place quinquennially, in such manner as the board shall consider equitable, the directors having the power to reserve a portion of the net profits, as a rest, whenever they may deem it expedient to do so. Bonuses accrue on all beneficial policies on which three annual premiums shall have been paid at the time a division occurs; and the holders of such policies have 110 LIFE ASSURANCE OFFICES. the option of having their bonuses apportioned in either of the following ways, provided a written declaration of such option be lodged at the office within three calendar months immediately after the division takes place :--lst, By an immediate payment in money. 2d, By the addition of an equivalent reversionary sum to the policy; or, by the issue of a distinct policy for the bonus; 3d, By an equivalent reduction in the future annual premiums. Every holder of a life policy on which five annual premiums, or premiums to the amount of £200, have been paid, has the right of voting for auditors, and of being present at the general meetings, at which the auditors report the state of the affairs of the society. Policies from £50 to £5000 are issued; proposers for £100 and under, have to pay a fine of ten shillings, and such addition to the ordinary premium as the board shall think proper. PROTEcToR-London, 1835-£1,000,000.-Amongst the assured, on the participation plan for the whole period of life, three-fourths of the profit realized by the association, including the dividends on the invested capital, will be divided quinquennially, in the proportions indicated by the value of each policy respectively. The bonus or profit thus apportioned may be applied, at the option of the parties, either in adding to the amount of their assurance such reversionary sum as may be equivalent to its share of profit, or in reduction of the premium thereafter payable on the policy. Claims on policies effected in Scotland will be discharged in Edinburgh. No English probate is required; and the directors will be satisfied with the forms prescribed by the law of Scotland. PROTESTANT DISSENTERs-London, 1838.-One-tenth of the entire profits is appropriated, by deed of settlement, to reducing the premiums payable for insuring the lives of Dissenting and Methodist ministers, or in other ways similarly beneficial to their families. Certificates of age and character not required from the parochial clergymen or elders, or churchwardens. I'ROVIDENT-London, 1806-£250,000.-The profits are divided The fourth septennial division was declared in every seven years. August 1834, and £40 per cent was added upon the premiums paid. In this division of profits, the shareholders' portion did not exceed an eighteenth part, and it is probable that on the next division in 1841, it will not exceed a twentieth part. Hence, subject to a deduction of five per cent to the subscribers, the remaining whole profits are divided among the assured. These periodical divisions of surplus are added to the policies, and made payable therewith, or applied to the reduction of the future annual premiums at the option of the assured. RocK-London, 1806..-The profits are divided periodically, at intervals of not less than seven years: two-thirdsbeing appropriated to the policies of the assured for the term of life, and the remaining third being added to the subscription capital stock, on which a dividend is paid annually to the proprietors. Additions appropriated to each £100 assured for the term of life, and payable when the policy shall become a 1819, a policy dated on or before 31st claim, were made as follows :-In December 1806, the bonus assigned was £24. In 1826, a further bonus LIFE ASSURANCE OFFICES. illI of £19 was added; and in 1833, £33, 16s. was declared-making in all £76, 16s. A policy opened in 1818, received in total additions up to 1833, £25, 4s.; and a similar policy dated 1825, received at the last investigation in 1833, £9, 2s. ROYAL NAVAL, MILITARY, AND EAST INDIA COMPANY.-The society will return once in every seven years to the assured for the whole term of life, who shall have paid premiums, entitling such assured to profits, and who shall have been three years contributing four-fifths of the divisible profits, with a proportionate share to the representatives of those who may have died in the interval, in case three years' premiums shall have been paid on their policies. Every person assured shall be at liberty to choose whether his share of the profits so divided shall be applied in augmentation of the sum assured, in diminution of the future premiums, in extinguishment of the premium altogether at a certain age; or be received in a sum of money payable at the time of division. The remaining one-fifth of the profits will belong to the shareholders. Those who are assured for life in £1000 or upwards, and have paid two yearly premiums, will have the privilege of electing either from their own, or from the proprietary body, two out of the four auditors for the year. A leading object of the present society is to extend the benefits of assurance to climates where they are almost unknown, and more especially to diffuse them among persons acting in any naval or military capacity, or resident where the flag of Great Britain is borne. Peculiar facilities will be given for assurance to captains and others of merchant vessels. The rate of premium for tropical climates are reduced to this class of assurance to its just dimension. SCOTTISH EQUITABLE-Edinburgh, 1833-Mutual Assurance.-At a special general court of the society, held 1st February 1838, those parts of the deed of constitution regarding the distribution and appropriation of the surplus funds were repealed, and the following articles and regulations were substituted :-That the first investigation of the affairs of the society shall be made 1st March 1841, and triennally thereafter; that at each investigation the directors shall have power to allot a sum, not exceeding two-third parts of the surplus, in vested additions to policies of not less than five years' standing; and a sum not less than one-third part of the surplus shall be reserved at each investigation, for the purpose of making contingent prospective additions. These vested additions and contingent prospective additions shall be regulated as hereafter specified; that at the first investigation on 1st March 1841, two third parts of the surplus shall be allotted in vested additions to such policies as were effected on or before 1st March 1836, in proportion to the amount assured, and the number of annual contributions which have fallen due; that at the second investigation, 1st March 1844, two third parts of the said surplus shall be allotted in vested additions to policies entitled thereto, as follows :-1. To policies effected on or before 1st March 1836, at such rate per cent per annum as the directors may fix, on the sums originally assured by the policies, and on the vested additions made thereto at 1st March 1841, and that for three years, being the number of years which shall have elapsed since the first investigation. 2. To policies effected after 1st March 1836, and on or before 1st March 1839, at the rate per cent per annum immediately before 112 LIFE ASSURANCE OFFICES. referred to, on the amount assured, and the number of annual contributions which have fallen due. That in like manner, at 1st March 1847, the third period of investigation, the directors shall have power to allot a sum not exceeding two third parts of the said surplus in vested additions to policies entitled thereto, on the same principles by which the second division is appointed to be regulated. That besides vested additions as aforesaid, contingent prospective additions shall be made on all policies of not less than five years' standing which may become claims between one investigation and another. These prospective additions shall be at the same rate per cent per annum as the vested additions which may have been declared at the investigation immediately preceding the period at which such policies become claims; and they shall be in proportion to the sums assured, and the duration of the policies, as follows :-1. On policies which have had vested additions made thereto, the rate per cent shall be calculated and allowed on the sum originally assured, and on the vested additions thereto, and one, two, or three annual additions shall be made, according as the policies may happen to become claims in the first, second, or third year succeeding the investigation. 