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BY TABLE MI.
We have 3,54595=present worth of 11. for 4 years.
Ans. £177,29750=present worth of the annuity.
2. What is the present worth of an annuity of 60 dols per annuin, to continue 20 years, at 6 per cent. compound interest?
Ans. $688, 19 cts. + 3. What is 301. per annum, to continue 7 years, worth in ready money, at 6 per cent. compound interest ?
Ans. £167 9s. 5d. + (1). To find the present worth of Annuities, Leases, &c. ta
ken 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 denood by the time of Reversion, (or the time to come before the ampuity 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. I gr. present worth of the annuity in reversion.
OR BY TABLE III. Find the present value of Il. 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.
Thus in Example 1
=0 years, gives 5,075692
Remainiler, 3,216282 x 50
Ans. £160,8141. 2. What is the present worth of 751. yearly rent, whict is not to commence until 10 years hence, and then to con: tinue 7 years after that time at 6 per cent. ?
Aus. £233 15s. Id. 1. 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, in the purchaser?
Ans. $431, 78 cts, 27.m.; IV. To find the present worth of a Freehold Estate, or at Annuity to continue forever, at Compound Interest.
RULE. As the rate per cent. is to 1001. : so is the yearly rent to the value required.
EXAMPLES. 1. What is the worth of a freehold estate of 401. per an. num, allowing 5 per cent to the purchaser ?
As £5 : £100 :: £40 : £800 Ans.' 2. An estate brings in yearly 1501, what would it sell ior, Allowing the purchaser 6 per cent. for his money?
Ans. £2500. V. To find the present worth of a Freehold Estate, in Rc.
version, at Compound Interest. Rule.-1. Find the present valuc 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 rever. . sion, and the quotient will be the present worth of the estate in re version.
EXAMPLES. 1. Suppose a freehold estate of 401. per annum to com mence two years hence, he put on sale; what is its value. allowing the purchaser 5l. per cent. ?
As 5 : 100 : : 40 : 800=present worth if entered on immediately. .
Then, 1,05=1,1025)800,00(725,62358=7251. 12s - 5ld.=present worth of £800 in two years reversion. Ans.
OR BY TABLE IN. Find the present worth of the annuity, or rent, for the time of reversion, whiclı subtract from the value of the immediate possession, and you will have the value of the esrate in reversion.
Thus in the foregoing example,
40=annuity or rent.
s 74,376400=present worth of the annuity or rent, foi
[thie tiine of reversion. From 800,0000=value of immediate possession. T'ake 74,3761=present worth of rent.
£725,6236=£725 125. 5;/. Ans. 2. Suppose an estate of 90 dollars per anvum, to coinnience 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 1001, 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 terın of 15 years is better than the reversion forever afterwards, by £75 18s. 7 d. A COLLECTION OF QUESTIONS TO EXERCISE
THE FOREGOING RULES.
Ans. 3497. 2. What is the difference between 41 eagles, and 4099 dimes?
Ans. 10 cts. 3. What number is that which being mutiplict sys1 the product will be 1365?
4. What sumber is that which being divided by 19, the quotient will be 72 ?
dns. 1368. 5. What mimber is that which being multiplied by 15. the product will be j?
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 161. 6s. 8d. ; how much money is there in the whole?
Ans. £123-18. 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,
For 90 dimes had I;
Will 14 eagles buy? Ans. 248 yds. 3 grs. 2; na. ! 9. A certain quantity of pasture will last 903 sleep 1 1 weeks, low many must be turned out that it will last the remainder 9 weeks?
Ans. 214. i 10, A grocer bought an equal quantity of sugar, ten, und coffee, for 740 dollars; he gave 10 cents per lb. for the suis gar, 60 cts. per lb. for the tea, and 20 cts. per lb. for che coilee ; required the quantity of' cach?
ins. 82.2 16.3 oz. 8. dr. 11. Bought cloth at $1. a yard, and lost 25 per cent., how was it sold a yard ?
Ans. 93 cts. 512 12. The third part of an army was killed, the fourtlı par taken prisoners, aud 1000 fled; how mauy were in this ar. my, 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 33. 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 melongi had Harry? Ans. Each rec'd $50, and Harry sold 200 melons,
14. Said John to Dick, my purse and money are worth a . 91. 2s., but the money is twenty-five times as much as the purse; I demand how much inoney was in it ?
Aus. £8 151.
15. A young man received 2101. which was of his el. jer brother's portion; now threc times the elder brother's
sortion was half the father's estate; what was the value of į he estate ?
ins. £1890. 16. A hare starts 40 yards before a grey-lound, and is jot perceived by him till she has been up 10 seconds ; slie ucuds away at the rate of ten miles an hour, and the dog, vr, view, makes after her at the rate of 18 miles an hour : How long will the course hold and what space will be rum over from the spot where the dog started ?
Ans. 60 sec. and 530 yds space. 17. What ruinber multiplied by 57 will produce just what 134 multiplied by 71 will do ? - Ans. 16654.
18. There are two numbers whose product is 1610, the greater is given 46; I demand the sum of their squares, und the cube of thicir difference ?
Ans, the sum of their squares is 3341. The cube of heir difference is 1331.
19. Suppose there is a mast erected, so that of its ength stands in the ground, 12 feet of it in the water, and
of its length in the air, or above water; I demand the vhole length ?
Ans. 216 feet. 20. What difference is there between the interest of 5001. #! 5 per cent. for 12 ycars, and the discount of the same sum at the same rate, and for the same time?
Ans. £112 10s. 21. A stationer sold quills at 11s. per thousand, by which he cleared of the money, but growing scarce raised them so 13s. 60. per thousand; what might he clear per cent. by the latter price ?
Ans. £96 78. 31d. 22 Three persons purchase a West-India sloop, towards "he payment of which A advanced 3, B2, and C 1401. How much paid A and B, and what part of the vessel had C?
Ans. A paid £267*, B £305,, and C's part of the
nessel was žš. C 23. What is the purchase of 12001. bank stock, at 103 per cent. ?
Ans. £1243 10s. 24. Bought 27 pieces of Nankeens, ench 111 yards, al