£200 at 4 months, and £400 at 6 months; but they agreeing to make but one payment of the whole, at the rate of 5 per cent. rebate, the true equated time is demanded? Ans. 4 months, 28 days. 3. E owes F £1200, which is to be paid as follows: £00 down, £500 at the end of 10 months, and the rest at the end of 20 months; but they agreeing to have one payment of the whole, rebate at 3 per cent, the true equated time is demanded? Ans. 1 year, 11 days. THE COMPOUND INTEREST. HE letters made use of in Compound Interest are, A the Amount. P the Principal. T the Time. R the Amount of £1. for 1 year at any given rate, which is thus found: As 100 105 :: 1: 105. Aɛ 100 Tuble of the Amount of £1 for One Year 105,5:: 1: 1,055 Table I. shews the Amount of £1. for any number of Years under 31, at 5 and 6 per cent. per annum. 1,075 10 Note: The preceding table is thus made: As 100: 105 :: 1: 1.05 for the first year; then, As 100: 105 :: 1.05: 1,1025, second year, &c. I. When P, T, R, are given, to find A. RULE. PXA. EXAMPLES. 1. What will £225 amount to in 3 years time, at 5 per cent. per annum? Ans. 1,05 × 1,05 × 1,05=1,157625, then 1,157625 × 225=£260...9...3. 3 grs: 2. What will £200 amount to in 4 years, at 5 per cent. per innum ? Ans. £243. .2,02bs. 3. What will £450 amount to in 5 years, at 4 per cent. per annum? Ans. £547...9...10. 2,0536368 grs. 4. What will £500 amount to in 4 years, at 5 per cent. per annum ? Ans. £619...8...2. 3,8323 grai II. When A, R, T, are given, to find P. a Rule.-P. gut EXAMPLES. 5. What principal being put to interest will amount to £260...9...3. 3 qrs. in 3 years, at 5 per cent. per annum ? 1,05 × 1,05 × 1,05=1,157625 260,465625 1,157625 £225. 6. What principal being put to interest will amount to £243 2,025s. in 4 years, at 5 per cent. per annum? Ans. £200. 7. What principal will amount to £547...9...10. (2,0538368 grs in 5 years, at 4 per cent. per annum? Ans. £450. 8. What principal will amount to £619...8...2, 3,8323 qrs. in 4 years, at 5 per cent. ? III. When P, A, T, are given to find R. a Ans. £500. which being extracted by the rules of extraction Rule., (the time given in the question shewing the power,) will give R. EXAMPLES. 3. At what rate per cent. will £225 amount to £260...9...3. 3 qrs. in 3 years? Ans. 5 per cent. 260,465625 225 =1,157625, the cube root of which (it being the 3d power) =1,05=5 per cent. 10. At what rate per cent. will £200 amount to £243. 2,025.s in 4 years? Ans. 5 per cent. 11. At what rate per cent. will £450 amount to £547...9...10 2,0538368 grs. in 5 years ? Ans. 4 per cent 12. At what rate per cent. will £500 amount to £619...8...2. 3,8323 qrs. in 4 years? Ans. 51 per cent. IV. When P, A, R, are given, to find T, α which being continually divided by R till othing RULE. -rt remains, the number of those divisions will be equal to T. EXAMPLES. 13. In what time will £225 amount to £260...9.....3. 3 grs. at 5 per cent.? =1, the number of divisions being three times sought. 14. In what time will £200 amount to £243. 2,025s. at 5 per cent.? Ans. 4 years. 1,05 15. In what time will £450 amount to £547...9...10. 2,053068 qrs. at 4 per cent. ? Ans. 5 years. 16. In what time will £500 amount to £619...8...24,8323 at 5 per cent.? Ans. 4 years. ANNUITIES, OR PENSIONS, IN ARREARS. NOTE. U represents the annuity, pension, or yearly rent; A, R, T, as before. Table II. shews the Amount of £1. Anuity for any number of Years under 31, at 5 and 6 per cent. per annum. Note. The above Table is made thus: take the first year's amount, which is £1. multiply it by 1,05+1=2,05=second year's amount, which also multiply by 1,05+1=3,1525—third year's amount. Table continued to 100 years, see page 183 RULE.A, or by the table thus: Multiply the amount of £1 for the number of years, and at the rate per cent. given in the question, by the annuity, pension, &c. and it will give the answer. EXAMPLES. 17. What will an annuity of £50 per annum, payable yearly, amount to in 4 years, at 5 per cent. Ans. 1,05 × 1,05 × 1,05 × 1,05 × 50=60,77531250 60,7753125-5 then 1,05-1 -=£215...10...1. 2 qrs. or, by the table thus, 4,31012× 50-£215...10...1. 1,76 qrs. 18. What will a pension of £45 per unnum, payable yearly amount to in 5 years, at 5 per cent.? Ans. £248...13...0. 3,27 gro. 19. If a salary of £40 per annum, to be paid yearly, be forborne 6 years, at 6 per cent. what is the amount? Ans. £279...0...3 2641 20. If an annuity of £75 per annum, payable yearly, be omitted to be paid for 10 years, at 6 per cent. what is the amount? Ans. £988...11...24. 235851424346112. II. When A, R, T, are given, to find U. ara RULE.=U. 1. EXAMPLES. 21. What annuity, being forborne 4 years, will amount to £215...10...1. 2 qrs. at 5 per cent.? 22. What pension, being forborne 5 years, will amount to £248...13...0. 3,27 grs. at 5 per cent.? Ans. £45. 23. What salary being omitted to be paid 6 years, will amount to £279...0...3. 2641 at 6 per cent. ? 390626' Ans. £40. 24. If the payment of an annuity being forborne 10 years, amount to £988.....11...24. 23585142 546112. at 6 per cent. what is the annuity? Ans. £75. III. When U, A, R, are given, to find T. BULE. artu-a which being continually divided by R, till nothing remains, the number of those divisions will be equal to T EXAMPLES.. 25. In what time will £50 per annum amount to £215...10...] 2 grs. at 5 per cent. for non-payment? Ans. 215,50625 × 1,05+50—215,50625 50 -=1,21550625 which being continually divided by R, the number of the divisions will be 4 years. 26. In what time will £45 per annum amount to £248...13...0. 3,27 grs- allowing 5 per cent, forbearance of payment ? 22641 Ans. 5 years. 27. In what time will £40 per annum amount to £279...0...3. Ans. 6 years. Ja, at 6 per cent. ? 28. In what time will £75 per annum amount to £988...11...2. 235851124346112, allowing 6 per cent. for forbearance of payment? Ans. 10 years, PRESENT WORTH OF ANNUITIES, PENSIONS, &c. Table III. shews the present worth of £1. Annuity for any Num ber of Years under 31, Rebate at 5 and 6 per cent. Years. 5 Rates. 6 5 Rates. 6 Years. 14 9,29498 29 15, 14107 13,59072 15,37245 13.76483 9,89864 15 10,37965 9,71225 30 NOTE. The above table is thus made: divide £1. by 1,05= ,95238, the present worth of the first year, which÷1,05= ,90703, added to the first year's present worth 1,85941, the second year's present worth; then 90703 -1,05 and the quotient added to 1,85941=2,72324, third year's present worth, 1. When U, T, R, are given, to find P. or, by the table, thus: Table continued to 100 years, see page 185 |