2. If a salary of 60 dollars per annum to be paid yearly, be forborne twenty years, at 6 per cent. compound interest, what is the amount? Under 6 per cent. and opposite 20, in Table II., you will find, Tabular number=36,78559 60 Annuity. Ans. $2207,13540=$2207, 13 cts. 5m.+ 3. Suppose an annuity of 1007. be 12 years in arrears, it is required to find what is now due, compound interest being allowed at 57. per cent. per annum? Ans. £1591 14s. 3,024d. (by Table II.) 4. What will a pension of 1201. per annum, payable yearly, amount to in 3 years, at 57. per cent. compound interest? Ans. £378 6s. II. To find the present worth of annuities at Compound In terest. RULE. Divide the annuity, &c. by that power of the ratio sig. nified by the number of years, and subtract the quotient from the annuity: This remainder being divided by the ratio less 1, the quotient will be the present value of the an nuity sought. EXAMPLES. 1. What ready money will purchase an annuity of 501. to continue 4 years, at 57. per cent. compound interest? 4th power of the ratio, Subtract Divis. 1,05-1=05)8,86487 BY TABLE III. Under 5 per cent. and even with 4 years, We have 3,54595-present worth of 17. for 4 years. Multiply by 50 Annuity. Ans. £177,29750-present worth of the annuity. 2. What is the present worth of an annuity of 60 dols. per annum, to continue 20 years, at 6 per cent. compound interest? Ans. $688, 19 cts.+ 3. What is 307. per annum, to continue 7 years, worth in ready money, at 6 per cent. compound interest? Ans. £167 9s. 5d.+ III. To find the present worth of Annuities, Leases, &c. taken in REVERSION at Compound Interest. 1. Divide the annuity by that power of the ratio denoted by the time of its continuance. 2. Subtract the quotient from the annuity: Divide the remainder by the ratio less 1, and the quotient will be the present worth to commence immediately. 3. Divide this quotient by that power of the ratio denoted by the time of Reversion, (or the time to come before the annuity commences) and the quotient will be the present worth of the annuity in Reversion. EXAMPLES. 1. What ready money will purchase an annuity of 501. payable yearly, for 4 years; but not to commence till two years, at 5 per cent.? 4th power of 1,05=1,215506)50,00000(41,13513 Subtract the quotient =41,13513 Divide by 1,05-1=,05)8,86487 2d power of 1,05=1,1025)177,297(160,8136=£160 16s. 3d. 1 qr. present worth of the annuity in reversion. OR BY TABLE III. Find the present value of 17. at the given rate for the sum of the time of continuance, and time in reversion added together; froin which value subtract the present worth of 11. for the time in reversion, and multiply the remainder by the annuity; the product will be the answer. 2. What is the present worth of 751. yearly rent, which is not to commence until 10 years hence, and then to continue 7 years after that time at 6 per cent.? Ans. £233 15s. 9d. 4. What is the present worth of the reversion of a lease of 60 dollars per annum, to continue 20 years, but not to commence till the end of 8 years, allowing 6 per cent. to the purchaser ? Ans. $131, 78 cts. 225m. IV. To find the present worth of a Freehold Estate, or an Annuity to continue forever, at Compound Interest. RULE. As the rate per cent. is to 100%. : so is the yearly rent to the value required. EXAMPLES. 1. What is the worth of a freehold estate of 401. per annum, allowing 5 per cent. to the purchaser ? As £5 £100 £40: £800 Ans. 2. An estate brings in yearly 1507, what would it sell for, allowing the purchaser 6 per cent. for his money ? Ans. £2500. V. To find the present worth of a Freehold Estate, in Reversion, at Compound Interest. RULE.-1. Find the present value of the estate (by the foregoing cule) as though it were to be entered on immediately, and divide the said value by that power of the ratio denoted by the time of reversion, and the quotient will be the present worth of the estate in reversion. EXAMPLES. 1. Suppose a freehold estate of 40l. per annum to com ence two years hence, be put on sale; what is its value, towing the purchaser 51. per cent.? As 5 100: 40: 800-present worth if entered on iminediately. 2 - Then, 1,0 1,1025)800,00(725,62358=7251. 12s. 5d.-present worth of £800 in two years reversion. Ans. OR BY TABLE III. Find the present worth of the annuity, or rent, for the time of reversion, which subtract from the value of the immediate possession, and you will have the value of the estate in reversion. Thus in the foregoing example, 1,859410-present worth of 17. for 2 years. 74,376400-present worth of the annuity or rent, for [the time of reversion. From 800,0000 value of immediate possession. £725,6236=£725 12s. 5ļd. Ans. 2. Suppose an estate of 90 dollars per annum, to commence 10 years hence, were to be sold, allowing the purchaser 6 per cent.; what is the worth? Ans. $837, 59 cts. 2 m. 3. Which is the most advantageous, a term of 15 years, in an estate of 1007. per annum; or the reversion of such an estate forever after the said 15 years, computing at the rate of 5 per cent. per annum, compound interest? Ans. The first term of 15 years is better than the reversion forever afterwards, by £75 18s. 71⁄2d. A COLLECTION OF QUESTIONS TO EXERCISE THE FOREGOING RULES. 1. I demand the sum of 1748 added to itself? Ans. 10 cts. Ans. 3497. 2. What is the difference between 41 eagles, and 4099 dimes? 3. What number is that which being multiplied by 21 the product will be 1365? R 2 Ans. 65. 4. What number is that which being divided by 19, the quotient will be 72? Ans, 1868. 5. What number is that which being multiplied by 15, the product will be ?? Ans. 6. There are 7 chests of drawers, in each of which there are 18 drawers, and in each of these there are six divisions, in each of which is 167. 6s. 8d. ; how much money is there in the whole? Ans. £12348. 7. Bought 36 pipes of wine for 4536 dollars; how must I sell it a pipe to save one for my own use, and sell the rest for what the whole cost? Ans. $129, 60 cts. 8. Just 16 yards of German serge, How many yards of that same cloth Ans. 248 yds. 3 qrs. 2 na. 9. A certain quantity of pasture will last 963 sheep 7 weeks, how many must be turned out that it will last the remainder 9 weeks? Ans. 214. 10. A grocer bought an equal quantity of sugar, tea, and coffee, for 740 dollars; he gave 10 cents per lb. for the sugar, 60 cts. per lb. for the tea, and 20 cts. per lb. for the coffee; required the quantity of each? Ans. 22 lb. 3 oz. Sz dr. 11. Bought cloth at $1 a yard, and lost 25 per cent., how was it sold a yard? Ans. 933 cts. 12. The third part of an army was killed, the fourth part taken prisoners, and 1000 fied; how many were in this arhow many killed, and how many captives? my, Ans. 2400 in the army, 800 killed, and 600 taken prisoners. 13. Thomas sold 150 pine apples at 334 cents apiece, and received as much money as Harry received for a certain number of water-melons, which he sold at 25 cents apiece; how much money did each receive, and how many melons had Harry? Ans. Each rec'd $50, and Harry sold 200 melons, 14. Said John to Dick, my purse and money are worth 91. 2s., but the money is twenty-five times as much as the purse; I demand how much money was in it? Ans. £S 15s. |