2. On policies which have had no vested additions, the rate per cent shall be calculated and allowed on the sum assured, and six, seven, or eight annual additions shall be made, according as the policies may happen to become claims in the sixth, seventh, or eighth year of their endurance; which contingent prospective additions shall be made out of that part of the surplus hereby appointed to be reserved at each investigation, and out of such surplus as may arise after such investigation, declaring, that whatever portion of the said sum may not be required for these prospective additions, shall form part of the surplus at the next investigation. That if any policies of five years' standing become claims on the society before 1st March 1841, the directors shall have power to make additions thereto, to an extent not exceeding two per cent on the amount assured for every annual premium which may have fallen due. This society .was instituted in 1832, and in 1840 the sums assured were £1,267,706; the annual revenue was £46,827; and the accumulated fund £118,900! ScoTTISH WIDOWS' FUND-MutualAssurance-Edinburgh, 1815.At last investigation of the affairs of this society, which took place on 31st December 1838, the profits were ascertained to be such, that the directors, after setting aside one third, in terms of the articles of constitution, as a guarantee for the stability of the institution, were not only enabled to declare a retrospective bonus of 14 per cent, or at the rate of 2 per cent per annum on the original sums insured, and on all bonuses that had been previously declared; but they at the same time ordered a sufficient sum to be retained out of the ascertained profits, to meet what is called the contingent prospective bonus, or an additional bonus of 2 per cent per annum to be paid on all policies that may happen to lapse or become claims upon the funds of the Society before the 31st December 1845, when the next investigation of the affairs takes place. The sum necessary to be set aside to meet this contingency was equal to about 32 per cent upon the original sum insured, added to the amount of the previously declared bonus. So that the free divisible profits of the society during these seven years, was 172 per cent, or 23 per cent per annum. LIFE ASSURANCE OFFICES.11 113 TABULAR VIEW of the amount of retrospective or vested additions on as at 1st January 1839, and of contingent prospective additions policies opened in the respective years, and for tbe respective sums undermentioned, according to the regulations of 1825, and the orders of the extraordinary courts of directors of ,13th January 1832, and 14th January 1839. ,, -,,, 11- - - Total SRetrospective YeAddf Sutio - 1815) to £1000 1819) 1820 3000 1821 3000 1822 3000 1823 3000 1824 3000 1825 4000 1826 4000 1827 4000 1828 4000 1829 4000 1830 5000 5000 1832 5000 1833 5000 1834 5000 *1835 5000 *1836 5000 * 1837 5000 *1838 5000 *1839 5000 *1840 5000 Sum payable Annual Contin- if decease take place gent Prospective after payment of Total Benefits the premium due Additions tin with Additions at from in 1845, being year 1st January 1839. eachs year 1845. preceding next 1839 to investigation. I *I-I 1I-1I £587 4 1035 984 933 881 830 1038 970 902 833 765 871 785 700 600 500 400 300 200 100 0 0 12 6 0 14 8 16 8 0 12 4 0 10 0 0 0 0 0 .0 0 0 0 £1587 4 4035 3984 3933 3881 3830 5038 4970 4902 4833 4765 5871 12 5785 5700 5600 5500 5400 5300 5200 5100 5000 5000 6 0 6 0 0 14 8 16 8 0 12 4 0 10 0 0 0 0 0 0 0 0 0 £31 14 10 80 14 3 79 13 9 78 13 3 77 12 9 76 12 3 100 15 8 99 8 0 98 0 8 96 13 4 0 95 6 0 0~ 117 8 4 0 115 14 2 0 114 0 0 0 112 0 0 0 110 0 0 0 108 0 0 0 106 0 0 0 104 0 0 102 0 0 0 100 0 0 0 000 0 0 0 0 0 0 0 0 0 £1809 8 7 4600 11 9 4542 4483 4425 4366 5744 5666 5588 5510 5432 6692 20 12 2 13 4 5 5 6 6 18 6 .19 0 S 0 8 0 8 9 6595 9 7 6498 6384 6270 6156 6042 5928 5814 5700 5600 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Every member has it in his option to commute not only his retrospective but also his contingent prospective addition. In the one case, if a party in January 1839, commute merely his retrospective bonus, and die previous to .the period of the next investigation in. December 1845, his representatives would still be entitled to a bonus of two per cent for each premium that might have been paid subsequent to 1st January 1839; or were he, after commuting his retrospective bonus, to survive 31st December 1845, there would, of course, be added to his policy a bonus applicable to these seven years. But, on the other hand, supposing he were to commute both retrospective and contingent prospective additions, if he die before 31st December 1845, his representatives will be SThe order for additions made to the policies in the above table will become ipso facto vacated if the parties assured die within five years from their respective dates. t The amount of these additions in their present value, was fully provided for out of the actual divisible surplus ascertained at 31st December 1838, and therefore depends in no degree on any assumption ofprofits or surplusfunds during the current septennial period. x 114 LIFE ASSURANCE OFFICES. entitled to no bonus whatever ; whilst, if he survive that date, he will still be entitled to a bonus for the seven years just expired, in the same manner exactly as he would have been if no commutation of his contingent prospective addition had taken place, for the value put upon them is just the value of the contingency of the party dying within the seven years; and if he survive the seven years the contingency is at an end, and the party has derived a benefit from having run the risk of losing his bonus altogether for that period. The future bonuses are not affected by the commutation of those previously declared, as the future additions are calculated according not only to the sum contained in the policy, but also to the amount of the already declared bonus, whether these have been commuted or not. The directors are empowered to lend money to members on the security of their policies to the extent of nine-tenths of their value, provided such value be not less than £50. The effect and extent of these loans may be judged of by a reference to the following tabular view, from which it will be seen that a person who insured his life in 1815, for £1000, when he was twenty years of age, might now, in 1840, borrow a sum of £480, being very nearly equal to the actual amount of premium which he has paid. TABULAR VIEW, showing the effect of the Additions made to Assurances, and the Sums which may be borrowed on the Security of Policies opened as undermentioned. of Entry. Year Age at Entry. 2 F0 Sum which may be had Originalby way of ignal Advance or Assured. Loan, on Deposit of Policy. In 1840. Equivalent Annual Deduction from future Premiums, if Additions be so commuted, in terms of the Regulations. Original Premium. Amount Deducted. Future Annual Premiums. 1825 1830 £480 590 750 900 1030 £20 25 32 44 62 15 10 15 3 13 0 10 0 4 4 FWholly extinguished, and a farther Surplus to be otherwise appropriated j to the benefit of the AsL sured. 120 30 40 50 L60 3000 3000 3000 3000 3000 920 1150 1430 1830 2310 62 76 98 132 188 5 12 5 10 0 0 6 0 0 0 4000 4000 4000 4000 4000 870 1100 1370 1740 2290 83 0 102 3 131 0 176 13 250 13 0 4 0 4 4 £36 1 4 £26 3 8 28 5 6 48 7 0 30 1 1 68 3 11 25 9 4 107 0 8 Wholly extinguished, &c. (same as above.) 50 7 2 32 12 10 59 9 6 42 13 10 72 8 0 58 12 0 90 8 0 86 5 4 145 13 4 105 0 0 F20 1820 £1000 1000 1000 1000 1000 F2 0 1815 30 40 50 60 5000 5000 5000 5000 5000 700 880 1110 1400 1880 103 15 0 127 4 2 163 15 0 220 10 8 313 6 8 30 40 50 60 30 40 50 60 25 12 32 13 43 16 6116 97 0 2 10 9 6 10 78 2 10 95 0 4 119 18 3 159 0 2 216 5 10 LIFE ASSURANCE OFFICES. 115 SCOTTISH AMICABLE--Glasgow---Mutual Assurance.-This Society was established only a few years ago ;and at the first investigation on 31st December 1832, a bonus of one and a-half per cent per annum was declared upon the sums assured, or from 24 to 72 per cent upon the premium paid, besides reserving one-third of the profits then ascertained to be added to the general funds of the society for the exclusive benefit of the assured. At the second investigation of the affairs of the society, which took place 31st December 1839, the directors declared a further bonus or retrospective addition of one and a-half per cent per annum on the accumulated amount of the benefits as they stood at 31st December 1832, as well as on the policies opened with the society since that date; and the directors then also declared that a prospective addition of one and a-half per cent per annum should be added to such claims as might emerge before the next septennial division in 1846. All these additions were made and provided for out of the surplus funds, after again setting aside considerably more than one-third directed to be reserved by the deed of constitution. ScoTTISH UNION--Edinburgh, 1824--£5,000,000.--Two-thirds of the profits are allotted at regular periods to the insured, without being subject to any deduction for charges of management. The first division will be made on 1st January, 1842. Two-thirds of the profits remaining, after providing for the outstanding risk of existing policies, and discharging all claims upon the profit fund, will be divided on the most equitable principles, in the proportion that each surviving person has contributed to that fund. A reversionary sum, equivalent to the present bonus will be added for the original sum insured; or a corresponding reduction will be made from the future annual payments, at the option of the parties insuring-to be declared in writing, at least three months before each division of profits. All contributions made by persons desirous of participating in the profits will be kept totally distinct from the other branches of the business of the incorporation; and every person entitled to participate will be permitted to examine the accounts of the company, relative to the profit fund, at their head-office in Edinburgh, during three months after each declaration of profit. ScoTTISH PROVIDENT - Edinburgh, 1838-Mutual Assurance.