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BY TABLE III.
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. 50. + . 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 oy 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 denoad 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)8,86187
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 INI. Find the present value of 11. 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)
=0 years, gives 5,075692
Remainiler, 3,216282 x 50
Ans. £160,8141. 2. What is the present worth of 751. yearly rent, which is not to commence until 10 years hence, and then to con. tinue 7 years aiter that time at 6 per cent. ?
Ans. £233 15s, 9d. 1. What is the present worth of the reversion of a lease «f 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, 78 cts. 2*om. IV. To find the present worth of a Freehold Estate, or a 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 for, 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 value of the estate (by the foregoing Tule) 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 ro version.
EXAMPLES. 1. Suppose a freehold estate of 401. per annum to com mence 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. Then, 1,05=1,1025)800,00(725,62358=7251. 12s
, . 5 d.=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 suitract froin the value of the immediate possession, and you will have the value of the escate 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, foi
[the time of reversion. From 800,0000=value of immediate possession. Take 74,3761=present wortlı of rent.
£725,6236=£725 12s. 5 d. Ans. 2. Suppose au estate of 90 dollars per annum, 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. 1. I demand the sum of 1748.1
, added to itself?
Ans. 3197. 2. What is the difference between 41 eagles, and 4099 dimes ?
Ans. 10 cts. 3. What number is that which being mutiplici by, the product will be 1365?
4. What imber is that which being divided by 19, the quotient will be 72 ?
Ans. 1368. 5. What number is that which being multiplied by 15, the product will be it?
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. (s. 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 L6 yards of German serge,
For 90 dimes had I ;
Will 14 eagles buy? Ans. 248 yds. 3 qrs. 2 110. 9. A certain quantity of pasture will last 963 sleep 9 weeks, low many must be turned out that it will last the remainder 9 weeks?
Ans. 211. 10. A grocer bought an equal quantity of sugar, ter, and coffee, for 740 dollars; he gare 10 cents per lb. for the sus gar, 60 cts. per lb. for the tea, and 20 cts. per lb. for che conlee ; required the quantity of cach?
Ans. 82.2 16.3 oz. &. dr. 11. Bought cloth at $!; a yard, and lost 25 per cent., how was it sold a yard?
Ans. 93 cts. 2 12. The third part of an army was killed, the fourth par taken prisoners, aud 1000 fled; how many were in this ar. my, how many killed, and how many captives ?
Ans. 2400 m 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 certaintnumber of water-melons, which he sold at 25 cents apiece;"! how much money did each receive, and how
melons i had Harry? Ans. Each rec'd $50, and Harry sold 200 melons.
14. Said John to Dick, my purse and money are worth: 1 91. 2s., but the money is twenty-five times as much as the purse; I demand how much inoney was in it ?
Ans. £8 151..
15. A young man received 2101. which was of his el. ier brother's portion; now threc times the elder brother's portion was half the father's estate ; what was the value of he estate?
ins. £1890. 16. A hare starts 40 yards before a grey-lound, and is 100 perceived by him till she has been up 10 seconds ; she uçuds away at the rate of ten miles an hour, and the dog, or view, makes after her at the rate of 18 miles an hour: How long will the course hold and what space will be run over from the spot where the dog started ?
Ans. 60 sec. and 530 yds. space. 17. What number multiplied by 57 will produce just what 134 multiplied by 71 will do ? Ans. 16631
18. There are two numbers whose product is 1610, the greater is given 46; I demand the sum of their squares, and the cube of their difference?
Ans, the sum of their squarcs is 3341. The cube of heir difference is 1:331. 19. Suppose there is a mast erected, so that I 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. at 5 per cent. for 12 years, 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. 6d. per thousand; what might lie clear per cent. by the latter price ?
Ans. £96 7s. 34d. 22 Three persons purchase a West-India sloop, towards "he payment of which A advanced , B 1, and C 1401. How much paid A and B, and what part of the vessel had C?
Ans. A paid £2673, B £305,-1, and C's part of the nessel was iš 23. What is the purchase of 12001, bank stock, at 1031
Ans. £1243 10s. 24. Bought 27 pieces of Nankeens, ench 115 yards, at
per cent. ?