2. If a salary of 60 dollars per annum to be paid yearly, be forborne 20 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, 13cls. 5m.+ 3. Suppose an Annuity of 100l. be 12 years in arrears, it is required to find what is now due, compound interest being allowed at 51. per cent. per annum ? Ans. £1591 14s. 3,024d. (by Table II.) 4. What will a pension of 120l. per annum, payable yearly, amount to in 3 years, at 51. per cent. compound Ans. £378 Gs. interest? II. To find the present worth of Annuities at Compound Interest. RULE. Divide the annuity, &c. by that power of the ratio signified 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 Annuity sought. EXAMPLES. 1. What ready money will purchase an Annuity of 501. to continue 4 years, at 5!. per cent. compound interest ? 4th power of the ratio, S Subtract =1,215506)50,00000(41,13513+ 50 41,13513 177,297-177 5s. 11id. Ans. Divis. 1,05-1=05)8,86487 BY TABLE II Under 5 per cent. and even with 4 years, We have 3,54595-present worth of 11. 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 30l. per annum, to continue 7 years, worth in ready mouey, 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(41,15513 Subtract the quotient 41,15513 Divide by 1,05-1,05)3,86487 2d. power of 1,05=1,1025)177,297(160,8156=£160 16s. 3d. 1gr. present worth of the Annuity in Reversion. OR BY TABLE III. Find the present value of 11. at the given rate for the sum of the time of continuance. and time in reversion added together; from which value subtract the present worth of Il. 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. 3. 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. $431 78cts. 22m. 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 1007. so is the yearly rent to the value required. EXAMPLES. 1. What is the worth of a Freehold Estate of 40l. per annum, allowing 5 per cent. to the purchaser ? As £5 £100 :: £40 £800 Ans. 2. An estate brings in yearly 1501. 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 1. Find the present value of the estate (by the foregoing rule) 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 401. per annum to commence two years hence, be put on sale; what is its value, allowing the purchaser 51. per cent.? As 5 100 40 800-present worth if entered on immediately. 2 Then, 1,051,1025)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. 51d. Ans. 2. Suppose an estate of 90 dollars per annum, to commence 10 years hence, were to be sold, allowing the pur chaser 6 per cent. ; what is it worth? Ans. $837, 59cts. 2m. ' S. Which is the most advantageous, a term of 15 years, in an estate of 100l. 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. 74d. A COLLECTION OF QUESTIONS TO EXERCISE THE FOREGOING RULES. 1. I demand the sum of 1748 added to itself? Ans. 3497. 2. What is the difference between 41 eagles, and 4099 dimes? Ans. 10cts. 3. What number is that which being multiplied by 21, the product will be 1365 ? Aus. 65. Ans. 1368. 4. What number is that which being divided by 19, the quotient will be 72 ? 5. What number is that which being multiplied by 15, the product will be ? "Ans. 20: 1 6. There are 7 chests of drawers, in each of which there are 18 drawers, and in cach of these there are six divisions, in each of which is 16l. 6s. 8d.; how much money is there in the whole ? Ans. 12348. 7. Bought 56 pipes of wine for 4556 dollars; hew must I sell it a pipe to save one for my own use, and sell the rest for what the whole cost? Ans. $129, COcts. 8. Just 16 yards of German s serge, For 90 dimes had I; How many yards of that same cloth Will 14-eagles buy? Ans. 248 yds. Sqrs. 23na. 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, 822lb. 3oz. 83dr. 11. Bought cloth at $14 a yard, and lost 25 per cent. how was it sold a yard? Ans. 93 cts. 12. The third part of an army was killed, the fourth part taken prisoners, and 1000 fled; how many were in this ariny, how many killed, and how many captives? Ans. 2400 in the army, 800 killed, and 600 taken prisoners. 13. Thomas sold 150 pine apples at 333 cents a piece, and received as much money as Harry received for a certain number of water-mellons, which he sold at 25 cents a piece; how much money did each receive, and how many mellons had Harry? Ans. Each received $50, and Harry sold 200 mellons. 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. £8 15s |