- The plan adopted by this society for dividing the profits is, that the surplus premiums are distributed among those members whose premiums created the fund for division-that is, the surplus is left entire for those members who survive the period at which their accumulated premiums amount to the sums in their policies. The ultimate effect of this mode of division may be illustrated by the following example :-Let it be assumed that 100 members, all of the age of 25, enter the society for an assurance of £1000, paying each such a rate of premium as will take 25 years to amount to the sum assured, and that one out of the hundred will die in each of these 25 years; assume further, that the profits are such as would afford a yearly bonus of 1 per cent on the capital sumit is evident that, by the usual mode of distribution, the accumulated fund at the end of 25 years will be diminished by the amount of a progressive annuity of £15. The member who dies in the first year will 116 LIFE ASSURANCE OFFICES. take out £15; the one who dies in the second year, £30; in the third, £45; and so on, increasing each year in the same arithmetical proportion. Now, the amount of such a progressive annuity, at 4 per cent will be no less than £6850. If these bonuses, then, had been reserved, this is the sum which would remain at the end of these 25 years, to divide among the remaining (100-25 =)75 members, in addition to what they might otherwise receive. If the low premiums of this office had been employed, the effect would be seen to be still more favourable in proportion; while by the more equitable plan followed of allotting the shares of the members according to the values of their policies, and not by a fixed percentage on the capital sums, the share falling to a member of long standing will be still farther increased, so that the scheme may truly be said to resemble in its results those of an ordinary Tontine. The directors are bound, by the deed of constitution, to purchase policies of seven years' standing at their fair value, according to a table already prepared. All the assurances may be made by yearly, half-yearly, or quarterly premiums. No entry money is charged. STANDARD-Edinburgh, 1825.-The principle adopted by this company for the division of profits among its policy holders, is similar to that originally acted upon by The Equitable Society of London. An investigation of the company's affairs, and a division of profits, took place at 15th November 1835; a second falls to be made as at 15th November 1840, and at intervals of five years thereafter. Policy holders may have their bonus applied either as a reversionary addition to the sum assured, or towards reduction of the premium. This company has also a reduced scale of premiums for assurers who do not wish to participate in the profits, and premiums can be made payable in one sum, or annually, halfyearly, or quarterly. There is no restriction as to residence, or travelling within the limits of Europe. Onerous assignees to policies opened by persons on their own lives, when duly admitted by the company as the holders, are held to stand in an equally favourable situation as if they had been the original assurers. Policies for the whole term of life are purchased by the company at an equitable rate after three premiums have been paid. In redeemable annuity, and other similar transactions, parties are entitled on redemption to a policy to the extent of the sum advanced, at the rate of premium chargeable upon the life at the original date of the transaction. SuN-London.-On all policies insuring £100 and upwards effected before or after Midsummer 1837, the nett profits of the society, shall be divided equally between the proprietors and the assured; such division to be made at such periods and in such manner as may appear most expedient to the managers. At every septennial valuation, the next of which will be at Midsummer 1843, the profits apportioned to each policy, and on which not less than five annual premiums may have been paid, will be appropriated at the option of the holder, either-1. By a payment in present money. 2. By an equivalent augmentation of the sum assured. 3. By an equivalent reduction of the annual premium. 4. By granting a separate policy of a sum which, at the time the profits were appropriated, was just worth those profits in then pre- LIFE ASSURANCE OFFICES. 117 sent money. Provided that a written declaration of such option be left at the office of the society within three months next after the division shall have been declared; and if such option be not so declared, the sum previously assured by the policy will receive an augmentation equivalent to the profits such policy may be entitled to in then present money. UNIoN--1714.-The profits are divided every seven years; it being declared in the deed of settlement, that a division of profits shall be paid with the sum assured by policies made for the whole continuance of life in force, when such division shall be declared. This division to be calculated, not from the profits of the year only in which the death may happen, and upon the mere amount of premiums paid, but from the whole number of years each policy has been effected, and on the sum assured. UNITED KINGDo M--London, 1834-£1,000,000.-Two-thirds of the profits will either be added periodically to the sum assured, or applied in reduction of the future premiums. Premiums may be paid quarterly, half-yearly, or annually, as may best suit the convenience of the assured. When an insurance is for life, half the premium may remain unpaid for five years at interest, to be deducted eventually from the policy, or be paid off at convenience. UNIVERSAL-London, 1834--£500,000.-Persons assured with this society for the whole term of life, will be entitled to three-fourths of the profits after they shall have made five complete annual payments; the profits will be divided for the first time in May 1840; and in the same month in every subsequent year, a similar division will take place, the profits being estimated from the average of the Jive preceding years; thus, one year's average profits will be annually divided. Extensive tables have been calculated expressly for the Indian branch of the society, distinguishing the civil service from the military, and giving the option of paying the premiums in rupees in India, or in sterling money in England. UNIVERSITY-London, 1825.-A division of profits is made every five years, and four-fifths appropriated to the assured, either by'a diminution of the premium, or by an increase of the amount of the policy, at the option of the party. The total additions to policies made in the years 1830 and 1835 amount, on a policy for £1000, as follow :-If it has been effected seven years, to the sum of £120; seven years, £140; eight years, £160; nine years, £180; ten years, £200. VICTORIA-1838.-The directors will advance money in amounts, varying from £200 and upwards, either by way of loan, or on annuity, to persons assured in the office, who will be required to give approved security for the payment of the principal and interest. Persons, therefore, of character and respectability, requiring a temporary or a permanent advance of money, will find this a most advantageous and desirable mode of attaining such object; while, at the same time, the advantage of assuring for the whole term of life, at this office, is manifest from the 118 LIFE ASSURANCE OFFICES. circumstance, that, at any future period, a loan, although not required, nor perhaps even contemplated, at the time of effecting the policy, may, whatever should happen to be the state of health of the assured, be obtained at the rate of five per cent per annum, on condition of the borrower providing approved security for the principal and interest. WESTMINSTER-1792.-By a regulation taking effect from the 13th May 1835, this company propose to make positive additions of £5 per cent at the end of five years, and £1 per cent every succeeding year, to all sums insured on single lives for the whole term of life by policies issued after that date. WEST OF ENGLAND-1807.-Persons effecting assurances for £100 and upwards for the whole duration of life, will be entitled to participate in the future disposable surplus premiums, to be ascertained at the end of every fifth year, commencing from Christmas 1827. The surplus allotted to each policy may be applied in either of the following ways, at the option of the assured, viz. 1st, By adding such surplus as a bonus to the sum assured by the policy, to be payable at the death of the life; 2d, Only applying the amount thereof in the reduction of the annual premiumn ; such option to be signified within three months after the surplus shall be declared. YORKSHIRE.-Has tables for assuring the lives of males and females respectively. YORK AND LoNDoN--1834.-This company have avoided the introduction of ascending and descending scales; the system of giving credit upon a portion of the premiums; or the practice of accepting quarterly or half-yearly payments. If, however, parties making proposals of £1000 and upwards prefer such mode of payment, their wishes will be met on terms duly proportioned to the general table rate. The lives of persons subject to any disease not attended with immediate danger, will, on full proof of the nature and extent of ailment, be assured on equitable terms. DESCRIPTION OF RISKS IN FIRE INSURANCE, WITH THE RATES OF PREMIUM USUALLY DEMANDED THEREFOR, &c. FIRE INSURANCE. See Cartwrights. See Farm Stock. AGRICULTURAL IMPLEMENT-MAKERS. AGRICULTURAL PRODUCE. ALUM- WORKS, 3s. ANATOMICAL PREPARATIONS, APOTHECARIES. 3s.-4s. Gd. Is. 6d.-2s. Building. S. & S.,* Stock in trade, and utensils therein, that is fixtures, drugs, glassbottles, &c., 4s. 6d.-5s. Drugs, &c. 2s. Gd., or Glass bottles, 4s. 6d. Stock in sale shop, 3s. d. Clause." Warranted that there is no laboratory nor process for refining or drying camphor or saltpetre, or distilling turpentine; likewise, that no ether is drawn, nor spirits of turpentine, experiments, nor medicinal lozenges made." ARTISTS. See Sculptors.See Floating Policies, Ship-builders, 855. CLAUSE. AVERAGE BAKERS. Shop without oven, is. Gd. If the oven is within the house, S. and B., 2s. Gd. 63d. If in a thatched building, Sea biscuit bakers, 4s. Gd. BARK-MILLS, 2s. 6d. With steam-boiler, slated, stone, and timber, 5s. If driven by water, 2s. 6d. I7s. B ASKET-MAKERS. Sale shop, 2s. 6d.