Case 9. When U, R, and T are given, to find P. Theorem 9. •-:*r-1=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 501. per annum, to continue 8 years, at 5 per cent. (28) What is the present worth of an annuity or yearly rent of 601. to continue 6 years at 4 per cent. ? (29) What is the present worth of a pension of 10001. per annum, for 21 years, at 4 per cent.? Case 10. When P, T, and R are given, to find U. prt xr-prt THEOREN 10. EU. rt-1 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 'Í'able 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. 38. 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. 6 d. at 4 per cent. for 6 years? (32) Suppose the present worth of a pension for 21 years, at 41 per cent. were 134046, 14s. 5d. what was the pension U Case 11. When U, P, and R are given, to find T. Which proceed with as THEOREM 11. -Rt. in Theorem 3: it will ptu-pr give T. By Table V. thus: divide the present worth by the annuity, and the quotient will be the amount of ll. 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 501. yearly rent for 3231. 3. 2 d. allowing 5 per cent to the purchaser? (34) If an annuity of 601. be purchased for 3141. 10s. 61d. 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 134046. 145. 5 d. is made at 4 per cent. Case 12. When U, P, and T are given, to find R. u Theorem 12.-=- R.+Rt.-Rt. +1, р P 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 il. annuity for the given time, over which will be the rate required. EXAMPLES. (36) If an annuity of 501. to continue for 8 years, be pur chased for 325l. 3s. 24d. what rate of interest has the purchaser for his money? (37) Suppose I give 3141. 10s. 6 d. for an annuity of 601. to continue 6 years, at what rate was interest allowed ? (38) If an annuity of 1000l. to continue 21 years, be pur chased for 134041. 145. 5 d. 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. RULE. 1. Find the present worth of the an. Thus, Treo. 13. nuity, &c. at the given rate, and for the time of its continuance, by U-:-1=P. Theorem 9. 2. Change P into A; and find what principal being put to interest will A amount to P, at the same rate and Thus P. Rt time to come before the annuity commences, by Theorem 2, which will give the present worth of the annuity. By Table V. thus: find the present value of 1l. 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 reinainder 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 80l. per annum, to continue 6 years, but not to commence 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. THEOREM 14. 1. Find the amount of the present worth at the given 2. Change A. into P, and find THEOREM 15. what yearly rent, &c. being sold, will produce P. at the same rate, and for the time ptr xr-prt Thus, gtal ofits continuance, by Theorem 10. 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. ld. 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. st = By the 4th table, thus: Multiply the tabular number for the given time and raie, by the sum to be purchased; the product will be the present worth. EXAMPLES. (43) What is the present worth of 1501. payable 4 years hence, at 5 per cent. ? (44) What is the present worth of 743l. 4s. Od. payable 6 years bence, at 4 per cent. ? L By Table IV. thus: Divide the present worth by the tabalar number for the given time and rate; and the quotient will be the sum to be purchased. EXAMPLES. (45) If 1231. 8s. 11d. 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? (46) Ifa sum of money, due 6 years hence, produce 5871. 7s. 9 d. for the present payment, rebate being made at 4 I demand how much the debt was, Which proceed with as in TheoTHEOREM 18. =rt. р rem 3. By Table IV. thus : Divide the principal by the sum to be purchased ; and the quotient will be the present worth of 1l, at the given rate, which will be found under the rate, and even with the time required. { EXAMPLES. (47) A person received 1231. 8s. 11d. for a debt of 1501., re bate being made at 5 per cent. I demand in what time the debt was payable. (48) The present payment of 5871. 7s. 9 d. is made for a debt of 7431. 4s. 9d. rebate at 4 per cent. I demand when the debt was payable. When S, P, and T are given, to find R. S THEOREM 19. P rem 4. By Table IV. thus: Proceed as in the last rule, and the quotient will be the present worth of 1l. for the given time, which will be found even with the time, and under the rate required. =R. { Whech proceed with as in Theo EXAMPLES. (49) The present worth of 1501. payable 4 years hence, is 1231. 8s. 11d. At what rate per cent. is the rebale made? |