EXAMPLES.

(29) If a Salary, payable Yearly, amounts to 16127 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?

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 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 250/ per Annum, payable Half-Yearly, amounts to 1623/ in 6 Years, what is the Rate per Cent.?

(34) Suppose a Pension of 250/ 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 250/ per Annum amount to 1612/ 10s at 3 per Cent.?

(36) If an Annuity of 250/ per Annum, payable Haif-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 1629/ 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 250/ 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 250/ 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 13764 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 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 1366/ 10s 6d for the present Worth at 3 per Cent. what is the Time of its Continuance?

2

(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 2501 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 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 801 per Annum, to continue 74 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 2 24d. allowing 3 per Cent. to the Purchaser. What is the Yearly Income?

(54) There is a Lease of a House taken for 74 Years, but not to commence until the End of five Years; the Lessee would sell the same for 419/15s 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 241/ 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.?