-workshop, 4s. Gd. BILLIARD-ROOMS, 2s. Gd. Gd. per cent. Some offices charged only Gd., stock, 2s. Gd. Building, BOOKSELLERS. Is. is. in a small scale, 3s. if bookbinding be carried on BOOKBINDERS. S. and B., 5s. Workshops having gas stoves only, 3s. BOAT-BUILDERS. With tar kettle, 4s. Gd., without do., 2s. Gd. BRASSFOUNDERS, 2s. Gd. BRICKMAKEB S. Without kiln, 2s. Manufactory, brick flues, and engine house, SS and S mean stone and statedbuildings-S and 5s.- Is. Gd. B signify stock and building. 122 FIRE INSURANCE. BROKERS, (Furniture,) 2s. 6d. BUILDINGS. Stone, and part wood, 2s. 6d. Stone and thatched, without chimneys, and not connected therewith, 2s. 6d. With chimneys, 4s. 6d. Building, during finishing, 2s. 6d. Stone, and thatched, and wood, 7s. 6d. Note.-Buildings not communicating must always have separate valuations. Abstract of an Act passed in the ninth year of the reign of his late Majesty George IV. " Be it therefore enacted, that from and after the fifth day of April, one thousand eight hundred and twenty-eight, in every case where any Insurance from Loss or Damage by fire shall be made or renewed or continued upon Two or more detached Buildings, or upon Two or more Buildings so separated from each other as to occasion a Plurality of Risks, or upon any Goods, Wares, Merchandize, or other moveable Property contained in Two or more such Buildings as above described, or lying or being in Two or more Places so separated from each other as to occasion a Plurality of Risks,) except the Implements and Stock upon any One Farm,) then and in any of the cases aforesaid every such separate Building shall be separately valued, and a distinct and separate Sum shall be insured thereon, and in like manner at least One distinct and separate Sum shall be insured upon the Goods, Wares, Merchandize, or other moveable Property contained in every such separate Building, or lying or being in every such separate place as aforesaid; and it shall not be lawful to insure One gross Sum upon Two or more such separate subjects or parcels of Risk as aforesaid taken collectively. " And be it further enacted, That if at any time after the said fifth day of April, one thousand eight hundred and twenty-eight, any Policy of Insurance shall be granted or renewed or continued, whereby any Insurance from Loss or Damage by Fire shall be made of or upon Two or more such separate subjects or Parcels of Risk as aforesaid collectively in One Sum, contrary to the true intent and meaning of this Act, such Policy of Insurance shall be void and ofnone efect, and shall be deemed and taken to be a fraudulent contrivance to evade the Duties by the said recited Acts respectively imposed; and the Person or Persons, or Body or Bodies politic or corporate, by whom or by which any such Policy of Insurance shall be granted, renewed, or continued, contrary to this Act, shallforfeit andpay the sum of One Hundred Pounds. "Provided always, and be it enacted, That nothing in this Act contained shall extend or be construed to extend to prevent the insuring from Loss or Damage by Fire collectively, in One Sum for the whole, any number of separate and distinct Buildings, or the Goods, Wares, Merchandize, or other moveable Property contained in any number of separate and distinct Buildings, or lying or being in any number of separate and distinct Places; provided that, in the Policy whereby such Insurance shall be made, there shall be contained a Clause stipulating that in the event of any Loss or Damage by Fire happening to such Property, or to any Part of such Property thereby insured, the Insurer or Insurers in such Policy shall be liable to pay or make good such Pro- FIRE INSURANCE. 123 portion only of the said Loss or Damage as the Sum insured shall bear to the whole collective Value of the said Property at the time when such Fire shall first break out or happen." BARLEY-MILLS. } With machinery, 5s. When connected with kiln, fire-proof. See Kilns. If kiln not fire-proof. Thatched, special. BLOCKMAKERS, 2s. 6d.--4s. 6d. BLACKMAKERS, Is. 6d. BLEACHERS OF CALICO. Building, stone and slated or tiled, having steam-engine with furnaces 6d. Band brick flues, 10Os. Boiling house apart, 2s. 6d. Building of stone or brick with tile or slated roof, and warranted that no unenclosed lights be used therein, heated by stoves with horizontal pipes, 12s. 6d. 1st. If heated by steam only, boiler outside, 7s. Gd. do. inside building, 10s. 6d. 2d. If heated by common fire places, or by metal pipes, not being more than two feet in length, the cockles or stoves of which stand on brick or stone hearths, surrounded by fixed fenders, 12s. 6d. 3d. If heated as above, but the pipes more than two feet, which must be specified, 15s. See Drying Stoves. BREWERS. Brew-house, malt-barn, tun-room, connected with kiln, fire proof, 5s. The above connected with kiln, not fire proof, 7s. Gd.; 10s. 6d. All the buildings and stock not connected with kiln, 3s. BLACKSMITHS, is. 6d. If connected with a wright's shop, stone and slated, 7s. 6d. If thatched, 10s. 6d. BARGES, 2s. 6d. BACON CURERS, 3s. CORNMILLS. Worked by wind or water without kiln, 7s. 6d. 6d. With kiln communicating, O10s. 6d. Worked by steam, without kiln, O10s. With kiln communicating, 15s. Clause.-" Warranted not to have more than two pair of stones wrought at one time." is. per cent for every pair of stones additional. 2s. per cent if oats are shelled in the mill. SPECIFICATION. Building. Millwright's work, &c. Stock in trade. Steam-engine. 6d. should Note.-The rate of O10s. kiln is of the best construction; 1. 2. 3. 4. 5. Kiln. 6. Stock therein. 7. Kiln adjoining. 8. Stock therein. apply only to a mill where the the kiln fire being exterior to 124 FIRE INSURANCE. 124 the mill walls, and the party wall going through the roof. In cases where the mill and kiln are under the same roof the kiln fire being within the mill walls, or when the kiln is heated by the burning of oat shellings, 15s. ought to be charged. COACLIMAKERS, S. and B., 5s. If adjoining smith-shop, &c., 7s. Gd. Warranted that no oil boiled, gold size, turpentine, or varnish, is manufactured on the premises." CORKCUTTERS, S. and B., 2s. sale shop, Is. burners, 4s. Gd. CALICO PRINTERS AND DYERS.-See Drying Stoves. COOPERS. Building and stock, stone and slated, no stove, 2s. Gd. Stone and wood, 4s. Gd. Stone and slated, with stove, 5s.; 7s. Gd. Thatched, no stove, 12s. d. Thatched, with stove, 15s. Clause.-" 6d.; CART AND 6d.; WHEELWRIGIHTS. With stove, S. and B., l1s. Gd. Without stove, 5s. CALENDERERS, 3s.; with steam-engine, 5s. .Note.-Building, machinery, and stock, (the latter usually in trust,) are subject to the same premium. The processes generally car. Tied on, are-calendering, lapping, hot-pressing, and packing. Furnaces are required for heating the iron cylinders, which are made red hot. Ovens are also used for heating iron plates for hot-pressing. COLOURMEN, 2s. Gd. Clause.-",No oil boiled, nor turpentine nor varnish made in the premises." CONFECTIONERS, no stove, 2s. d.; with candy stove, 4s. Gd. CARTGREASE-MAKERS, s. d. CARVER AND GILDERS. Sale shop, with glass, 4s. Gd. ; prints and drawings, 2s. Gd.; framemaker's shop, no stove, same as Elabinetmakers. CURRIERS. Sale shop, is. Gd. Workshops, drying shades, having stoves, stone or brick and timber, 4s. Gd. Scouring house, 2s. Gd. CURIOSITIES, natural and artificial, 4s. Gd. COWFEEDERS, 2s. Gd. ; with boilers inside of byre, 4s. Gd. CHEMISTS. See Laboratories. CHINA, 4s. Gd. COPPERPLATE PRINTERS. No stoves, 2s. 6d. ; with stoves, 4s. Gd. Gd.; workshop, with small forge, 2s. Gd. CUTLERS.-Stock, CANIDLEMAKERS. is. Stock in shop, 2s. Gd. Workshop, boiler- heated inside of building, 4s. Gd. Do., boiler heated outside, 3s. Clause.-",No rough tallow allowed to be melted." FIRE INSURANCE. 125 CABINETMAKERS AND WRIGHTS. Workshop built of stone, no pipe stove, 5s. Do., with stoves, 10s. 6d. Stove for drying wood and feathers, 21s. With stove thatched, 12s. 6d. Without stove, 7s. 6d., 10s. 6d. All timber having a brick flue, 15s. Note.-The premiums for these very hazardous risks are regulated by the number of stoves, and length and direction of pipe. JOINER SOCIETIES, 15s. Clause.-" Tools and tool-chests, belonging to all or any of the members of said society, whose names and value of whose tools and tool-chests shall be inserted in the register of said society, in all or any of the workshops, or their dwelling-houses in Scotland, in which stoves may or may not be used therein; and the value of the same in all cases of loss or damage by fire, shall be proved by the register kept by the society, a copy of which is lodged with this company." CHANDLERS. Wax or tallow chandler's workshop, 5s. Ship chandlers, 2s. 6d. CLOCK AND WATCHMAKERS, 2s. 6d. CARPET MANUFACTURERS. Dye-house, with stoves, Stuff-house, weaving-rooms, warping and bussing-rooms, stove-house with twine-mill, having cast-metal pipe, 10s. 6d. Brimstone stove-house, 10s. 6d. Looms in workshop, 3s. Woollen dying-house, brick stoves with pipes, 7s. 6d. CoINs, 4s. 6d. COTTON MILLS. Built of stone or brick; Heated or wrought by steam, or driven by water, the fire for heating the boilers being outside of the mill. Lighted by gas, no deviling, blowing, or batting by unenclosed artificial light therein, 14s. When lighted by lamps or candles, those in carding-room being enclosed by glass and the fire of the steam-engine inside of the mill walls, 18s. When heated by rarefied air from stove with upright metal-pipe enclosed in brick, the whole apparatus being outside the mill walls, 17s. Clause.