and allow him 5 per cent for present payment; I demand how much the debt is? Ans. 1617 10s. 3 A legacy was left me the 24th of July, 1798, to be paid on the Christmas-Day following, but I agree with the Executor, and allow him 6 per cent for the present payment of 9751 3s Od 3 qrs. I demand what the Legacy was? Ans. 1000l. CASE 3. Q. When S, P, and R, are given to find T, how is it discovered? A. Taus; s-P rp. EXAMPLES.. The present worth of 795 11s 2d due for a certain time to come, is 7541 18.8d at 6 per cent. I demand in what time the first sum should have been paid, if no rebate had Deen made? Ans. 11 months. 2 There is 161/ 10s due at a certain time to come, but I allow 5 per cent to the debtor, for the present payment: of 1497 138 0 3 qrs. I demand when the sum should have been paid without any rebate? Ans. 19 months. 3 I have received 9751 3s od 3 qrs. for a legacy of 10001. allowing the executors 6 per cent. I demand when the legacy was payable without rebate? Ans. 155 days. CASE 4. Q. When S, P, and T, are given to find R, how is it discovered? 1 At what rate per cent will 795 11s 2d payable 11 months hence produce 745 is 3d for the present payment? Ans. 6 per cent. 2 At what rate per cent will 1617 10s payable 19 months hence, produce the present payment of 1491 13s od 3 qrs.? Ans. 5 per cent. 3 Suppose a legacy of 1000l is left me the 24th of July, 1798, to be paid on the Christmas-day following, but I agree with the executor for the present payment of 975 85 Od 3 qrs I demand the rate per cent allowed for his money? Ans, 6 per cent. OF EQUATION OF PAYMENTS. Q. How is the equated time for the payment of a sum of money due at several times, found out? A. Thus; 1. find the present worth of each payment for its respective time, as in Rebate, that is; 2 Add all the present worths together, and call that sum also P; then is s―p=d the Rebate, 3 d pr e is the true equated time. EXAMPLES. 1 A owes B 2001 to be paid as follows, viz. 1'007 at 3 months; and 100l at 4 months: but they agree to have but one payment of the whole, Rebate being made at 6 per cent. I demand the true equated time? Ans. 3 months. 2 A Merchant hath owing him 300l to be paid as follows; 501 at 2 months, 100l at 5 months, and the rest at 8 months; and it is agreed to have but one payment of the whole, Rebate being made at 5 per cent. I demand the equated time? Ans. 5.9796 months. 3 Fowes to H 1000l whereof 2001 is to be paid present; 400l at 5 months; and the rest at 10 months; but they agree to have but one payment of the whole, at the rate of 3 per cent Rebate; I demand the true equated time? Ans. 181 days. 4 A man owes a merchant 1200l to be paid as follows> 2001 down, 500l at the end of 10 months; and the rest at the end of 20 months; and they agree to have but one payment of the whole, Rebate at 8 per cent. I demand the true equated time? Ans. 1 year, 11 days. OF COMPOUND INTEREST. Q. WHAT particular Letters are used here? A. These: P, the Principał. T. the Time; R. the amount of 11 for 1 year at any given Rate; Q. How is the amount of 1l for 1 year, at any propos ed rate per cent found? A. Thus: As 100: 106 :: 1 : 1.06 100 105 :: 1 : 1.05, &c. A Table of the Amounts of 11 for 1 Year. Rates per Ct.]Amts. of 17.]Rates per Ct. Amts. of 17. Q. When P. T, and R, are given to find A, how is it discovered? t A. Thus: pxr=a. Note, R must be involved so many times as the number of t direct, and that will be r. EXAMPLES. 