EXAMPLES. (29) If a salary, payable yearly, amount to 16127. 10s. in 6 years, at 3 per cent. what is the salary? (30) The amount of a salary payable half-yearly, for 6 years, at 3 per cent. is 16237. 15s. What is the salary? (31) If the amount of an annuity, payable quarterly, be 16297. 7s. 6d. for 6 years, at 6 per cent. what is the annuity? Case 12. When U, A, and T are given, to find R. When the payments are half-yearly, take 4a-4ut for a dividend; if quarterly, take 8a-ut, and proceed with the annuity and time as is mentioned in theorem 9. EXAMPLES. (32) If a salary of 2501. per annum amount to 16127. 10s. in 6 years, what is the rate per cent. ? (33) If a salary of 250l. per annum, payable half-yearly, amount to 16231. in 6 years, what is the rate per cent.? (34) Suppose a pension of 250l. per annum, payable quarterly, amount to 16291. 7s. 6d. in 6 years, what is the rate per cent.? Case 13. When U, A, and R are given, to find T. 12a XX THEOREM 12. First -1=X. Then :=T. 2 ur 4 When the payments are half-yearly or quarterly, proceed with the ratio and annuity as mentioned before, and T will be equal to those half-yearly or quarterly pay ments. EXAMPLES. (35) In what time will a salary of 250l. per annum amount to 16127. 10s. at 3 per cent.? (36) If an annuity of 250l. per annum, payable half-yearly, amount to 16231. 15s. at 3 per cent. what time were the payments forbornę? (37) If an annuity of 250l. per annum, payable quarterly, amount to 16291. 7s. 6d. at 3 per cent. what was the time of forbearance ? LXIII. PRESENT WORTH of ANNUITIES, &c. HERE P represents the present worth, U, T, and R, as before. Case 14. When U, T, and R are given, to find P. The same is to be observed here for half-yearly and quar terly payments as before mentioned. EXAMPLES. (38) What is the present worth of 2507. per annum, to continue 6 years? (39) What is the pension of 250l. per annum worth in ready money, payable half-yearly, at 3 per cent. for 6 years? (40) What is the present worth of 2501. payable quarterly, for 6 years, at 3 per cent.? Case 15. When P, T, and K are given, to find U. When the payments are half-yearly, multiply by 4p; for quarterly, by 8p; and proceed with t and r as before directed. EXAMPLES. (41) What annuity is that which, for 6 years' continuance, produces 13667. 10s. 6d. present worth, at 3 per cent.? (42) There is an annuity, payable half-yearly, for 6 years to come; what is the yearly income, when the present worth, at 3 per cent. is 13761, 5s.? (43) There is an annuity, payable quarterly, for 6 years to come; what is the yearly income, when the present worth is 1380. 17s. 6d. at 3 per cent.? Case 16. When U, P, and T are given, to find R. When the payments are half-yearly or quarterly, proceed with the annuity and time as before directed; and the quotient will be the answer accordingly; i. e. if for half-yearly, the quotient will be half the ratio, and if for quarterly, a fourth part of the ratio. EXAMPLES. (44) At what rate per cent. will an annuity of 250l. per annum, to continue 6 years, produce the present worth of 1366l. 10s. 6d. ? (45) If an annuity of 250l. per annum, payable half-yearly, having 6 years to come, be sold for 13761. 5s. what is the rate per cent.? (46) At what rate per cent. will an annuity of 250l. per annum, payable quarterly, to continue 6 years, produce 1380%. 17s. 6d. for the present worth? Case 17. When U, P, and R are given, to find T. When the payments are half-yearly, or quarterly, proceed with the annuity and ratio as before directed, and the quotient will be the number of payments. EXAMPLES. (47) If an annuity of 250l. per annum produce 1366l. 10s. 6d. for the present worth at 3 per cent., what is the time of its continuance? (48) An annuity of 250l. per annum, payable half-yearly, is sold for 13761. 5s. at 3 per cent. I desire to know the number of payments and time to come. (49) Suppose a lease of a house of 250l. per annum, payable quarterly, be sold for 1380l. 17s. 6d. at 3 per cent. demand the number of payments, and time to come. LXIV. ANNUITIES, &c. taken in REVERSION. I Case 18. To find the present worth of an annuity taken in Reversion. (50) What is the present worth of 2501. per annum, to continue 6 years, but not to commence until the end of 4 years, allowing 3 per cent. to the purchaser ? (51) What is the present worth of a lease of 80l. per annum, to continue 71⁄2 years, but not to commence until the end of 5 years, allowing 4 per cent. to the purchaser ? (52) There is a legacy of 40l. per annum, for 10 years, left to a person of 14 years of age; the time of payment is not to commence till the said person's age be 21; but he, wanting a sum of money, is inclined to sell the same at 5 per cent. I demand the present worth. Case 19. To find the yearly income of an annuity, &c. in reversion. (53) A person having an annuity left him for 6 years and 5 months, but not to commence till the end of 4 years, has disposed of it for the present payment of 12201. 2s. 24d. allowing 3 per cent. to the purchaser. What is the yearly income? (54) There is a lease of a house taken for 7 years, but not to commence until the end of 5 years: the lessee would sell the same for 4191. 15s. 14d. present payment, allowing 4 per cent. to the purchaser. What is the yearly rent? (55) There is a legacy of a certain rate per annum, for 10 years, left to a person of 14 years of age; but the time of payment is not to commence till the said person's age be 21 years; but he, wanting a sum of money, sold it for 2411. 19s. 6d. allowing 5 per cent. to the buyer. I demand the yearly rate. LXV. REBATE or DISCOUNT. HERE S represents the sum to be discounted, P the present worth, T and R as before. Case 20. When S, T, and R are given, to find P. (56) What is the present worth of 1507. due 9 months hence, at 5 per cent. ? |