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2. If a salary of 60 dollars per annum to be paid year .y, be forborne 20 years, at 6 per cent. compound inerest; what is the amount ?
Under 6 per cent. and opposite 20, in 'Table II, you will find, Tabular number=36,78559
Ans. 82207,15540=82207, 13cts. 5m. + 5. Suppose an Annuity of 1001. be 12 years in arrears, it is required to find what is now due, compound interest being allowed at 5l. per cent. per annum?
Ans. £1591 14s. 3,024d. (by Table III.) 4. What will a pension of 120l. per annum, payable yearly, amount to in 3 years, at 51. per cent. compound interest :
Ans. £578 6s. II. To find the present worth of Annuities at Compound
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 Annuity sought.
1. What ready inoney will purchase an Annuity of 50l. to continue 4 years, at gl. per cent. compound interest ? 4th power
177,297=£177 5s. 111d. Ans.
BY TABLE III. Under 5 per cent. and even with 4 years: We have 3,54595=present worth of il. 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 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 de. noted 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.
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 1,03=1,1025)177,297(160,8136=£160 16s. 3d. 1gr. pregent worth of the Annuity in Reversion.
OR BY TABLE III. Find the present value of ll. 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.
Thus in Example 1. 'fimne of continuance, 4 years. Ditto of reversion,
6 years, gives 5,075092 "Time in reversion, =2 years,
1,853410 Pemaindler, 5,216282 X50
Ins. £160,8141 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. :
ins. 6:235 15s. Ill. 3. What is the present worth of the reversion of a lease of 60 dollars per annum, ta continue 20 years, but not to commence till the end of 8 years, allowing 6 per cent to the purchaser ? Hus. 8431 78cts. 2 N. IV. To find the present worth of a Freehoid Estate, or an Annuity to continue forever, at Co:npound Interest.
RCLE. As the rate per cent is to 100l. : 60 is the yearly rent to the value required.
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 1501. what would it seli for, allowing the purchaser 6 per cent. for his money?
Ins. £2500 V. To find the present worth of a Frechold Estate, in Reversioll, at Compound Interest.
RULE. 1. Find the present vakie of the estatc (by the foregoing Tyle), 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.
1. Suppose a freehold estate of 401. per annuun to conmence two years herice, be put on sale; what is its value, allowing the purchaser 51. per cent. B
As 5 : 100 : : 40 : 800=present worth if entered on immediately
Then, 1,05=1,1025)800,00(725,62358=7251. 12s. 53d. =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 iminediate possession, anu you will have the value of the estate in reversion.
Thus in the foregoing example, 1,859410=present worth of il. for 2 years.
40=annuity or rent. 74,376400=present worth of the annuity or rent, for
(the time of reversion. From 800,0000=value of immediate possession. Take 74,3764=present worth of rent.
£725,6236=4725 12s. 51d. Ans. 2. Suppose an estate of 90 dollars per annum, to commence 10 years hence, were to be sold, allowing the purchaser 6 per what is it worth?
Ans. 8837, Sİcts. 2n. 3. 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 version forever afterwards, by £75 18s. 73d.
A COLLECTION OF QUESTIONS TO EXERCISE
THE FOREGOING RULES.
Ans. 3497. 2. What is the difference between 41 eagles, and 4099 Jimes ?
Ans. 10cts. 3. What number is that which being rultiplied by 21, the product will be 1365 ?
4. What number is that which being divided by 19, the quotient will be 79?
is. 1568. 5. What number is that which being multimized by 15. the product will be ?
6. There are 7 chests of drawers, in cach of which there are 18 drawers, and in each of these there are six divisions, in each vf which is 161. Gs. &d.; how muci inoney is there in the whole :
Ins. f, 123+8. 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: .Yus. $129, 60ets. 8. Just 16 yards of Gerinan serge,
For 90 dimes liad I;
Will 14 eagles buy? Ans. :34Byils. Surs. 210. 9. A certain quantity of pasture will last 063 sheep i 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 lu. Bir the sugar, 60 cts. per lb. for the tea, and 20 cts. Herib. for the coffee; required the quantity of cach :
3!1s. 8991). Suž. Rir. 11. Bought cloth at 814 a yard, and lost 25 per ceiit. how was it sold a yarıl ?
os. Os gris. 12. The third part of an arıny was killed, the fourth part taken prisoners, and 1000 fled; how many were in arıny, low many
killeil, and bow mary captires Ans. 2400 in the army, 800 Lilled, and
600 taken prison's. 13. Thomas sold 150 pine apples at $5.cents a piece, and received as much money as Harry reserved for ? certain number of water-mellons, which lie soll it :) cents a piece; how much money lid each receive, anid how many mellons liad Harry ?
Ans. Each received $50, anul Ilarry sold 200 mil.):25.
14. Said John to Dick, iny purse and money are worth 91. 25. but the money is twenty-five times as much as the purse; I demand how much money was in it :
Jins. 48 15s.