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• Thus in Example 1.
Time of continuance, 4 years.
Ditto of reversion, 2
The sum,

=6 years, gives 5,075692
Time in reversion, 52 years,

1,859410 Remainder, 3,916282 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 continue 7 years after that time at 6 per cent. ?

Ans. £233 155. 9d. 3. What is the present worth of thể 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 ? Ans. $431 78cts. % jin. 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 : : £40 : £800 Ans. 2. An estate brings in yearly 1501. what would it sell for, allowing the purchaser 6 per cent. for luis money?

Ans. 9500 V. To find the present worth of a Freehold Estate, in Reversion, at Compound Interest.

RULE. 1. Find the present value of the estate (by the foregoing rule) as though it were to be entered on jinnredliately, 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 Reversiun.

EXAMPIES. 1. Suppose a freeholil estate of 401. per annuin tu coinmence two years lience, be put on sale; what is its valuc,

; allowing the purchaser 51. per cent.?

EXAMPLES

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2

As 5 : 100 : : 40 : 800=present worth if entered on immediately.

Then, 1,05=1,1025)800,00(725,62358=7251. 12s. 531.=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. fur2

ycars. 40=annuity or rent. 74,376400=present worth of the annuity or rent, for

[the time of reversion. From 800,0000=value of iminediate possession. Take 74,3764=present worth of rent.

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£.725,6236+6725 12s. 5d. Ins. 2. Suppose an estate of 90 dollars per annum, to commence 10 years hence, were to be sold, allowing the pur chasei 6 per cent.; what is it worth ?

Aris. 8837, 59cts. 2m. 3. Which is the most advantageous, a term of 15 years, in an estate of 100l. per annum; or the reversion of sucha 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 rcversion forever afterwards, by £75 18s. 7 d.

A COLLECTION OF QUESTIONS TO EXERCISE

TIIE FOREGOING RULES. 1. I demand the sum of 17481 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, the product will be 1365 ?

Aus. 65.

4. What number is that which being divided by 19, tie quotient will be 79

Anis. 1363. 5. Viliatasi ber is that which being inultiplieil by 15, the product will be ?

ns. fi. There are 7 chosts of drawers, in cach of which there are 18 dhaters, and in cach of these there are six divisions, in each of which is 161. 6s. 8d.; how much money is there in the whole ?

Sus. £ 12348. 7. Bonglit 36 pipes of wine for 4556 dollars; liew must I sell it a pipe to save one for any own use, and sell the rest for what the whole cost: Ans. $129, COcts: 8. Just 16 yards of German scrgc,

For 90 dimes hart I;
líow many yards of that same cloth

Will 14-eagles buy? Ans. 24&yds. Sqrs. 2a. 9. A certain quantity of pasture will last 965 sheep 7 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 coikee, for 740 dollars ; lie gave 10 cents per lb. for the sugar, 60 cts. per lb. for the teag and 20 cts. per Ib. for the coffee ; required the quantity of each ?

Ans. 82216. 30. 8 r. 11. Bought cloth at 814 a yard, and lost 25 per cent. how was it sold a yard ?

Ans. 93acts. 12. The third part of an army was killeil, the fourth part taken prisoners, and 1000 lied'; how many were in this arıny, low 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 a picce, 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 had llarry ? Ans. Ench received $50, and Harry sold 200 meļlons.

14. Said Jolin to Dick, my purse and money are worth 9l. 2s. but the money is twenty-five times as inuch as the purse; I deinand how much money was in it ?

Ans. £ 8. 155

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13. A young man received 2101, which was 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 scads away at the rate of ten miles an hour, and the dogany un view, inakes after her at the rate of 18 miles an hour : llow long will the course hold, and what space will be ran over, from the spot where the dog started'?

Ans. 60 sec, and 550yds, space. 17. What number multiplied by 57 will produce just what 154 multiplied by 71 will do? Ans. 16632

18. There are two numbers, whose product is 1610, the greater is given 46; I demand the suin 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 length stands in the ground, 12 feet of it in the water, and

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 statiorier sold quills at 11s. per thousand, by which he cleared of the money, but growing, scarce, raised them to 13s. 6d. per thousand ; what might he clear

l per cent. by the latter price?

Aes. 496 7. 37. 22. Three persons purchase a West-India sloop, to. wards the payment of which A advanced }, B }, and C 1401. How much paid A and B, and what part of thọ vessel had CP Ans. A paid £267ii, B £50511, and C's part of

the vessel was to 23. What is the purchase of 1200l. bank stock, at 103%

Ans. £ 1243 10$. 24. Bought 27 pieces of Nankcens, eaede 118 pads, at

3

per cent. ?

!

5

148. 48d. a piece, which were sold at 18d. a yard; required the prime cost, what it sold for, and the gain.

{. s. d. Prime cost, 19 8 Ans. Sold for, 23 5 9

Gain, S.17 75 25. Three partners, A, B and C, join their stock, and buy goods to the amount of £1025,5 ; of which A putin a certain sun; B put in.... I know not liowo much, and C the rest; they gamed at the rate of 2+l. per cent. : A's part of tho gain is , Bos , and C's the rest. Required each man's particular stock.

4 I's stock uns 512,75 Ans. B's

205,1

C's -- S07,65 26. What is that number which being divided by 1, the quotient will be 21 :

Ans. 151. 27 If to my age there 'added be,

One-halt, one-third, and three times three,
Six score and ten the sum will be ;
Wat is my age, pray shew it me?

Jils. 66. 28. A gentieman divided his fortune among his three sons, giving A 91. as often as B 5l. and to C but 31. as often as Bil. and yet C's dividend was 25841. ; what did the whole estate amount to

Ans. 419466 25. $d. 29. A gentleman left his son a fortune, of which he spent in three months; of the remainder lasterl lim 10 months longer, when he had only 2524 dollars left; pray what did his father bequeath him?

Ans. $5889, 33cts. + 30. In an orchard of fruit trees, of them bear apples,

pears, à plums, 40 of tien peaches, and 10 cherries; how many trees does the orchard contain ? Ans. 600.

31. There is a certain number, which being divided by 7, the quotient resulting multiplied by 3, that product divided by 5, from the quotient 20.being subtracted, and 30 added to the remainder, the half suin shall inake 65 ban vou tell me the number?

Aas. 1400.

a

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