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DY TAELE II Under 5 per cent. and even with 4 years, We have 3,54593=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
6, interest ?
Ans. $688 19} cts.-t 3. What is 30l. per annum, to continue 7 years, worth in ready money, at 6 per cent. coinpound interest ?
ns. £,167 9s. 5d. + TII. To find the present worth of Annuities, Leases, &c.
taken in REVERSIOx, at Compound Interest? 1. Divide the Annuity by that power of the ratio denoteil 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 rcady money will purchase an Annuity of 501. pasyable yearly, for 4 years : but not to commence till two years, at 5 per cent. ?
5 4th power of 1,05 = 1,215506)50,00000(41,13513
Subtract the quotient=41,15515
Divide by 1,05--1=,039.86487
2d. power of 1,05=1,1023)177,297(160,8136=2,150 16s. 3d. 1gr. present worth of the Annuity in Reversion.
OR BY TABLE III. Find the present value of il. at the given rate for thre sum of the time of continuance, and time in reversion added together; froin 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.
—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 lience, and then to continue 7 years after that tiine at 6 per cent. ?
Ans. £233 15s. 9d. S. Vyhat 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. 8431 78cts. 2 21. IV. To find the present worth of a Freehold Estate, or an Anouity to continue forever, at Compound Interest.
RULE. As the rate per cent is to 1Cbl. : so is the yearly rent to the value required.
1. What is the worth of a Freehold Estate of 401. per annum, a Nowing 5 per cent to the purchaser ?
As £5 : £100 :: 640 : £800 Ans. 2. An estate brings in cearly 1501. what would it sell for, allowing the purchaser 6 per cent. for big money?
Aris. £2500 V. To find the present worth of a Freehold Estate, ia
Reversion, at Compound Interest. 1. Find the present value of the estate (by the foregoing rule) as though it ne o to be entered on immediately, and divide the said valve liy that power of the ratio denoted by the time of reversion, and the quotient will be the present worth of the estate in Reversión.
1. Suppose a freehold estate of 401. per annum to commence two years hence, bo put on sale; what is its value, allowing the purchaser õli per cent. ?
As 5 : 100 :: 40 : 800=present worth if entered on immediately.
Then, 1,05=1,1025)800,00(725,62358=7251. 12s. 51d.=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 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.
£795,6236=4725 198, 5jd. Ans. 2. Suppose an estate of 90 dollars per annum, to commence 10 years hence, were to be sold, allowing thc
purchaser 6 per cent. ; what is it worth?
Ans. $857, 59cts. 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. 730.
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, ule product will be 1565 ?
4. What number 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 ?
6. There are 7 chests of drawers, in each of whick there are 18 drawers, and in each of these there are six divisions, in each of which is 101. Cs. 81.; how much money is there in the whole :
Ans. £,12348. 7. Bought 56 pipes of wine for 4556 dollars; how must I sell it a pipe to save one for my own use, and sell the rest for what the whole cost! Bus. $129,* 60cts. 8. Just 16 vares of Corman serge,
For 90 dimes hadi;
Will 14 eagirs buy? s. 949ys. Sqrs. 2na. 9. A certain quantity of pasture will last 963 sheep 7 weeks, low many must be turned out that it will last the remainder 9 weeks?
Jins. 214. 10. A grocer beurhit an equal quantity of sugar, tea, and coffee, for 40 dollars ; he gave 10 cents per lb. for the sugar, 60 cts. perib). for the tea, and 20 cts. per lb. for the coffee; required the quantity of cach?
Ans. 89910. Soz. S dr. 11. Bought cloth at $15 a yard, and lost 25 per cent. how was it sold a yard ?
Hrs. 95jcts. 12. The third part of an ormy was kille:, the fourth part taken prisoners, ansi 1000 Hled; how many were in lis army, how many kille ?, and how many captives :
dans., 3.100 the driny, 800 killed, and
000 takzeil m'isoners. 13. Thomas soli 150 pine apples at 331 cents a piece, and received as much inoney as llarry received for a certain number of water-wellons, which he sold at 25 cents a piece; how much money clici cach receive, and how many mellons liad llarry?
Ins. Each received $50), unti umry sold 900 millons.
14. Said John tu Dich, my purse and money are worth Ol. 2s. but the money is twenty-five times as inuch as the purse; I demand low inuch money was in it ?
Ans. $8 15$
15. A young man received 2101. which was ļ of his elder brother's portion ; now three times the elder brother'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 greyhound, and is not 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 3541. The cube of
their wiference is 1531. 19. Suppose there is a mast erected, so that į of its length stands in the ground, 19 feet of it in the water, and
of its length in the air, or above water; I demand the whole length ?
Sns. 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 suin, at the saine rate, and for the same time?
Ans. [112 10s. 21. Å stationer soli quills at us. per thousand, by which he cleared of the money, but growing scarce, raised them to 15. Cd. per thousandi ; what might he clear per cent. by the Intier price?
S. 22. Three persons purchase a West-ladia sloop, towards the payment of which A advances, and C 1401. How much paid A and 1, and what part of the vessel had c.. Ans. I puiil 4, 2651i, B 45056, 0's part of
the vessel icas } 23. What is the purchase of 12001. bani stock, at 1035
his. £1245 104. 24. Bought 97 pieces of Nankeens cask !! *
per cont. ?