ANNUITIES AT COMPOUND INTEREST. An annuity is a sum of money payaole yearly, half yearly, or quarterly, for a number of years, during life, or for ever; and may draw interest if it remain unpaid after it becomes due. Tables to facilitate the calculations of annuities. TABLE III. Shewing the amount of 1 L. annuity. 7 7.898294 8.019152 8.142008 8.266894 8.393837 71 9.380014 9.549109 9.721573 9.897468 8 11.491316 9 8 9.214226 68.528117 28 TABLE IV. Shewing the present worth of L. 1 annuity for any number of years, from 1 to 40. Year. 4 per 4 per 5 per 5 per 6 per cent. cent. cent. cent. cent. 0.96154 0.95694 0.95231 0.94786 0.94339 2.77509 2.74876 2.72325 Year. 2.69793 2.67301 3.50514 3.4651 9.10589 16 16 11.65229 11.23401 10.83777 10.46216 13.66250 13.00316 26 The annuity, time, and rate of interest given, to find the amount: RULE. From the ratio involved to the time take an unit or one for the dividend; which divide by the ratio less one; and multiply the quotient by the annuity for the amount or answer. Or, by Table III. Multiply the number under the rate, and opposite to the time, by the annuity, and the product will be the amount for yearly payments. If the payments be half yearly or quarterly, the amount for the given time, found as above, multiplied by the proper number in Table V. will be the true amount. EXAMPLES. 1. What will an annuity of 50L. per annum, payable yearly, amount to in 4 years at 5 per cent. ? 1.05 x 1.05X1.05 × 1.05-1.21550625 4.310125 50 Ans. L. 215.506250=215L. 10s. 1d. 2qrs. 1 2. What will an annuity of 30L. per annum, payable yearly, amount to in 4 years, at 5 per cent. per annum, and what would be the respective amounts, if the payments were to be half yearly or quarterly? Ans. Amount for yearly payments is L. 129.30375 L. 130.9004 L. 131.7035 3. If a salary of 35L. per annum to be paid yearly, be emitted for 6 years at 51 per cent. what is the amount? Ans. 241L. 1s. 7d. 2.5+qrs. CASE 2. The annuity, time, and rate given, to find the present worth: RULE. Divide the annuity by the ratio involved to the time, and subtract the quotient from the annuity; divide the remainder by the ratio less one, and the quotient will be the sent worth: Or, by Table IV. pre Multiply the number under the rate, and opposite the time by the annuity, and the product will be the present worth. When the payments are half yearly or quarterly, multiply the present worth so found, by the proper number in Table V. EXAMPLES. 1. What is the present worth of a pension of 30L. per annum for 5 years, at 4 per cent. ? Number from Table IV. 4.45182 Ans. 133L. 11s. 1d. × 30 annuity. L. 133.55460 Or, 133L. 11s. 1.104d. 2 What is the present worth of 20L. a year for 6 years, payable either yearly, half yearly, or quarterly, computing at 5 per cent. per annum? 3. What is the yearly rent of 50L. to continue 5 years, worth in ready money, at 5 per cent.? Ans. 216L. 9s. 10d. 2.24qrs. ANNUITIES TAKEN IN REVERSION, Annuities taken in reversion, are certain sums of maney payable yearly for a limited period, but not to commence till after the expiration of a certain time. CASE 1. The annuity, time of reversion, time of continuance, and rate given, to find the present worth of the annuity in reversion: RULE. Divide the annuity by the ratio involved to the time of continuance, and subtract the quotient from the annuity for a dividend; multiply the ratio involved to the time of reversion by the ratio, less one, for a divisor; the quotient of this division will be the present worth. Or, Take two numbers under the given rate in Table IV. viz. that opposite the sum of the two given times, and that against the time of reversion, and multiply their difference by the annuity of the present worth. When the payments are half yearly or quarterly, use Table V. EXAMPLES. 1. What is the present worth of a reversion of a lease |