1 What sum will 450l amount to in 3 years time, at 5 per cent per ann.? Answer 520l 18s 7d 2 qrs. 2 What will 400/ amount to in four years at 6 per cent. per ann,? Answer 5041 19s 9d 3.15264 qrs. 3 What will 480l amount to in 6 years, at 5 per cent per ann.? Answer 643/ 4s 41.0178d. 4 What is the amount of 500l at 44 per cent per ann. for 4 years? Answer 590 11s 5d 2.95+qrs. CASE 2. Q. When A, R, and T, are given to find P, how is it discovered? 1 What principal must be put to interest to amount to the sum of 520l 18s 7d 2 qrs. in 3 years, at 5 per cent. per ann.? Answer 450l. 2 What principal will amount to 504/ 19s 9d 3.15264 qrs. in 4 years, at 6 per cent. per ann.? Answer 400l. 3 What principal will amount to 6437 48 11.0178d in 6 years, at 5 per cent. per ann. ? Answer 48Bol, 4 What principal will amount to 590l 11s 5d 3qrs in 4 years, at 41 per cent? Ans. 5001. CASE 3. Q. When P, R, and A, are given to find T, how is it discovered? 1) which being continually divided by r, till nothing remains, the Num ber of those divisions will be=t. EXAMPLES. 1 In what time will 450l amount to 5201 18s 7d 2qrs at 5 per cent. per ann? Ans. 3 years. 2 In what time will 400l amount to 504/ 19s 9d 3.2qrs. at 6 per cent. per ann? Auswer 4 years. 5 3 In what time will 480l amount to 643 14s 11.1d at per cent per ann? Answer 6 years. 4 In what time will 500l amount to 590 11s 5d 3qrs. at 4 per cent per ann? Ans. 4 years. t CASE 4. Q. When P, A, and T, are given to find R, how is it discovered ? which must be extracted by the rules of extraction; the time given in the question t shewing the power. EXAMPLES. α A. Thus -=r 1 At what rate per cent will 450l amount to 520l 18s 7d 2qrs in 3 years? Ans. 5 per cent. 2 At what rate per cent will 400/ amount to 504/ 19s 9d 3.2qrs in 4 years ? Ans. 6 per cent. 3 At what rate per cent will 480l amount to 643/ 4s 11 1d in 6 years? Answer 5 per cent. 4 At what rate per cent will 500l amount to 590l 11s 5d 3qrs in 4 years? Answer 41 per cen1. OF ANNUITIES, OR PENSIONS IN ARREARS. CASE 1. Note. U represents the Annuity, Pension, &c. T, R & A as before. Q. When U, T, and R, are given to find A, how is it discovered? t A. Thus; ur-u r-1 EXAMPLES. What will an annuity of 30% per ann. payable year P ly, amount to in 4 years, at 5 per cent? Ans. 1291 65 Od 3.6qrs. 2 Suppose a Pension of 50l per ann. payable yearly, be granted to a superannuated Officer; what is the amount for 5 years forbearance at 4 per cent? Ans. 270l 16s 3d 3.4+qrs. 3 If the yearly rent of a house which is 40l be forborn 7 years at 6 per cent. what is the amount? Ans. 335 15s od 3.3+qrs. 4 If a salary of 351 per annum to be paid yearly, be omitted for 6 years at 54 per cent. what is the amount? An. 241 is 7d 2.5qrs. CASE 2. Q. When R, T, and A, are given to find U, how is it discovered? A. Thus ; ra-a t-1 r 1 What annuity, being forborn for 4 years, will amount to 129/ 6s 1d at 5 per cent Ans. 30l per ann. T 2 If a pension being forborn for 5 years, at 4 per cent. per annum amounts to 270/ 16s 4d I demand how much it is per ann? Ans. 50l per ann. 3 If the yearly rent of a house, being forborn for 7 years, at 6 per cent amounts to 3357 158 Od 3.4qrs. I demand what the rent is? Ans. 40l per ann. 4 If the payment of a salary be omitted 6 years; I demand how much the salary is, when the amount is 2417 1s 7d 2.6 qrs at 5 per cent ? Ans. 35l CASE 3. per ann. Q. When U, A, and R, are given to find T, how is it discovered? which being continually divit ded by r, till nothing remains, the Number of those divisions will be=t. a+ru-a A. Thus ; น =r EXAMPLES. 1 In what time will 30 per annum amount to 129/ 6s id allowing 5 per cent for the forbearance of payment? Ans. 4 years. 2 In what time will a pension of 50l per annum amount to 270-68 4d at 4 per cent? Ans. 5 years. 3 In what time will the yearly rent of a house, being |