BY TABLE III. Under 5 per cent. and even with 4 years. We have 3,54595=present worth of 1l. for 4 year. Multiply by 50 - Annuity. Ans. £177,29750=present worth of the annuity. 2. What is the present worth of an annuity of 60 dois. per annum, to continue 20 years, at 6 per cent. compound interest? Ans. $688, 19fcts.+ 3. What is 30l. per annum, to continue 7 years, worth in ready money, at 6 per cent. compound interest ? Ans. £167 9s. 5d. t MI 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 deno. ted 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 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 = 1,215506)50,00000(41,18513 Subtract the quotient=41,13513 EXAMPLES. Divide by 1,05—15,05)8,86487 2d. power of 1,05=1,1025)177,297(160,8136160 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 the sum of the time of continuance, and time in reversion added together; from which value subtract the present wurth of il. for the time in reversion, and multiply the remainder by the Annuity ; the product will be the anspen Thus in Example L 2 The sum =6 years, gives 5,075692 Time in reversion, >2 years, 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 unul 10 years hence, and then to con. tinue 7 years after that time at 6 per cent. ? Ans. £233 158. 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. 215 m. 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 40%. per annum, allowing 5 per cent to the purchaser ? As 15 : £100 :: £40 ; £800 Ans. 2. An estate brings in yearly 1506. 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 Vasue 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 deno ted oy the time of reversion, and the quotient will be the present worth of the estate in Reversion. EXAMPLES. EXAMPLES. 1. Suppose a freehold estate of 401. per annum to come mence two years hence, be put on sale ; what is its value, allowing the purchaser 5l. per cent. ? As 5 : 100 : : 40 : 860=Epresent -worth if entered on immediately. Then, 1,05=1,1025)800,00(725,62358=7251. 128. 5{d.: =present worth of £800 in iwo 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 possessim, Take 74,3764=present worth of rent. £725,6236=£725 128. 5.d. Ans. 2. Suppose an estate of 90 dollars per annum, to commence 10 years hence, were to be sold, allowing the pur. chaser 6 per cent.; what is it worth ? Ans. $837, 59cts. 200. 3. Which is the most advantageous, a term of 15 years, in an estate of 100l. per annum; or the reversion of sucli an estate forever after the said 15 years, computing at thc rate of 5 per cent. per annum, compound interest ? Ans. The first term of 15 years is better than the reversion forever afterwards, by £75 188. 7 d. A COLLECTION OF QUESTIONS TO EXERCISE THE FOREGOING RULES. Ans. 3497. 2. What is the difference between 41 eagles, and 4099 dimes ? 499. 10cts. 8. What number is that which being multiplied by 21, the product will be 136? Ans. 65. Ans. ' 4. What number is that which being divided by 19, the quotient willbe 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 which there are 18 drawers, and in each of these there are six divisions, in each of which is 161. 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, 60cts. 8. Just 16 yards of German serge, For 90 dimes had I : Will 14 vagles buy ? Ins. 248yils. 3grs. 2; nu. 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? Anze. 214. 10. A grocer bough an equal quantity of sugar, tea, and cofios, for 740 dollars ; lie, gave ten cents per lb. for the sugar, 69 cts per lh, for the tea, and 20 cts. per lb. for the coffee ; required the quantity of each? Ans. 8221b. Soz. 83 dr. 11. Bought cloth at $11 a yard, and lost 23 per cent. how was it sold a yard ? Ans. 93cte. 12. The third part of ar army was killed, the fourth part taken prisoners, and 1000 ted; how many were in this army, how mary killed, and how mary captives? ins. 2400 ir t'e army, 800 killed, and 000 takcie prisoners. 13. Thomas sold 150 pine apples at 33 cents a piece, and received as much money as Harry received for a certain nunber 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 receiveil $50), and Harry sold 200 mellons. 14. Said Joht tv Dick, my purse and money are worth 9l. 2s. but the story is twenty five times as niuch as the purse ; I demand how much money was in it? Ans £8 15A 15. 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 va lue of the 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 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 vhat 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 prorlnce just what 134 multiplied by 71 will do ? Ans. 1663) 18. There are 2 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 ihat of its !ength 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 betrveen 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 raisartheni to 13s. 6d. per thousand ; what might he clar per cent by the latter price ? Ans. £96 7s. 38. 22. Three persons purchase a West-India sloop, towards the paymant of which A advanced , B , and C 1401. How much paid A and B, and what part of the vessel had C? Ans. A paid £267, B £305ft, and C's part of the vessel was to 23. What is the purchase of 12001. bank stock, at 103 Ans. £1243 10s. 24. Bought 27 pieces of Nankccns, eich 11! yards, per cent. ? |