-" Warranted that no night work shall be performed in the mill above described by a double set of hands or workers, without leave having been obtained from this office, and a suitable extra premium having been paid for same, with the exception of repairing the machinery, which is allowed without extra premium." COTTON WooL, S. & B., no fires, 2s. 6d. Clause -" No cotton waste allowed in the store." DISTILLERIES. Buildings, stock in trade and utensils, still-house, mash and ferment 126 FIRE INSURANCE. ing tubs, malt mill with rollers, malt kiln, fire-proof boilers, and other apparatus, adjoining and communicating, 10s. 6d. Stock, and in detached buildings, 3s. Highland distilleries not being generally so well built and constructed as those in the Lowlands, are therefore more hazardous; and 20s. per cent and upwards is usually demanded for such risks. DRAWINGS, 2s. 6d. With glass frames, 4s. 6d, Drawings and paintings, when above £20, should be catalogued, and a separate value put on each. DYERS OF WOOLLEN AND STUFFs.-See Drying Stoves. DRUGGISTS.-See Apothecaries. DRYSALTERS, 2s. 6d. DRYING STOVES. General Observations.-1. Drying stoves not conformable to any of the following descriptions, can be insured only upon special agreement. 2. No drying stove is deemed insurable, unless the precaution is taken of enclosing the lights therein in glass. 3. In no case is it permitted to expose goods to dry in any way, in the chamber or apartment under a trellised or metal floor; and such a practice will make void the policy. 4 No loose Cotton, Sheep's Wool, Hemp, or Flax, will be allowed to be dried in any stove insured under this Table; such insurances can only be specially granted 1. All lights to be enclosed. 2. No goods to be dried under incombustible floor. 3. No loose cotton, wool, &c., to be dried. First Class.-5. Stoves heated by Steam only, conveyed into them by pipes, the boiler being outside the building. 10s. 6d. per cent per annum. 6. The same stoves, the boiler being within the building, 12. 6d. per cent per annum. Second Class.-7. Stoves heated by Fire, fed from the outside of the building, and the heat communicated through brick flues in the nature of a hot-house flue, or through strong metal pipes, having an entire trellisedfloor of metal, or perforated tiles, at a height of at least four feet above such flues or pipes, 25s. per cent per annum. 8. Ditto, fire not fed from the outside, 42s. per cent per annum. Third Class.-9. Stoves heated by fire, fed from the outside of the building, and the heat communicated as in the Second Class, but not having the precaution of an incombustiblefloor as in that Class, 42s. per cent per annum. 10. Ditto, fire not fed from the outside, 52s. 6d. per cent per annum. 11. Turkey red stoves. From the frequent accidents experienced in these stoves in Scotland, they will there be charged 21s. per cent extra, according to the Class to which they may respectively belong, 12. Padding stoves, 21s. per cent per annum. Warranted not to be answerablefor goods damaged under process of padding. 127 FIRE INSURANCE. 13. Fustian dressing stoves, or singeing stoves, 42s. per cent per annum. Warrantednot to be answerablefor goods damaged under process of singeing or dressing. 14. Sizers' drying stoves, 84s. per cent per annum. Drying Stoves Jbr Woollen Cloth.-15. Drying stoves for woollen cloth only on tenters, heated by steam, 7s. 6d, per cent. 16. Ditto, heated by brick flues or strong metal pipes, not less than 18s. per cent. Calico Printing Shops.-First Class.--17. Calico printing shops, heated by steam only, the boiler being outside the building, 7s. 6d. per cent per annum. 18. Ditto, the boiler being within the building, 10s. 6d. ditto. Second Class.--19. Calico printing shops, heated by common fire places, or by brick flues, or by metal pipes not being more than 2 feet in length, the cockles or stoves of which stand on brick or stone hearths, surrounded by fixed fenders, 12s. 6d. per cent per annum. Third Class.-20. Calico printing shops heated by brick flues or metal pipes more than 2 feet in length, the length of such flues or pipes to be specified, not less than 15s. per cent per annum. Instruction to Agents.-21. It is desirable that a particular and clear description should be given of the construction of every drying stove, and a personal inspection made, if near at hand, to see that the flues, pipes, and heating implements are sound, and kept in good condition; and the lights all enclosed, as required by the regulations. 22. In sending an order, it should refer by number to the article in the above regulations, which describes the risk-pointing out any deviation. 23. The agent's attention should be particularly drawn to the general observation above, requiring in ALL cases-enclosed lights; the exclusion of goods from under the incombustible floor described in the second class, even in the case of fustians; and the prohibition of drying loose cotton, woollen goods, &c. 24. No existing Policy can be renewed, nor fresh Policy issued, but at the above rate, and subject to the new regulations. 25. Risks adjoining to drying stoves, necessarily partake of their hazard, but the varieties under which such risks present themselves, preclude the possibility of laying down an absolute rule for rating them. In every case, however, some extra charge will be made. 26. Cases not comprehended in these arrangements, and particularly the process of drying loose cotton, &c., are either deemed uninsurable, or must become the object of special contract. 27. The following will be the form of stating an insurance upon a drying stove:" On the Building of a Drying Stove for in the above warrantedconformable to Article No. Table. No unenclosed Lights ; no Goods placed to dry under the incombustible Floor (if there be one); nor any loose Cotton, Sheep's Wool, Flax, or Hemp, dried therein, " On Utensils and Stock therein, - £ £ " 128 FIRE INSURANCE. DYERS, (common, in town.) Stone, and slated, 2s. 6d. Partly timber, 3s. Thatched, 5s. DUTY per cent, payable annually to Government, in great Britain, (Act 55 Geo. III.), 3s. The duty in Ireland is 2s. 8d per cent. The duty is chargeable on any fractional part of L.100, the same as on the L.100; but for short period insurances, it is charged for the actual proportion only of the yearly, that is, ls. 6d. per cent for six months, Is. per cent for four months, and 9d. for three months, and so on. No.duty chargeable on public hospitals. Charitable institutions, other than public hospitals, are not exempt. Farm stock, comprehending crop, implements of husbandry, and live stock on the farm, are duty-free by Act of the 3d and 4th Will. IV. Goods in foreign kingdoms, and in amity with her Majesty, are also exempt from duty. Duty on each policy in Great Britain, is. Renewal receipts for premium only. EARTHENWARE, 4s. 6d. ENGINE AND MACHINE MAKERS, 5s., 7s. 6d., 15s. ENGRAVERS, with stoves, 2s. 6d., 5s. FARM STOCK, &C. Farm dwelling-house, slated, and detached, 2s. If thatched, 5s. Offices with stock therein, S. and S., 2s. 6d.; if thatched, 3s. Stock standing in barn-yard, for the year, 2s. 6d. Ditto, for shorter period, 2s. Ditto, within risk of steam-engine, 4s. 6d. Note.-Farm-stock and crop, whether housed in slated, tiled, or thatched offices, or elsewhere on a farm, may be insured without specification, or in cumulo without the average clause at 2s, per cent per annum; if with the average clause, Is. 6d. FLAX-MILLS. Built of stone or brick, slated or tiled, heated or wrought by steam, or driven by water, with fire outside the building, lighted with gas, and warranted that there be no heckling, or dressing of flax, or carding of tow, by unenclosed lights therein, 16s. With carding of tow, 18s. And heckling, 20s. Note.-Fire-proof mills are charged only half these rates, but if heckling be carried on in upper flat, the mill is not to be considered fire proof. Some offices demand the following premium on building and on stock Buildings. When no carding or heckling . With carding, With heckling, . . . . . . 0 14 0 16 0 18 Stock. 0 0 16 0 0 0 0 18 0 20 0 0 FIRE INSURANCE. 129 F LAX-DRESSERS. Having no artificial light, 5s. If lighted from without, 7s. 6d. If lighted from within, 10s. 6d. FLAX in WAREHOUSES. Having fire-places well secured, S. and B., 4s. 6d. If there are no fire places, 2s. 6d. FLOATING POLICIES, 2s. 6d. General insurances on merchandise or on the floating stock in trade of manufacturers in different places, may be covered under one sum, specifying the places to which such insurance is to extend; subject however to the conditions and stipulations of the following AVERAGE CLAUSE. " It is hereby declared and agreed, that in case the merchandise (or stock in trade) aforesaid, belonging to the above assured, or held by him in trust or on commission, (if so declared) in all or any of the buildings or places described in this policy of insurance, shall, at the breaking out of any fire or fires be collectively of greater value than the sum assured thereon, this Company shall pay or make good to the assured, only such a proportion of the said loss or damage as the sum assured shall bear to the whole value of the goods aforesaid, at the time when such fire or fires shall first happen." EXPLANATION OF THE AVERAGE CLAUSE. If a merchant has goods in various detached warehouses worth L.10,000 when a fire happens, and he is assured for only L.5000, and his loss is estimated at L.1500, the Company will have to pay only a proportion of such loss. As L.10,000 : L.5000 : : L.1500 5000 X 1500 -1 00 L.750, ans. 10,000 FOUNDERIES. Founderies, smithy, mould-room, blast furnaces, forge in smithy adjoining and communicating, 5s. FLOOR-CLOTH MAKERS. Working premises, 4s. 6d. FISH CURERS. Smoking house, Cooper's shed, under one roof, B. and S., 4s. 6d. FLOUR-MILLS Driven by water, three pair of stones worked, no kiln communicating, 10s. 6d. FIRE. Any person convicted of setting fire, through carelessness or negligence to any house or building, &c., is liable to a fine of L.100. GAS LIGHTS. When gas lights are used, the greatest care should be taken to keep the flame sufficiently distant from timber or any combustible matter. I 130 FIRE INSURANCE. GRANARIES, communicating with Kilns.