CASE 3. The present worth and annuity given, to find the ratio ; RULE. Divide the sum of the present worth and annuity, by the present worth; the quotient will be the ratio. EXAMPLES 1. If a real estate of 401. per annum be sold for 8007. what s the rate per cent. ? Ans. 51. per cent, 800 800)840(1.05 the ratio of 5 per cent. 2. If a freehold estate of 696 dol. per annum, be bought for 17400 dol. the rate per cent. is required. Ans. 4 per cent. CASE 4. The ratio given to find the year's purchase; RULE. Divide an unit by the ratio less one, and the quotient will be he year's purchase. EXAMPLES. 1. How many years purchase should a gentleman offer for perpetuity, to have 6 per cent. for his money? .06)1.00(16 years, Ans. 2. In selling a freehold estate at 8 per cent. how many years purchase does it bring? Ans 124. CASE 5. The year's purchase given to find the ratio. RULE. By the year's purchase divide the same more one, and the quotient will be the ratio. EXAMPLES. 1. Bought a ground rent for 15 years purchase: what rate per cent. was allowed in this contract? 15)16.00(1.0666, &c.=63 per cent. Ans. 2. What rate of interest is allowed in selling a perpetuity at 20 years purchase? Ans. 5 per cent PERPETUITIES IN REVERSION. CASE 1. THE rent of a freehold estate, time of reversion, and rate per cent. given, to find the present worth; RULE. Multiply the ratio involved to the time of reversion, by the ratio, less one, for a divisor; by which divide the yearly pay. ment, and the quotient will be the present worth. EXAMPLES. 1. Suppose a freehold estate of 60l. per annum, to commence 2 years hence, be put up to sale; what is the value, allowing the purchaser 6 per cent.? 1.06×1.06×.06=.067416 £. £. s. d. .067416)60(889 19 11 Ans. 2. What is an estate of 696 dol. per annum, to continue for ever, but not to commence till the expiration of 4 years, worth in present money, allowance being made at 4 per cent. ? CASE 2. Ans. 14873.595 do The present worth of a perpetuity, time of its reversion, and rate per cent. given, to find the yearly payment; RULE. The continual product of the present worth, the ratio in volved to the time of reversion, and the ratio, less one, will be the salary. EXAMPLES. 1. A freehold estate is bought for 889.99657. which does not commence till the end of two years; the purchaser being allowed 6 per cent. for his money; what was the yearly income? 2. There is a freehold estate bought for 14873.595 dol. which does not commence till the expiration of four years; the buyer was allowed 4 per cent. for his money; what was the yearly income? Ans. 696 dol. t LIFE ANNUITIES. ANNUITIES for Lives are estimated by probabilities drawn from the usual period of human life, according to observations made by men of eminence on regular bills of mortality. Construction of the following Table. With the rate per cent. and complement of the given age to 86, take a number from table IV, multiply it by the ratio, and take the product from the said complement for a dividend; multiply the complement by the ratio, less one, for a divisor; the quotient will be the tabular number. EXAMPLES. To find the tabular number for 50 years at 5 per cent. Table VI. Value of 17. or dol. annuity for a single life 3p.ct. 3pct. 4 p. ct.4 pct. 5p. ct. Opct.s Age. 14,20 12,50 14,12 | 12,45 14,05 12,40 5 or 17 18,90|17,46|16,21 | 15,10 | 18 18,76 17,33 16,10 15,01 19 18,61 17,21 15,99 14,92 13,97 12,35 4 or 20 18,46 17,09 15,89 14,83 18,89 12,30 21 18,50 16,08 15,78 14,73 13,81 12,20 22 18,15 16,83 15,67 14,64 13,72 12,15 25 17,99 16,69 15,55 14,54 | 18,64 | 12,10 3 or 24 17,83 16,56 15,43 14,44 13,55 | 12,00 25 17,66 16,42 | 15,3114,34 13,46 11,95 26 17,50 16,28 15,19 14,23 13,37 11,90 27 17,53 18,13 15,04 14,12 13,28 11,80 28 17,16 15,98 14,94 14,02 18,18 11,75 2916,98 15,83|14,81 13,90 | 15,09 | 11,65 S0 16,80 15,68 14,68 13,79 12,99 | 11,60 2 or 31 16,62 15,53 14,54 | 13,67 12,88 11,50 32 16,44 15,37 14,41 18,55 | 12,78 84 16,06 15,05 14,12 13,30 12,56 11,40 11,25 36 15,67 14,71 18,82 13,04 12,83 11,05 38. 15,29 14,84 | 19,52 | 12,77 | 12,09 | 10,90 14,16 | 13,36 | 12,63 | 11,96 | 10,801 13,98 | 13,20 | 12,18 | 11,83 | 10,70 13,59 12,85 12,18 | 11,57 | 10,45| or 39 15,85 9,75 44 13,96 13,20|12,50|11,87 11,29 10,25 9,15 9,99 9,20 54 11,48 10,95 10,47 10,04 9,63 8,85 10,01 9,61 9,24 8,55 56 10,90 10,44 60 9,73 9,36 9,01 62 9,11 8,798,48 8,69 *8,39 7,80 8,19 64 8,46 8,19 7,92 CASE 1. To find the present worth of an annuity for a single life of a given age; RULE. Multiply the value of 17. or dol. for the given age and rate of interest, in table VI. by the annuity. EXAMPLES. 1. What sum should a person of 50 years of age give for an annuity of 100l. per annum, during his life, reckoning interest at 41 per cent. ? Tabular number 10,82 × 100=10827. Ans. 2. A merchant who married a widow of 40, would sell her jointure of 786 dol. a year, for ready money; what should it bring at 3 per cent. ? Ans. 10988.28 dol. CASE 2. To find the value of an annuity for the joint continuance of two lives, one life failing, the annuity to cease. RULE. Multiply the product of the 2 tabular numbers for the given ages by the ratio less one, and deduct this result from the sum of those numbers for a divisor; multiply the first product by the annuity for a dividend; the quotient will be the value required. EXAMPLES. 1. What is the value of 707. annuity for the joint lives of 2 persons, one of 40 and the other of 50 years of age, reckoning interest at 5 per cent. ? 2. What is 240 dollars annuity worth for the joint lives of 2 persons of the age of 30 years each, at 4 per cent. ? Ans. 2493.7 dol.+ CASE 3. To find the value of an annuity upon the longest of 2 lives; that is to continue as long as either of the persons shall be living. |