and allow him 5 per cent for present payment; I demand how much the debt is? Ans. 161l 10s. 3 A legacy was left me the 24th of July, 1798, to be paid on the Christinas-Day following, but I agree with the Exeeutor, and allow bim 6 per eent for the present payment of 9751 3s 0d 3 qrs. I demand what the Legacy was ? Ans. 1000l. OASE 3. Q. When S, P, and R, are given to find: T, how is it discovered? 4. Tau8; 8-p mp. EXAMPLES * The present worth of 7951 11s 2d due fór 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 been made? Ans. 11 months. 2 There is 1611 :Os due at a certain time to come, but I allow 5 per cent to the debtor, for the present payment of 1491 133 01 3 qrs. I demand when the sum should have been paid without any rebate ? Ans. 19 months. 3 I have received 975l 38 od 3 qrs. for a legacy of 1000l. 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 7951 11s 2d payable 11 months hence produce 7451 is 8d for the present payment? Ans. 6 per cent. 2 At what rate per cent will 1611 10s payable 19 months hence, produce the present payment of 1491 135 0d 3 qrs.? Ans. 5 per cent. 3 Suppose a legacy of 10002 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 9751 I demand the rate per cent allowed for his money? Ans, 6 per cento 85 od 3 qrs OF EQUATION OF PAYMENTS. (THE TRUE WAY.) 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; S EXAMPLES. t=1. 2 Add all the present worths together, and call that sum also P; then is smp=d the Rebate, d 3 =e is the true equated time. pr 1 A owes B 2001 to be paid as follows, viz. 1'ool at 8 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 3001 to be paid as follows; 501 at 2 months, 1001 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 F owes to H 1000l whereof 2001 is to be paid present; 4001 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? Ang. 181 days. 4 A man owes a merchant 1200l to be paid as follows-> 2001 down, 5001 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. W HAT particular Letters are used here? Q. How is the amount of 11 for 1 year, at any propora ed rate per cent found? 7 / A. Thus: As 100 : 106 :: 1 : 1.06 100 : 105 :: 1 : 1.05, &c. A Table of the Amounts of 1l for 1 Year. Rates per C1.Amts. of 11.Rates per Ct. Amts. ofl. 2 1.02 6 1.65 1.07 1.075 1.08 1.085 1.09 1.095 1.1 CASE 1. Q. When P. T, and R, are given to find' A, how is it discovered? t A. Thus: pxr=d. 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 5201 188 7d 2 qrs. 2 What will 4001 amount to in four years at 6 per cent. per ann,? Answer 5041 19s 9d 3.15264 qrs. 3 What will 4801 amount to in 6 years, at 5 per cent: per ann.? Answer 6431 4s 41.0178d. 4 What is the amount of 500l at 41 per cent per ann. for 4 years ? Answer 5901 11s 5d 2.954 qrs. CASE 2. Q. When A, R, and T, are given to find P, how is it discovered? i What principal must be put to interest to amount to the sum of 5201 18s 7d 2 qrs. in 3 years, at 5 per cent. per ann. ? Answer 4501. 2 What principal will amount to 5041 198 9d 3.15264 qrs. in 4 years, at 6 per cent. per ann.? Answer 4001. 3 What principal will amount to 6431 4s 11.0178d in 6 years, at 5 per cent. per ann. ? Answer 4801. 4 Wlat principal will amount to 5901 11s 5d 3qrs in 4 years, at 44 per cent ? Ans. 500l. 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 NumP ber of those divisions will be=t. A. Thus ; EXAMPLES 1 In what time will 4501 amount to 5201 18s 7d 2qrs at 5 per cent. per ann? Ans. 3 years. 2 In what time will 4001 amount to 5041 19s 9d 3.2qrs. at 6 per cent. per ann? Auswer 4 years. 3 In what time will 4801 amount to 6431 145 11.id at 5 per cent per ann? Answer 6 years. 4 In what time will 500l amount to 5901 11s 5d 3ers. at 44 per cent per ann? Ans. 4 years. CASE 4. Q. When P, A, and T, are given to find R, low is it discovered? which must be extracted by the rules of extraction ; the time givA. Thus ; en in the question=t shewing the P power. t EXAMPLES. 1 At what rate per cent will 4501 amount to 5201 18s 7d 2qrs in 3 years ? Ans. 5 per cent. 2 At what rate per cent will 400l amount to 5041 19s 9d 9.2qrs in 4 years ? Abs. 6 per cent. 3 At what rate per cent will 480l amount to 6431 4s 11 1d in 6 years ? Answer 5 per cent. 4 At what rate per cent will 500l amount to 5901 11s 5d 3qrs in 4 years ? Answer 41 per cent. OF ANNUITIES, OR PENSIONS IN ARREARS. CASE 1. Note. U represents the Annuity, Pension, &c. T, R & A as be. fore. Q. When U, T, and R, are given to find A, how is it discovered? t A. Thus; ür 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 501 per ann. payable yearly, be granted to a superannuated Officer ; what is the amount for 5 years forbearance at 4 per cent ? Ans. 2701 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. 3351 158 od 3.3+qrs. 4 If a salary of 35l per annum to be paid yearly, be omitted for 6 years at 51 per cent. what is the amount? An. 2411 18 7d 2.5qrs. Q. When R, T, and A, are given to find U, how is it discovered ? CASE 2. 1 What annuity, being forborn for 4 years, will amount to 1291 68 1d at 5 per cent'Ans. 301 per ann. 2 If a pension being forborn for 5 years, at 4 per cent. per annum amounts to 270l 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 per cent amounts to 3351 158 Od 3.4qrs. I demand what the rent is ? Ans. 401 per ann. 4 If the payment of a salary be omitted 6 years ; I demand how much the salary is, when the amount is 2411 15 3d 2.6 qrs at 54 per cent ? Ans. 351 per ann. CASE 3, Q. When U, A, and R, are given to find T, how is it discovered? which being continually diviatru-a ded by r, till nothing remains, A. Thus ; the Number of those divisions will be=t. t U EXAMPLES. 1 In what time will 301 per annum amount to 1291 6s id allowing 5 per cent for the forbearance of payment ? Ans. 4 years. 2 In what time will a pension of 501 per annum amount to 270! 6s 4d at 4 per centi Ans. 5 years. 3 In what time will the yearly rent of a house, being |