-See Kilns. GLUE-MAKERS. Stock and building, stone and slated, 3s. GOLD-EATERS, S. and B., 2s. 6d. GOLD SIZE-MAKERS, S. and B., 7s. 6d. GLASS, 4s. 6d. GLASSWORKS, 5s, GUNSMITHS, ls. 6d. With warranty same as ironmongers. GROWING WOODS. See Timber. GooDs, &c. in various places, belonging to one person, or held in joint trust, or in copartnership, may be insured in one policy, but a separate value is required to be put on each building, and the same on the furniture and goods therein; otherwise in terms of the act 9, Geo. IV. cap. 13, the policy will be null and void, and the insurers liable to a penalty of £100. HEMP in warehouses, 2s. 6d. HE MP-DRE SSERS, Stock in workshop not lighted, 2s. 6d. If lighted, 4s. 6d. HOT-HOUSES, 4s. 6d. HOT-PRESSERS. See Calenderers. HAT MANUFACTURERS, Sale shop, is. 6d. Manufactory, S. and B, 2s. 6d-10s. 6d. HERRING-CURERS, S. and B., 2s. 6d.-4s. 6d. HECKLERS, Heckling house, no stove or artificial light, 7s. 6d. With stoves, and lighted from without, 10s. 6d. Do. lighted within, 15s. HOTELS, 2s. 6d. HOUSEHOLD FURNITURE, wearing apparel, bed and table-linen, printed books, plate, and liquors in private use, are insured in one sum, under the general denomination of household-furniture. Some offices, how. ever, exclude " printed books" and " wearing apparel," unless specified in the policy. INDORSEMENTS.-Indorsements on fire policies become necessary when the party assured ceases to have any interest therein by sale or conveyance of the property, by removal of household furniture, goods, &c. from one place to another, or when an additional insurance is effected on the subjects mentioned in the policy with another office, &c. This should be particularly attended to, because in all cases where such indorsements are not regularly applied for, and entered in the company's books, the insured will not be entitled to recover in case of loss. It should also be particularly observed, that the total sum assured can neither be increased nor diminished by indorsement, such being strictly prohibited by Act of Parliament; but the premium may be altered as circumstances may occur, and in this case the future annual premium should be written in the indorsement in words at length. FIRE INSURANCE. 131 FORMS OF INDORSEMENTS. 1. Removal of Property.-Theproperty insured by this policy is now removed, (or the 1st, 2d, or 3d article of the policy, as the case may be,) to his new dwelling-house, stone or brick built, and slated or tiled, situated No. 19, Rutland Square, in the city of Edinburgh where the same only is insured. 2. Transferoflnterest.-- The interest in this policy is now transferred to A. B. of ; he or she having right thereto (by purchase, or as heir, as the case may be.) 3. When a Joint Insurance is effected with another Office on the same Property.-One thousand pounds being insured on the within property (or on the 1st, 2d, or 3d articles within mentioned, as the case may be,) in the office, the same is hereby allowed and agreed to; and, in case of loss, each office shall pay its rateable proportion thereof. 4. In case of an Alteration in the Building Insured.-The within insured having opened a communication with the next adjoining house, (or other building, stone or brick, and slated or tiled, and no hazardous trade carried on therein,) it is hereby agreed that this policy shall extend to and cover the same in both houses so adjoining and communicating with each other, and not elsewhere. INNKE EPERS. Stone and slated, 2s. 6d. If stone and thatched, 5s. 6d. Clause.--" Not more than 12 lbs. of gunpowder allowed to be kept in shop, and the company not liable for loss, &c., by explosion." IRONMONGERS, Is. JEWELLERS. Sale-shop, or work-shop, stone and slated, the latter with stoves, furnaces, is. 6d.-2s. 6d. Stock, all over, 3s. If specified, For stock of Jewellery, 4s. 6d. Plate and plated goods, 2s. Clause.-" That diamonds, pearls, and other real jewels, shall only be held to be included, provided they form part of articles of stock actually manufactured, and provided in case of loss, no single manufactured article of which diamonds, pearls, or other real jewels form a part, be valued at more than £ ," not exceeding £30. JAPANNERS.-Workshop, 10s. 6d. KILNs.-The premium for Kilns depend entirely on their construction and mode of heating. The following rates are generally required:1. Built of stone or brick, slated or tiled, the bedding of perforated iron or tile, supported by iron or stone joists, and heated by coal or cinders, calledfjire proof, 3s. Heated by peat, 5s. 2. If the joists or supporters are of wood, 5s. If the above are heated by the burning of oat-shellings, 10s. 6d. 3. If kiln, having wooden joists, is covered with hair-cloth, 7s. 6d. FIRE 132 132 INSURANCE. 4. Bedded with straw, under hair-cloth, 1 6 s.-21s. The two last uninsurableif heated by oat-shellings. 5. Kiln called enclosed, constructed internally with lath and plaster, and bedded with iron, 7s. 6d. 6, Do. if bedded with hair-cloth, 10s. 6d. Do. bedded with straw, uninsurable. LINT-MILLS and SKUTCIIING.MILLS, 15s. If without fire or stoves, or flues, and driven by water, 7s. 6d. LATHSPLITTERS. Without stove, S. and B., 2s. 6d. With stove, 5s. LEATHER-DRESSERS, 2s. Gd. LABORATORIES, 10s. If tallow melted, 4s. 6d. Gd. With distillation, 12s. Gd. LAPIDARIES, is. 6d. LooMs. When not connected with any part of the macbinery, and when on looms only, 2s. Gd. LAMP-BLACKMAKERS, 5s. Some offices decline this risk. LACE-MAcHINE-MAKERS, 5s. LABOUR. Note. This applies to printers who may insure the value of the labour of compositors put up in types standing in forms. The premium will be the same as for the risk of stock in trade, &c. LAPPERS (Cloth,) is. Gd. hot-pressing allowed. Losses by fire from lightning made good. LIGHTNING. LONDON.-Buildings and goods in the waterside districts, from the Tower to Limehouse, and on the opposite shore, are, on account of the additional hazard in those places, charged one class higher-that is, hazardous, as doubly hazardous-than such buildings, &c., would be rated in other situations. No MACHiNEMAKERS, MILLWRIGHTS, 7s. 5s.-7s. Gd. Gd. 6d1-i0s. MALTSTERS. Having no kiln, 3s. Do. fire-proof. Do. not fire-proof.f See Kils MUSICAL INSTRUMENT-MAKERS, Having stove, S. and B., MUSIOSELLERS. Stock in sale-shop, jis lOs. Gd. 15s. Gd. 2s. Gd. MEDALS, 2s. Gd. MINERALS, 2s. Gd. MUSEUMS, 2s. Gd. MANsIONHOUSES, 2s. MUSLIN GOODS IN WAREHOUSE, 2s. MEAL MILL AND MACHINERY, with MONEY, not insurable. MILLS, cotton, silk, &c. Kilns. See Kilns. FIRE INSURANCE. 133 REMARKS. 1. Every proposed insurance on any of the several descriptions of mills to be accompanied by a sketch or outline of the ground-plan of the premises, stating the relative distances of the several buildings, the situation of stoves if so heated, and the length and direction of the pipe leading therefrom to the chimney. 2. If there should be any peculiar circumstances, either of danger increasing the risk of fire, or of precaution in precluding the probability of its occurrence, the agent ought to state his opinion, accompanying the order to the office; and in all cases of insurance on mills, to answer every question in the printed form of mill questions supplied by the Company to him; the particulars of which are given below. 3. In every kind of insurance, a separate sum must be affixed to each separate building, or division of building, although adjoining and communicating; and a separate sum on the several items in each of the said separate buildings or divisions of building. 4. The specification or form of words adapted to the different kinds of mills, &c., must be invariably adhered to in orders for insurance. SPECIFICATION. 1. Sum on the building. 2. On the steam-engine. 3. Millwrights' work, including all standing and going gear. 4. Clockmakers' work, carding and breaking engines mounted and in use, and all moveable utensils. 5. Stock in trade, including only the article in its rough state, under process or manufactured. 6. Unfinished mill-work machinery, and such articles as are dismounted wanting repair, repairing, or otherwise not in use. Any separate buildings, as well as their contents, must be specified by themselves State what other insurances on the above property in this or any other office ; also in which office the plan is lodged. EXPLANATION of PHRASES in INSURANCES on MILLS. Millwrights' Work.-The principal wheels, all shafts movements, drums and gears, by which any carding, stubbling, spinning, or other small machinery is set in motion. Clockmakers' Work. - Spinning frames, with the spindles mounted thereon, carding machines, with the cards affixed, and the apparatus of all other kinds of hand-spinning, as mules, roving, spinning, carding, slubbing or scribbling machines. Moveable Utensils.-The utensils insured under this head are such as are not fastened or attached to any of the frames or machines, namely, lamps, weights, brooms, shovels. NURSERY and SEED-SIHOr, S. and B., ls. 6c NET MANUFACTURERS, S. and B., Is. 6d. Heckling-house, 4s. 6d, OIL, boiled from blubber, S. and B., 5s, 134 FIRE 134 INSURANCE. OIL-DEALERS, 3s. Warranty.-No oil boiled, &c. OIL LEATHER-DRESSERS, 3s. OIL MILLS, (seed crushing) 15s. OIL of VITRIOL, 4s. Gd. OPTICAL INSTRUMENTS, 2s. 6d. PRINTERS, 5s. SPECIFICATION. 1. Building. 2. Printing materials. 3. Labour, that is, types standing in forms. 4. Property in trust. PAINTERS, 2s. Gd. Clause.