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BY TABLE III.
Under 5 per cent. and even with 4 years.
Ans. £177,29750-present worth of the annuity.
3. What is 30l. per annum, to continue 7 years, worth
III. To find the present worth of Annuities, Leases, &e.
1. Divide the Annuity by that power of the ratio der
2. Subtract the quotient from the Annuity: Divide thé 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 ready money will purchase an Annuity of 501.
4th power of 1,051,215506)50,00000(41,15513
Divide by 1,05-1,05)8,86487
2d. power of 1,05-1,1025)177,297(160,8136-160 16s. 3d. 1gr. present worth of the Annuity in Reversion. OR BY TABLE III.
Find the present value of 17. at the given rate for the sum of the time of continuance, and time is reversion added together; from which value subtract the present worth of I. for the time in reversion, and multiply the remainder by the Annuity; the product will be the answer
Thus in Example 1.
Time of continuance, 4 years.
6 years, gives 5,075692
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. ?
3,216282 X50 160,8141
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. 8431 78cts. 22m. IV. To find the present worth of a Freehold Estate, or | an Annuity to continue forever, at Compound Interest.
As the rate per cent. is to 100l.: so is the yearly rent to the value required. EXAMPLES.
1. What is the worth of a Freehold Estate of 40. per annum, allowing 5 per cent. to the purchaser ?
As £5 £100 £40 £800 Ans. 2. An estate brings in yearly 150l. 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 de.. noted 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 ent immediately.
Then, 1,051,1025)800,00(725,62358=72 5d.-present worth of £800 in two years reversic
OR BY TABLE III.
Find the present worth of the annuity, or rent, time of reversion, which subtract from the value immediate possession, and you will have the value estate in reversion.
Thus in the foregoing example, 1,859410-present worth of Il. for 2 years. 40annuity or rent.
74,376400-present worth of the annuity or re [the time of revers From 800,0000-value of immediate possession. Take 74,3764-present worth of rent.
£725,6236=£725 12s. 54d. Ans.
2. Suppose an estate of 90 dollars per annum, te mence 10 years hence, were to be sold, allowing th chaser 6 per cent.; what is it worth?
Ans. $837, 39cts.
3. Which is the most advantageous, a term of 15 in an estate of 100l. per annum; or the reversion of an estate forever after the said 15 years, computing rate of 5 per cent. per annum, compound interest?
Ans. The first term of 15 years is better than th yersion forever afterwards, by £75 18s. 7d.
A COLLECTION OF QUESTIONS TO EXERC THE FOREGOING RULES.
1. I demand the sum of 1748} added to itself? Ans. 345 2. What is the difference between 41 eagles, and dimes? Ans. 10c.
5. What number is that which being mastiplied by the product will be 1365?
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 ? Ans. 20
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. £12548.
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, 60cts.
8. Just 16 yards of German serge, For 90 dimes had I;
How many yards of that same cloth Will 14 eagles buy? Ans. 248yds. Sqrs. 23na. 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?
10. A grocer bought an equal quantity of sugar, tea, and coffee, for 740 dollars; he 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?
Ans. 822lb. Soz. 88dr. 11. Bought cloth at $14 a yard, and lost 25 per cent. how was it sold a yard? Ans. 933cts. 12. The third part of an army was killed, the fourth part taken prisoners, and 1000 fled; how many were in this army, how many killed, and how many captives? Ans. 2400 in the army, 800 killed, and 600 taken prisoners.
15. Thomas sold 150 pine apples at 533 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 had Harry?
Ans. Each received $50, and Harry sold 200 mellons. 14. Said John to Dick, my purse and money are worth 91. 28. 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 elder brother's portion; now, three times the elder br er's portion was half the father's estate; what was value of the estate ? Ans. 1890 16. A hare starts 40 yards before a grey-hound, and not perceived by him till she has been up 40 seconds; scuds away at the rate of ten miles an hour, and the d on view, makes after her at the rate of 18 miles an ho How long will the course hold, and what space will ran over, from the spot where the dog started? Ans. 60 sec. and 530yds. space 17. what number multiplied by 57 will produce j what 154 multiplied by 71 will do? Ans. 1662
18. There are two numbers, whose product is 1610, greater is given 46; I demand the sum of their squar and the cube of their difference?
Ans. the sum of their squares is 3341.
19. Suppose there is a mast erected, so that of
21. A stationer sold quills at 11s. per thousand, which he cleared of the money, but growing scarc raised them to 13s. 6d. per thousand; what might h clear per cent, by the latter price?
Ans. £96 7s. S&d. 22. Three persons purchase a West-India sloop, te wards the payment of which A advanced 3, B, and 1401. How much paid A and B, and what part of th vessel had CP
Ans. A paid £267, B £505, and C's part of th vessel was
23. What is the purchase of 12007. bank stock, at 103 per cent.? Ans. £1243 10s. 24. Bought 27 pieces of Nankeens, each 11 yards, a