When the Interest is for any number of Days. KULE. AS 365 days are to the interest of the given sum for a year, so are the days given to the interest required. 23. At 5 per cent. per annum, what is the interest of, £985 2. 7 for 5 years, 127 days? Ans. £289. 15.2. 24. What is the interest of £2726. 1. 4 at 4 per cent. per annum, for 3 years, 154 days? Ans. £419. 15. 6. When the amount, Time, and Rate per cent. are given, to find the Principal. RULE. As the amount of £100 at the rate and time given is to £100::so is the amount given to the principal required 25. What principal being put to interest will amount to £402 10.0 in 5 years, at 3 per cent per annum ? 3x5+100 £115; 100::402...10 2300)805000) £350 Ans. 26. What principal being put to interest for 9 years, will amount to £734.8.0 at 4 per cent. per annum? Ans. £540. 27. What principal being put to interest for 7 years, at 5 per cent. per annum, will amount to £384. 16.0? Ans. £248. When the Principal Rate per cent. and the amount are given to find the time. RULE. As the interest of the principal for 1 year: is to 1 year :: so is the whole interest: to the time required. 28. In what time will £350 amount to £402. 10.0 at 3 per cent. per annum ? £ 350 £ s. S yr. £ yrs. As 10...10:1::52...10:5 10/50 20 1000 210 210)1050(5 years. cent. per annum? 105 29. In what time will £540 amount to £734.8.0 at 4 per Ans. 9 years. 30- In what time will £248 amount to £334. 16.0 at 5 per cent. per annum? Ans. 7 years. When the Principal, Amount, and Time are given, to find the Rate per cent. RULE. As the principal is to the interest for the whole time :: so is £100 to the interest of the same time. Divide that interest by the time, and the quotient will be the rate per cent. 31. At what rate per cent. will £350. amount to £402. 10. in 5 years time? £402...10...0 350... O As £350 £52 10::£100 : £15 20 350)1050010(300s. £15 5 3 per cent. 32. At what rate per cent. will £248 amount to £334. 16 in 7 years time? Ans. 5 per cent. 33. At what rate per cent. will £540 amount to £734.8 in 9 years time? Ans. 4 per cent. COMPOUND INTEREST IS that which arises both from the principal and interest: that is, when the interest on money becomes due and not paid, the same interest is allowed on that interest unpaid, as was on the principal before. 9 RULE 1. Find the first year's interest, which add to the principal, then find the interest of that sum, which add as before; and so on for the number of years. 2. Subtract the given sum from the last amount, and it will give the compound interest required. EXAMPLES. 1. What is the compound interest of £500 forborne 3 years at 5 per cent. per annum? for 3 years. 2. What is the amount of £400 forborne 31 years, at 6 per cent. per annum compound interest? Ans. £190 13: 111. 3. What will £650 amount to in 5 years, at 5 per cent. per annum, compound interest? Ans. £829: 11: 71. 4. What is the amount of ££50 10s. for 3 years and 6 months, at 6 per cent. per annum, compound interest? Ans. £675; 6: 5. 5. What is the compound interest of £764 for 4 years and 9 months at 6 per cent. per annum? Ans. £243 18.8. 6. What is the compound interest of £57. 10. 6 for 5 years, 7 months, 15 days, at 5 per cent. per annum? Ans. £18.3.84. 7. What is the compound interest of £259. 10.0_for 3 years, 9 months, and 10 days, at 41 per cent. per annum? Ans. £46.19.10 REBATE OR DISCOUNT S the abating so much money on a debt to be received before it is due, as that money, if put to interest, would gain in the same time, and at the same rate. As £100 present money would discharge a debt of £105 to be paid a year to come, rebate being made at 5 per cent. RULE. AS £100 with the interest for the time given is to that interest :: so is the sum given to the rebate required. Subtract the rebate from the given sum, and the remainder will be the present worth. EXAMPLES. 1. What is the discount and present worth of £487. 