-" Warranted that no oil is boiled, gold-size, turpentine, or varnish is manufactured in the premises." PERFUMERS. Working premises or preparing room, 5s. POTTERIES. Having kilns communicating with workshop, and printing shop, 5s. PAINTINGS, &c., 2s. 6d.-4s. 6d. Note.-When the sum is large, a catalogue to be lodged in the office, and the Company not liable for more than the sums specified on each picture or print. PEARLS AND TRINKETS, 2s. d. PLUMBERS, 2s. 6d. PUBLIc-HOuSEs, 2s. Gd. PUBLIC LIBRARIES, 2s. Gd. PLANEMAKERS.-See Cabinetmakers. PRINTING INK MANUFACTORY, 3s. Clause.-" No oil boiled in the premises." PHILOSOPHICAL INSTRUMENTS, 2s. 6d. POWER-LOOM FACTORIES, 5s. PAWNBROKERS, 5s. Clause.-" It is hereby declared and agreed to, that in case of loss or damage by fire, this company shall pay or make good to the assured the sum advanced on each pledge, with the legal interest due thereon, which shall be proved by the books of the assured required to be kept by Act of Parliament, if not destroyed by fire." PAPER MILLS. When the process of manufacture is carried on exclusively by steam, boilers and furnaces outside mill walls, 5s. If on the old construction, having stoves with flues, 21s. Mills on the old construction have the pulp-vats heated by iron pots, the paper made by hand-frames, and dried on lines in a stove-room heated by iron or brick flues. The modern papermills are worked entirely by steam, using the new patent machine. Paper-mills are termed white-mills, brown-mills, or colour-mills. Brown-mills are inure hazardous than white, in conisequence of the quantity of flax waste used in the manufacture of brown 135 FIRE INSURANCE. paper, and from the quantity of the article being kept in the building. Where coloured paper is made, coppers with furnaces are required for the process of dyeing. POLICIES.-When the sum insured does not exceed £300, 2s. is usually charged for the policy, besides the old rates of premium, that is, 2s., 3s., and 5s. per cent. PIPE STOVEs.---The stoves used are of various descriptions, such as, warm-air stoves; stoves with descending flues, or with horizontal pipes running into the chimney. The pipes or flues should be free from wood work, and the stoves placed on stone. Stoves being much used in places of public worship, shops, warehouses, &c., if not properly secured, are the cause of numerous fires. The clause in the Act of Parliament, 14th Geo. III., requires that no pipe stoves shall be fixed inside any building nearer than fburteen inches to any timber or combustible material whatever. Stoves should stand either on iron plates or stone slabs. PREMIUMS PAYABLE.-In Scotland the premiums are paid for annual insurances at the respective terms of Candlemas, Whitsunday, Lammas, and Martinmas; and in England the quarter terms are Ladyday, Midsummer, Michaelmas, and Christmas; but should an insurance be proposed which is to continue from year to year, during the interval of any of the quarters, odd or additional time will be charged by the Office over and above the annual premium and duty. RULE for calculating the premium: multiply the sum to be assured by the rate of premium per cent, and divide the product by 100, the quotient will give the answer. RULE for finding the duty : multiply the number of L.100 by .15, and the product is the duty, which, added to the premium, gives the full expense. What is the expense of assuring L.1870 for one year, the premium being 5s., and the duty 3s. per cent ? 1870 x .25 100 19 X .15 - 4.675 or L.4 13 = 2.85 or The total expense is . 2 17 L.7 10 6 = premium. 0= duty. 6 The sum to be insured is multiplied by .25, being the decimal of 5s.; and the duty by .15, the decimal of 3s. The latter is calculated on L.1900, because fractional parts pay the same duty as L.100. 136 FIRE INSURANCE* 136 TABLE-showing the number of weeks to be charged from any given time, to the Quarter-day then next following. CANDLEMAS, 29 to Dec. 5, 6 to 12, 13 to 19, 20 to 26, 27 to Jan. 2, Jan. 3 to 9, lO to 16, 17 to 23, Dec. SCOTCH TERMS. L AMMAS, AUG. 2. FEB. 9 Weeks. 8 do. 7 do. 6 do. 5 do. 4 do. 3 do. 2 do. ~IM~I June 2 to June 8, 15, 9 to 22, 16 to 29, 23 to 30 to July 6, 13, July 7 to 14 to 20, MARTINMAS, 1. 8 Weeks. 7 do. 6 do. 5 do. 4 do. 3 do. 2 do. Nov. 11. WHITSUNDAY, MAY 25. Feb. 20 to Feb, 27, 28 to Mar. 5, 12, Mar. 6 to 19, 13 to 20 to 26, 27to April 2, 9, April 3 to 10 to 16, 23, I7 to 24 to 30, 11 Weeks. 10 do. 9 do. 8 do. 7 6 5 4 3 2 do. do. do. do. do. do. Aug.19 to Aug. 26 to Sept. Sept. 2 to 9 to 16 to 23 to 30 to Oct. Oct. 7 to 14 to 21 to 25, 11 Weeks. 1, 10 do. 9 do. 8, 8 do. 15, 22, do. 7 do. 6 29, 5 do. 6, do. 4 13, 20, do. 3 do. 2 27, ENGLISH TERMS. LADY DAY, MARCH 25. From December 26th to January 6th, charge from Christmas. Jan. 7 to Jan. 13, 11 Weeks. 20, 10 do. 14 to 27, 9 do. 21 to 8 do. 28 to Feb. 3, 7 do. 10, Feb. 4 to 6 do. 17, 11 to 24, 5 do. 18 to 4 do. 25 to Mar. 3, 10, 3 do. Mar. 4 to 2 do. 17, 11 to MIDSUMMER, JUNE 24. From March 26 to April 7, charge from Ladyday. April 8 to Apr. 14, 11 Weeks. 21, 10 do. 15 to 9 do. 28, 22 to 8 do. 29 to May 5, 7 do. 12, May 6 to 6 do. 19, 13 to 26, 5 do. 2Oto 4 do. 27 to June 2, 3 do. 9, June 3 to 10Oto 16, 2 do. MICHAELMAS, SErT. 29. From June 25 to July 13, charge from Midsummer. July 14 to July 20, 11 Weeks.: 27, 10 do. 21 to 9 do. 28 to Aug. 3, 10, 8 do. Aug. 4 to 17, 7 do. 11 to 24, 6 do. 18 to 5 do. 25 to 31, 4 do. Sept. 1 to Sept. 7, 14, 3 do. Sto 21, 2 do. 15to CHRISTMAS, DEC. 25. From Sept. 30 to Oct. 8, cherge from Michaelmas. Oct. 9 to Oct. 15, 11 Weeks. 22, 10 do. 16 to 9 do. 29, 23 to 8 do. 30 to Nov. 5, 7 do. 12, Nov. 6 to 6 do. 19, 13 to 5 do. 20 to 26, 4 do. 27 to Dec. 3, 3 do. 10, Dec. 4 to 17, 2 do. 11 to FIRE INSURANCE.17 137 TABLE for calculating the Premium and Duty on any number of odd weeks before quarter-day. Ann. Prem. 2 Wks. 3 Wks. 4 Wks. 5 Wks. 6 Wks. £ , s. d. s. d,( s. d.1 s. d.. s. d, 7 Wks. 8 Wks. 9 Wks. 10 Wks. s. .s .s d . d 11 Wks. . d 0 0 0 3 0 0 0 3 0 3 0304060606 0003 0 3030 4 050607 09 09 0 3 0 3 0 4 0 5 0607 08 09 09 10 5 0 3 0 3 0 0 6 0 901011 1013 6 0 3 0 4 0 6 0 7 0 9 010 1 0 1 1 1 3 1 6 0 7 0 3 0 5 0 7 0 8 010 12 13 16 16 0 8 0 3 0 6081010 1 01214161919 0 9. 60 6 0 901 111316181920 010 060 7 0 1 11 3 15181112023 0 11 060 8 0 1 1 1 417110202326 0 12 0 60 9 1 0 1 3 1 6. 1920232629 0 13 0 60 9 1 1 4 1 7 1022252930 0 14 0 0 10 1 2 1 5 1 9 2024273033 0 15 0 60 11 1 3 1 6 1 10 2226293036 0 16 0 1 '0 1 4 18202428303339 0 17 0 9 1 0 1 5 1 9 2 1 25210323640 0 18 0 9 1 2 1611 2 4 28335394 0 19 0 9 1 2 1 71 11 2 4293236 4043 1 0 0 9 1 3 1 82 1 2 6211 34394346 11091319 2 7130363114649 1 2 1 0 1 4 1 10 2 3 2 93238414650 1 3 1 01 5 1 11 2 4 2 10 34310434953 1 4 1 0 1 6 2 2 6 3 36446 5056 151016 2 112 7 3 13742485359 1 61 0 1 7 2 2 2 8 3 3 39444105660 1 7 10 18232 9341311 46505663 1 8 1 1 9 2 4 21 3 6 ;1 46 1 9 1 3 1 9 2 513 0 3 7 4 2 410 5 5 6 0 6 9 1 10 13 1 1026313944505 7 6369 1 11 1 3 1111 2 7\I3 2'3 104 65 25 96 67 0 1 121 32 0 2 83 44 04 8 546 06 97 3 1 131 32 02 913 54 1 4 9 566 26 97 6 1 14 1 6 2201 64 34115 86 47 37 9 1 15 1 6 2 2 2 11 3 7 4 4 51 510 667 38 0 1 16 161 23 30 3 9 4653 6 0 69 7 68 3 1 17 1 6'23 3 1 310 471 4 62 6117 98 6 1 18 1 61 2 4 3 2~311 4 9I 6 6 4 7 1 8 0 8 9 1 19 1 62 53314 0 41015 86 67 38 39 0 2 01 92 63 44 25 0 5106 87 68 69 3 21 19 26 35 4 35 1\5 11 6107 88 99 6 0 0 0 0 0 2 3 4 5 6 9 22 0 3 23 24 2 5 2 6 2 7 2 8 2 9 2 10 2 11 212 19 28 37 4 55 4 6 3,72 80 9 310 20 29 38 4 75 616 574 83 9 310 202 93 94 8 5 7 6 676 85 9 610 2 0 2 10 3 10 4 9 5 9'6 8 7 8 8 7 9 9 10 2 02 1 13 1 14 10 59 6 10 7 1 08910 010 2 3\3 04 05 06 07 0 80 9 010 311 2 3 3 04 15 16 17 1'82 9 210 311 2 3j3 14 2 526 37 3 84 94,10 611 2 3 3 2 4 35 31 6 47 5 86 9 610 911 2 3l3 34 45 5 667 7 88 9911 012 0 0 3 9 9 0 3 6 9 0 138 INSURANCE. FIRE 138 Wks. Ann.Prern.2 Wks 3 Wks. 4 Wks. 5 Wks. 6 Wks. i -I . . 2 13 2 14 2 15 2 16 2 17 2 18 2 19 3 0 3 1 3 2 33 3 4 3 5 3 6 3 7 3 8 3 9 3 10 3 11 3 12 3 13 3 14 3 15 3 16 3 17 3 18 3 19 4 0 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 4 4 5 6 7 8 9 10 8 9 10 0 0 0 0 0 0 . 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 13 3 '4 6 d. 3 3 3 6 6 6 6 6 6 6 6 9 9 9 9 9 0 0 0 0 0 0 0 3 3 3 3 3 3 3 s. 6 6 6 6 6 9 9 3 0 9 9 6 3 r 'I-1-1 i' d. s. d. 33 34 35 36 3 6 37 38 39 3 9 3 10 3 11 4 0 4 1 41 42 43 43 4 4 45 4 6 4 6 47 48 49 4 9 4 10 4 11 50 5 0 51 52 53 53 5 4 5 5 5 6 5 6 5 7 6 3 7 6 8 9 10 0 11 3 12 6 3 9 Wks. 10 Wks. 11 Wks. 8 Wks . 4 5 5 4 6 5 4 7 5 4 8 5 4 9 5 4 10 6 4 11 6 5 0 6 5 1 6 52 6 5 3 6 5 4 6 5 5 6 5 6 6 5 7 6 5 8 7 5 9 7 5 10 7 5 11 7 6 0 7 6 1 7 62 7 6 3 7 6 4 6 5 7 6 6 8 8 6 7 8 8 6 10 8 8 6 11 8 7 0 8 7 1 8 72 8 73 9 7 4 7 5 9 7 6 9 8 4 10 10 0 12 11 8 14 13 4 16 15 0 18 16 8 20 d. s. 6 6 7 6 8 6 10 7 11 7 1 7 1 7 37 4 7 5 7 6 7 8 8 9 8 10 8 11 8 1 8 2 8 38 4 8 6 9 7 9 8 9 9 9 11 9 0 9 1 9 2 9 4.10 5 10 6 10 7,10 9,10 10 10 11 10 0 10 2 11 3 11 4 11 5 12 6 15 7 17 8 20 3 22 10 25 I dZ. s. d. s. d. 7 8 8 10 9 11 7 10 9 0 10 1 10 3 8 0 92 8 2 9 4 10 6 8 3 9 6 10 8 10 11 8 5 98 8 7 9 10 .1 0 8 9 10 0 11 3 8 10 10 2 11 5 9 0 10 4 11 7 9 2 10 6 11 9 9 4 10 8 12 0 9 5 10 10 12 2 9 7 11 0 12 4 9 9 11 2 12 6 9 11 11 4 12 9 10 0 11 6 12 11 10 2 11 8 13 1 10 4 11 10 13 3 10 6 12 0 13 6 10 12 2 13 8 10 9 12 4 13 10 10 11 12 6 14 0 11 1 12 8 14 3 11 2 12 10 14 5 11 4 13 0 14 7 11 6 13 2 14 9 11 8 13 4 15 0 11 9 13 6 15 2 11 11 13 8 15 4 12 1 13 10 15 6 12 3 14 0 15 9 12 4 14 2 15 11 12 6 14 4 16 1 12 8 14 6 16 3 12 10 14 8 16 6 12 11 14 10 16 8 13 1 15 0 16 10 14 7 16 8 18 9 6 20 0- 22 6 17 20 5 23 4 26 3 23 4 26 8 30 0 26 3 30 0 33 3 29 3 33 4 37 6 . 10 0 1 3 4 6 7 9 10 0 1 3 4 6 9 10 0 1 3 4 6 7 9 10 0 1 3 4 6 7 9 10 0 1 3 6 0 6 0 6 0 ~11 i l r _ s.9 . 