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BY TABLE III. Under 5 per cent. and, even with 4
years. We have 5,54595=present worth of il. for 4 years. Multiply by 50=Annuity.
Ins. £177,09750=present worth of the annuity.
2. What is the present worth of an annuity of 60 dols. per anpun, to continue 20 years, at 6 per cent. compound interest ?
Ans. $688, 19 cts. + 3. What is 501. per annum, to continue 7 years, worth in ready money, at 6 per cent. compound interest'?
Ans. £,167 Os. 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 tiine 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 immediaely
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=1,215500)50,00000(41,i9513
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. 1yr. present 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 reversion, and multiply the remainder by the Annuity; the product will he theam
Thus in Example 1.
6 years, gives 5,075692
1,859410 Remainder, 3,216282 x 50
Ans. £160,8141 2. What is the present worth of 75l. 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. 2m. 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 1001, : so 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 :: 6.40 : £800 Ans. 2. An estate brings in yearly 1501. what would it sell for, allowing the purchaser 6 per cent. for his money?
Ans. £o 2500 W. To find the present worth of a Freehold Estate, in Revern, at Compound Interest.
RULE. 1. Find the present value of the estate (by the foregoing rv'e) 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 40l. per annum to commence two years hence, be 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. 54d.present worth of 6800 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 il. for 2 years.
40=annuity or rent. 74,376400=present worth of the annuity or rent, for
[the time of reversion. From 80040000=value of immediate possession. Take 74,
74,3764=present worth of rent. £725,6236=5725 12s. 51d. Ans. 2. Sappose an estate of 90 dollars per annum, to commence 10 years hence, were to be sold, allowing the purchaser 6 per cent. ; what is it worth?
Ana $837, 39cts. 2m. 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 reversion forever afterwards, by £75 18s. 71d.
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 mutiplied by 21, the product will be 1365 ?
QUESTIONS FOR EXERCISE.
4. What number is that which being divided by 19, the quotient will be 72 ?
sus. 1308. 5. What number is that which being multiplied by 13, the product will be ?
Ains, 1 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. Cs. 8d.; liow muchi, inoney 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, COcts. 8. Just 16 yards of German serge,
For 90 dimes had I;
Will 14 eagles buy? Ans. 248yds. Syi's. n. 9. A certain quantity of pasture will last 965 sheep? weeks, how
must be turned out that it will last the remainder 9 weeks?
Ans. 211. 10. A grocer bought an equal quantity of sugar, tea, and coffee, for 740 dollars; lie 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 ?
Ins. 82916. 3oz. 8i/r. 11. Bought cloth at $11 a yard, and lost 25 per cent. how was it sold a yard ?
Ans. 93 gols. 12. The third part of an army was killed, the fourth part taken prisoners, and 1000 Hed; how many were in this army, how many killed, and how many captives?
Ans. 2400 in the army, 800 killeil, and
600 taken prisoners. 13. Thomas sold 150 pine apples at 53į 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 liad Harry :
Airs. Each received $50, und Harry sold 200 nellons.
14. Said John to Dick, my purse and money are worth 91. 2s. but the money is twenty-five times as much as the nurse; I demand how much money was in it?
Aris. £8 15s.
15. A young man received 210!. which was of his elder brother's portion ; now, three times the elder broth
:er's portion was half the father's estate; what was the value of the estate ?
Ans. £1890. 16. A hare starts 40 yards before a grey-lound, and is riot perceived by him till she has been up 40 seconds ; she scuds away at the rate of ten miles an hour, and the dog, on view, makes after her at the rate of 18 miles an hour: How long will the course hold, and what space will be ran over, from the spot where the dog started ?
Ans. 60 sec. and 530yds. space. 17. what number multiplied by 57 will produce just what 134 multiplied by 71 will do ?
Ans. 16657 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 squares is 3341. The cube of
their difference is 1331. 19. Suppose there is a mast erected, so that of its hength stands in the ground, 12 feet of it in the water, and 중 of its length in the air, or above water; I demand the whole 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 to 13s. Ed. per thousand ; what might he clear per cent. by the latter price?
Ans. £96 7s. Sid. 22. Three persons purchase a West-India sloop, towards the payment of which A advanced }, B and C 1401. How much paid A and B, and what part of the vessel had C: ins. A paid £ 267 11, B £505 [1, and C's part of the
vessel was j. 23. What is the purchase of 12001. bank stock, at 1055 per cent.:
Fris. £ 1245 10s. 24. Bought 27 pieces of Nankeens, each 115 yards, at