EXAMPLES. (29) If a Salary, payable Yearly, amounts to 1612/ 10s in 6 Years, as 3 per Cent. what is the Salary? (30) The Amount of a Salary, payable Half-Yearly, for 6 Years, at 3 per Cent. is 1623/ 15s. What is the Salary? (31) If the Amount of an Annuity, payable Quarterly, be 16291 7s 6d for 6 Years, at 3 per Cent. what is the Annuity? Gase 12. When U, A, and T, are given, to find R. ut -ut = 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 at is mentioned in Theorem 9. EXAMPLES. (32) If a Salary of 250 per Annum amounts to 1612/ 10s in 6 Years, what is the Rate per Cent? (33) If a Salary of 2501 per Annum, payable Half-Yearly, amounts to 1623/ in 6 Years, what is the Rate per Cent.? (34) Suppose a Pension of 2501 per Annum, payable Quarterly, amounts to 1629/ 7s 6d in 6 Years, what is the Rate per Cent? Case 13. When U, A, and R, are given, to find T. 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 2501 per Annum amount to 1612/ 10s at 3 per Cent.? (36) If an Annuity of 2501 per Annum, payable Half-Year ly, amount to 16231 15s at 3 per Cent. what Time were the Payments forborne ? (37) If an Annuity of 250/ per Annum, payable Quarterly, amounts 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 Quarterly Payments, as before mentioned. EXAMPLES. (38) What is the present Worth of 2501 per Annum, to con tinue 6 Years? (39) What is a Pension of 250/ per Annum worth in ready Money, payable Half-Yearly, at 3 per Cent. for 6 Years? (40) What is the present Worth of 25C/ payable Quarterly, for 6 Years, at 3 per Cent.? Case 15. When P, T, and R, are given, to find U. When the Payments are Half-Yearly, multiply by 4p; for Quarterly, by 8p; and proceed with and r as before directed. EXAMPLES. (41) What Annuity is that which, for 6 Years' Continuance, produces 1366/ 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 1376/ 5s. ? (43) There is an Annuity, payable Quarterly, for 6 Years to come,; what is the Yearly Income, when the present 12 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 HalfYearly, 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 2501 per Annum, to continue 6 Years, produce the present Worth of 1366/ 10s 6d. ? (45) If an Annuity of 250 per Annum, payable HalfYearly, having 6 Years to come, is sold for 1376/ 5s what is the Rate per Cent.? (46) At what Rate per Cent. will an Annuity of 250/ 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 2501 per Annum produces 13667 10: 6d for the present Worth at 3 per Cent. what is the Time of its Continuance ? (48) An Annuity of 2501 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 250/ per Annum, payable Quarterly, is sold for 1380/ 17s 6d at 3 per Cent. I demand the Number of Payments, and Time to come? LXIV. ANNUITIES, &c. taken in REVERSION. Case 18. To find the present Worth of an Annuity taken in Reversion. (50) What is the present Worth of 250/ 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 801 per Annum, to continue 7 Years, but not to commence until the End of 5 Years, allowing 44 per Cent. to the Purchaser ? (52) There is a Legacy of 401 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 minded 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 25 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 five Years; the Lessee would sell the same for 419/ 15s 14d. present Payment, allowing 44 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 2417 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 150/ due 9 Months hence, at 5 per Cent.? |