11 11 11 11 12 12 12 12 12 13 13 13 13 13 14 14 14 14 14 15 15 15 15 15 16 16 16 16 17 17 17 17 17 18 18 18 18 [8 12 12 12 13 13 13 13 13 14 14 14 14 15 15 15 15 15 16 16 16 16 17 17 17 17 17 18 18 18 25 29 33 37 41 27 18 19 19 19 19 19 20 20 20 23 32 36 41 45 FIRE, INSURANCE.13 139 Explanation of the foregoing Table, for charging premium and duty for odd time preceding Quarter-day. If an order for insurance is given between 20th and 26th December inclusive, and the risk to run one year from Candlemas next, charge premium and duty for six weeks thus:L.1 12 0 Suppose the annual premium In the column marked 6 weeks, and opposite to L.1, 12s. in the annual premium column is found 0 4 0 1 10 The total is PREMIUMS If the Yearly Premium is for periods less than One For Six Months. s. d. 1 310 s. d. 1 6 3 9 L.3 . 0 0 And if the duty is In the column 6 weeks is found 9 9 Year. For Three Months and under. s. d. 20 16 13 26 30 19 26 16 19 30 5 0 60 76 90 10 6 20 36 40 50 60 7 0 46 26 30 36 46 5 0 9 0 12 6 15 0 21,0 12 15 6 0 7 6 10 10 0 6 QUILL DRESSERS, having boiler heated by a small furnace, 4s. 63d. RENEWAL OF INSURANCES- The future payments for the renewal of annual policies should be made within fifteen days of the period limited for their expiration, otherwise the insurance becomes void. Policies for short periods expire at six o'clock on the last day of the term for which such policy is granted. RECTIFIERS OF SPIRITS, lOs. 6d. If on a small scale, 7s. 6d. ROPEMAKERS. Stock in boiling-house, workshop, and rope-walk, 2s. RESIN, 2s. 6d. RETAIL SPIRIT DEALERS, 2s. 6d. REED MAKERS, 2s. 6d. RAG DEALERS, 2s. 6d. RICE MILLS, 2s. 6d.--7%. Gd. 6d1-5s. 140 FIRE INSURANCE. RENTS. A separate sum on these, and the premium according to the risk of the property. Clause.-" The said insurance on rents, recoverable only in the event of the said building or buildings being destroyed by fire, or so damaged as to become untenantable; and the said sum of £ is declared to be the full annual rent of the whole premises, and the proportion thereof only to be exigible, corresponding to the proportion of the property destroyed or rendered untenantable from the time of such accident, until the period of reinstatement, or of perfeci repair; but in no case exceeding one year's rent." SCULPTORS, 4s 6d. SILK PRINTERS. Service-room and block-house, with small stove, 2s. 6d. Printing-house and colour-house, stove, 7s. 6d. SINGEING HOUSES, S. and B,, 42s. Company not liable for goods destroyed in process of singeing. STOCKING-MILLS. Driven by water, heated by stoves with pipes, and lighted with lamps or candles, 7s. 6d. SMITHY, 2s. 6d. Do., with dwelling-house, under one roof, thatched, 7s. 6d. STABLES, LIVERY, 2s. 6d. SALTWORKS, 5s. STRAW-HAT PLAITERS, 2s. 6d. SODA AND SACCHARUM MAKERS, 3S. See Wrights. SQUARE WRIGHTS. STEREOTYPE FOUNDERIES, 5s. STEAM-ENGINES, 5s. STARCH WORKS. With stoves and flues, 10s. 6d. With flues and boilers, and furnace outside of the works, 7s. 6d. STATIONERS, 2s. SAIL-MAKERS. No tar kettle, 2s. 6d. SEPTENNIAL INSURANCES. Insurances effected for seven years are charged by all offices for six years only ; also for any number of years more or less than seven, there will be a discount of five per cent per annum, compound interest on premium and duty for every year after the first. SNUFF MILLS, 5s. Kiln, 7s. 6d. Engine, 10s. 6d. SALTPETRE REFINERS. In working premises, 10s. Gd In warehouse, detached, 5s. STAMPS, not insurable. SnIP-BUILDERS. separate value must be declared on each ship, otherwise Note.-A the following clause must be inserted in the policy:- FIRE INSURANCE. 141 ' It is hereby declared and agreed, that in case the utensils, ves- sels building, repairing, or lying in the dock or yard abovementioned, either the property of the assured, or held by him in trust, shall, at the breaking out of any fire or fires, be collectively of greater value than the sum assured," &c. (See average clause, p. 129.) SuIPS. In dock or harbour, &c., where fires allowed, per annum, 2s. 6d. Do., for six months, Is. 9d.; for three months, ls. 6d. Do., where no fires are allowed, 2s. In London, 4s. 6d. At sea, 2s. Clause.-" Warranted that the Company shall not be liable for any loss arising by explosion of gunpowder, or combustion of government or other stores." STEAM-VESSELS. In dock or harbour, &c., 2s. 6d. Clause.-" This assurance is not to embrace the risk of said ship when worked as a steam-vessel. The machinery may occasionally be put in motion for preserving the same from rust, and likewise for proving it previous to the vessel being sent to sea; but this Company shall not be liable for any loss or damage arising by, and in consequence of, such use of the machinery and of the steam boilers." If plying, 10s. 6d. Clause.--" Warranted that this Company shall not be liable for any damage arising by the bursting of the boilers, or from the explosion of gunpowder. It is declared that the assured have only one vessel of each of the above names belonging to them." SPECIFICATION. 1. Sum on the hull. 2. Sum on the machinery. 3. Sum on the furniture, &c. SIZING-HOUSES (in Scotland STARCHING-HOUSES.) Built of stone or brick, with slate, tile, or metal roof, Heated by cockle or iron stove, the floor above the stove, cockle, fireplace, pipe, or flue, being of perforated stone, brick, or iron, of the kind called fire-proof, Heated by steam only, with the fire outside the building. Clause.-" Warranted that no goods are at any time dried on the lower floor, and that no unenclosed lights are used therein," Note.-In all policies of insurance on the building of sizing-houses and their contents the above warrantry must be inserted. See Drying Stoves. SILK MILLS. Built of stone or brick, with slate, tile, or metal roof, 5s. Heated or worked by steam, or driven by water, with the fire outside the building, 5s. Heated by stoves, with upright or horizontal metal pipes enclosed in brick, 6s. With the fire for steam-engine inside the walls, 6s. 142 FIRE INSURANCE. SAW MILLS. Driven by water, 5s., 7s. 6d., 10s. 6d. Driven by steam, having vertical, circular, or veneer saws, 21s. SADDLETREE MAKERS. Having small forge, 2s. SOAPMAKERS. Furnishing house, salting house, framing house, &c., 5s. STOVES.--See Pipe Stoves, Drying Stoves. SUGAR REFINERS. OLD SYSTEM. Building, 31s. 6d. Stock and utensils, 42s. STEAM PROCESS. Building, 16s. Stock, &c., 21s. MIXED PROCESS. Building, 25s. Stock, &c., 31s. 6d. Clause.-" Warranted to have arched stoves with iron doors, and no cockles, except what are in stoves or enclosed in brick. " Also, that no muscovado or clayed sugars are dried in baskets therein." 5 per cent extra for every cockle not covered with brick arch. The building of stone or brick with slate, tile, or metal roof. TANNERS. No stove or steam-engine, 2s. 6d. With these, 5s. THEATRES. In Scotland, 31s. 6d. In London, 42s. SPECIFICATION. 1. Sum on the building. 2. Do. scenery. music. 3. Do. 4. Do. dresses. 5. Do. machinery. TOOL-MAKERS. Workshop, no stove, 2s. 6d. Weaving tool-makers, with small forge, 4s. 6d. TALLOW-MELTERS. Stock and utensils, 4s. 6d. THREAD-MILLS. Driven and heated by steam, lighted with oil, enclosed, boiler outside, 10s. 6d. When the machinery is driven by the hand-No stove, 2s. 6d. With stove, 5s. Cotton thread-mill and bobbin manufactory driven and heated by steam, lighted by gas, 10s. 6d. TRUNK-MAKERS. With pitch-kettle, &c., 4s. 6d. FIRE INSURANCE.13 143 & TURNERS of wood, S. B. 5s. Having stoves, 7s. Gd. TAR, 3s, TINsMITHs, 2s. Gd. TAVERN KEEPERS, 2s. Gd. TURPENTINE WORKS, lOS. 6d. Stock, 4s, 6d. TIMBER. In wood-yard, and detached from joiners' workshops, 2s. 6d. In yards adjoining workshop, 4s. 6d. TIMBER, GROwING, 2s. 6d. If the wood is growing in different estates, &c., the average clause must be added to the policy. TIMBER BUILDINGS, 3s. to 5s. TOBAccoIsTs-Sale shop, is. Gd. See Snuff-ills. Toy DEALERS, 4s. Gd. TRINKETS, 2s. 6d. Tow SPINNERS, 15s. to S. &18s. B. 5s. THRASHING-MILLS. Wrought by horse or wind, Water, 2s. 6d. Steam, 4s. Gd. TYPE-FOUNDERS, is. Gd. UPHOLSTERERS. Sale shop, is. Gd. Workshop, warranted not to dry feathers, 5s. If feathers are dried, 21s. UMBRELLA-MAKERS. Workshop, 2s. 6d. Sale shop, is. Gd. UNINSURABLE PROPERTY.--Bonds, bills, books of account, deeds, gunpowder, money, notes, stamps, written securities. MAKERS. Premises not connected with stove-house or fermenting-rooms, 2s. Gd. VINEGAR When connected with these, 5s. VARNISH MAKERS, iOs. Gd. Stock, 3s. VITRIOL-MAKERS, iOs. Gd. Stock, 3s. WATCHMAKERS, 2s. Gd. WAX REFINERS, 4s. Gd. WAX CHIANDLERS' stock, 2s. Gd. WAULK-MILLS, 5s. to lOs. Gd. Driven by water, 3s. WIND-MILLS, See corn-mills. WAFER-MAKERS, 2s. Gd. WHIP-MAKERS-Small WIRE-WORKERS, 2s. Gd. pitch-kettle, 2s. Gd., 144 INSURANCE. FIRE 144 WINE MERCHANTS. Stock in shop, 2s. 6d. In vaults, is. 6d. WORSTED AND WOOLLEN MILLs, S. & S. If heated or wrought bysteam, or driven by water, with fire outside of the mill, and lighted by gas, 7s. Gd. to l0s. 6d. If heated by stoves, with horizontal metal-pipes enclosed in brick, 10s. 6d. to 21s. Lighted by lamps or candles, 12s. d. If used for fulling ,only, and no heckling, carding, or other process carried on therein, 5s. to 7s. Gd. See drying stoves. Some offices fix the premiums from the number of stoves in use, thus mill S. & B., without stove, 7s. 6d. With one or two stoves, l0s. 6d. With three or four stoves, l2s. Gd. or more stoves, l5s. With five YARN BOILERS, with brick flues, 5s. EDINBURGH; PRINTED) BY-$ALANTYNE AND HUGHES, PAUL'S WORK. This book is a preservation facsimile produced for the University of Illinois, Urbana-Champaign. It is made in compliance with copyright law and produced on acid-free archival 60# book weight paper which meets the requirements of ANSI/NISO Z39.48-1992 (permanence of paper). Preservation facsimile printing and binding by Northern Micrographics Brookhaven Bindery La Crosse, Wisconsin 2010