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 after that time at 6 per cent.?

Ans. £233 15s. 9d. 4. 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, 78 cts. 23⁄4m. IV. To find the present worth of a Freehold Estate, or as Annuity to continue forever, at Compound Interest.

RULE.

As the rate per cent. is to 1007. so is the yearly rent to the value required.

EXAMPLES.

1. What is the worth of a freehold estate of 40%. per an num, allowing 5 per cent. to the purchaser?

As £5 £100 :: £40 £800 Ans. 2. An estate brings in yearly 1507. 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 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 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.

EXAMPLES.

1. Suppose a freehold estate of 40%. per annum to com mence two years hence, be put on sale; what is its value, allowing the purchaser 57. per cent.?

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

Then, 1,05=1,1025)800,00(725,62358=7251. 12s. 5d.-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 17. 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.

£725,6236=£725 12s. 51d. Ans.

2. Suppose an estate of 90 dollars per annum, to commence 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 1007. 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. 10 cts. 3. What number is that which being multiplied by 21, the product will be 1365?

quotient will be 72?

4. What number is that which being divided by 19, the Ans. 1368. 5. What number is that which being multiplied by 15, the product will be ??

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 167. 6s. 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 16 yards of German serge,

For 90 dimes had I;

How many yards of that same cloth
Will 14 eagles buy?

Ans. 248 yds. 3 qrs. 23 na.

9. A certain quantity of pasture will last 963 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 coffee, for 740 dollars; he gave 10 cents per lb. for the su gar, 60 cts. per lb. for the tea, and 20 cts. per lb. for the coffee; required the quantity of each?

Ans. 822 lb. 3 oz. 8§ dr. 11. Bought cloth at $1 a yard, and lost 25 per cent., how was it sold a yard? Ans. 933 cts. 12. The third part of an army was killed, the fourth part taken prisoners, and 1000 fled; how many 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 melons had Harry? Ans. Each rec'd $50, and Harry soid 200 melons.

14. Said John to Dick, my purse and money are worth 91. 2s., but the money is twenty-five times as much as the purse; I demand how much money was in it? Ans. £8 15s.

15. A young man received 210l. which was of his el ier brother's portion; now three times the elder brother's portion was half the father's estate; what was the value of he estate? Ans. £1890.

16. A hare starts 40 yards before a grey-hound, and is not perceived by him till she has been up 40 seconds; she ucuds 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. 166.

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 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 5007. 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. 6d. per thousand; what might he clear per cent. by the latter price? Ans. £96 7s. 3d. 22. Three persons purchase a West-India sloop, towards the payment of which A advanced 3, B, and C 1407. How much paid A and B, and what part of the vessel had C?

Ans. A paid £267, B £305T, and C's part of the vessel was

.

23. What is the purchase of 12007. bank stock, at 103 Ans. £1243 10s. per cent. ? 24. Bought 27 pieces of Nankeens, each 11 yards, at

14s. 4 d. a piece, which were sold at 18d. a yard; required the prime cost, what it sold for, and the gain.

25. Three partners, A, B and C, join their stock, and buy goods to the amount of £1025,5; of which A put in a certain sum; B put in...I know not how much, and C the rest; they gained at the rate of 241. per cent.: A's part of the gain is, B's, and C's the rest. Required each man's particular stock.

A's stock was 512,73

26. What is that number which being divided by 3, the

quotient will be 21 ?

27. If to my age there added be,
One-half, one-third, and three times three,
Six score and ten the sum will be;
What is my age, pray show it me?

Ans. 153.

Ans. 66.

28. A gentleman divided his fortune among his three sons, giving A 97. as often as B 51. and to C but 31. as often as B 71. and yet C's dividend was 25847.; what did the whole estate amount to? Ans. £19466 2s. Ed.

29. A gentleman left his son a fortune, of which he spent in three months; of the remainder lasted him 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, plums, 40 of them 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 sum shall make 65; can you tell me the number? Ans. 1400.