Case 9. When U, R, and T are given, to find P. By Table V. thus: multiply the tabular number for the given time and rate by the annuity, &c. the product will be the present worth required. EXAMPLES. (27) What is the present worth of an annuity of 50l. per annum, to continue 8 years, at 5 per cent. (28) What is the present worth of an annuity or yearly rent of 60l. to continue 6 years at 4 per cent.? (29) What is the present worth of a pension of 1000l. per annum, for 21 years, at 4 per cent.? Case 10. When P, T, and R are given, to find U. By Table V. thus: divide the present worth by the tabular number for the given time and rate; and the quotient will be the annuity required. Or by Table VI. thus: multiply the tabular number (for the given rate and time) by the present worth; and the product will be the annuity. EXAMPLES. (30) If the present worth of 3231. 3s. 24d. were required for a pension of 8 years to come, at 5 per cent. what was the pension? (31) What annuity or yearly rent may be purchased for 3141. 10s. 6d. at 4 per cent. for 6 years? (32) Suppose the present worth of a pension for 21 years, at 4 per cent. were 134041. 14s. 51d. what was the pension? Case 11. When U, P, and R are given, to find T. u THEOREM 11. = Rt. p+u-pr Which proceed with as in Theorem 3: it will give T. By Table V. thus: divide the present worth by the annuity, and the quotient will be the amount of 17. at the given rate, which will be found under the said rate, even with the time required. EXAMPLES. (33) How long may one have a lease of 50l. yearly rent for 3231. 3s. 2 d. allowing 5 per cent. to the purchaser? (34) If an annuity of 604. be purchased for 314l. 10s. 6d. at 4 per cent. what time ought it to continue ? (35) I demand what time a lease of 1000l. may be purchased for, when the present worth of 184047. 14s. 52d. is made at 4 per cent. Case 12. When U, P, and T are given, to find R. This being a very high equation, requires the assistance of Algebra to determine R. By Table V. proceed as in the last Rule; and the quotient will be the amount of 17. annuity for the given time, over which will be the rate required. EXAMPLES. (36) If an annuity of 50l. to continue for 8 years, be purchased for 3251. 3s. 24d. what rate of interest has the purchaser for his money? (37) Suppose I give 3142. 10s. 63d. for an annuity of 60l. to continue 6 years, at what rate was interest allowed? (38) If an annuity of 1000l. to continue 21 years, be purchased for 134047. 14s. 5d. what rate of interest is the purchaser allowed for his money? LXX. ANNUITIES, LEASES, &c. taken in RE VERSION. To find the present Worth of Annuities, &c. in Reversion. 2. Change P into A; and find what > By Table V. thus: find the present value of 17. per annum, at the given rate, both for the time being, and also for that and the time in reversion added together; then subtract the time in being from the other, and multiply the remainder by the annuity: the product will be the present worth required. EXAMPLES. (39) What is the present worth of a reversion of a lease of 801. per annum, to continue 6 years, but not to com mence till the end of 2 years, allowing 5 per cent. to the purchaser? (40) What ought a person to give down in ready money for the reversion of 1000l. a-year, to continue: 20 years, on a lease which cannot commence till 5 years are at an end, allowing the purchaser 5 per cent.? To find the Yearly Income of an Annuity taken in Reversion. RULE. 1. Find the amount of the present worth at the given THEOREM 14. rate, and for the time before Thus, pre-A. the annuity commences, by Theorem 1. By Table V. thus: proceed as in the last rule, and divide the present worth by the remainder: the quotient will be the annuity required. EXAMPLES. (41) What annuity, to be entered upon two years hence, and then to continue 6 years, may be purchased for 3681. 6s. 1d. ready money, allowing 5 per cent. to the purchaser ? (42) Suppose the present worth of a lease of an estate be 81321. 14s. 8d. taken in reversion for 20 years, but not to commence till the end of 5 years, allowing 5 per cent. to the purchaser: what is the yearly rent? LXXI. REBATE or DISCOUNT. Here S represents the sum to be purchased. By the 4th table, thus: Multiply the tabular number for the given time and rate, by the sum to be purchased; the product will be the present worth. EXAMPLES. (43) What is the present worth of 150l. payable 4 years hence, at 5 per cent.? (44) What is the present worth of 7431. 4s. 9d. payable 6 years hence, at 4 per cent. ? When P, T, and R' are given, to find S. THEOREM 17. pxrts. L By Table IV. thus: Divide the present worth by the tabular number for the given time and rate; and the quotient will be the sum to be purchased. EXAMPLES. (45) If 1237. 8s. 13d. be received for a debt payable 4 years hence, and an allowance of 5 per cent. to the debtor for the present payment, what was the debt? If a sum of money, due 6 years hence, produce 5871. 78. 92d. for the present payment, rebate being made at 4 per cent. I demand how much the debt was. (46) By Table IV. thus: Divide the principal by the sum to be purchased; and the quotient will be the present worth of 17. at the given rate, which will be found under the rate, and even with the time required. EXAMPLES. (47) A person received 1237. 8s. 14d. for a debt of 150l., rebate being made at 5 per cent. I demand in what time the debt was payable. I demand when (48) The present payment of 5871. 7s. 93d. is made for a debt of 7431. 4s. 9d. rebate at 4 per cent. the debt was payable. When S, P, and T are given, to find R. =R. S THEOREM 19. = {Which proceed with as in Theo By Table IV. thus: Proceed as in the last rule, and the quotient will be the present worth of 11. for the given time, which will be found even with the time, and under the rate required. EXAMPLES. (49) The present worth of 1507. payable 4 years hence, is 1231. 8s. 14d. At what rate per cent. is the rebate made? : |