12 for 6 months, at 6 per cent. per annum? 2. What is the present payment of £357.10.0 which was agreed to be paid nine months nence, at 5 per cent. per annum? Ans. £344. 11. 7. 3. What is the discount of £275. 10.0 for 7 months, at 5 per cent. per annum? Ans. £7. 16. 14. 4. Bought goods to the value of £109. 10. 0 to be paid at 9 months, what present money will discharge the same, if I am allowed 6 per cent. per annum discount? Ans. £104. 15. 81. 5. What is the present worth of £527 . 9. 1 payable 7 months hence, at 41 per cent? Ans. £514. 13. 10. 6. What is the discount of £85. 10 due September the 8th, this being July the 4th, rebate at 5 per cent. per annum? Ans. 15s. 31. 7. Sold goods for £875. 5.6 to be paid 5 months henc., what is the present worth at 4 per cent? Ans. £859.3.3. 8. What is the present worth of £500 payable in 10 months, at 5 per cent. per annum? Ans. £480 9. How much ready money can I receive for a note of £15. due 15 months hence, at 5 per cent. ? Ans. £70.11.9 10. What will be the present worth of £150 payable at 3 four months, i. e. one-third at 4 months, one-third at 8 months, and one-third at 12 months, at 5 per cent. discount? T Ans. £145.3.8. 11. Sold goods to the value of £575. 10 to be paid at two 3 months, what must be discounted for present payment, at 5 per cent.? Ans. £10. 11. 4. 12. What is the present worth of 2500 at 4 per cent. £100 being to be paid down, and the rest at two 6 months? Ans. £488.7.81 EQUATION OF PAYMENTS S when several surns are due at different times to find a mean time for paying the whole debt; to do which, this is the common RULE. Multiply each term by its time, and divide the sum of the products by the whole debt, the quotient is accounted the mean time. EXAMPLES. 1. A owes B £200 whereof £40 is to be paid at 3 months, £60 at 5 months, and £100 at 10 months; at what time may the whole debt be paid together, without prejudice to either? £ m. 1 7 months, 10 200) 14/20 2. B owes C £800, whereof £200 is to be paid at 3 months, £100 at 4 months, £300 at 5 months, and £200 at 6 months; but they agreeing to make but one payment of the whole, I demand what time that must be ? Ans. 4 months,174 days. 3. I bought of K a quantity of goods to the value of £360 which was to have been paid as follows: £120 at 2 months, £200 at 4 months, and the rest at 5 months; but we afterwards agreed to have it paid at one mean time, the time is demanded? Ans. 3 months,124 days. 4. A merchant bought goods to the value of £500 to pay £100 at the end of 3 months, £150 at the end of months, and £250 at the end of 12 months; but afterwards they agreed to discharge the debt at one payment; at what time was this payment made? Ans. 8 months, 11 days. 5. H is indebted to L a certain sum, which is to be paid at 6 different payments, that is, at two months, at 3 months, at 4 months, at 5 months, at 6 months, and the rest at 7 months; but they agree that the whole shall be paid at one equated time, what is that time? Ans. 4 months, 1 quarter. 6. A is indebted to B £120 whereof is to be paid at S months, at 6 months, and the rest at 9 months, what is the equated time of the whole payment? Ans. 5 months, 7 days. BARTER S the exchanging one commodity for another, and informs the traders so to proportionate their goods, that neither may sustain loss. RULE 1st, Find the value of that commodity whose quantity is given: then find what quantity of the other, at the rate proposed you may have for the same money. 2dly. When one-has goods at a certain price, ready money, but in bartering advances it to something more, find what the other ought to rate his goods at, in proportion to that advance, and then proceed as before. EXAMPLES. 1. What quantity of choco- 2. A and B barter; A hath late at 4s. per lb. must be deli-20 cut. of prunes, at 4d. per lb. vered in barter for 2 cwt. of tea ready money, but in barter will at 94. per lb. 2 cwt. 119 224 9 have 5d, per lb. and B hath hops |