EXAMPLE Interest on £l for 24 years = .05 X 4£ = .1375£. 1.1375£. 1137.5£. 1137.5 = 1000. Ans. £1000. 1.1375 B.—Compound Interest. TO FIND THE AMOUNT OF A GIVEN PRINCIPAL AT A GIVEN RATE Rule. Find the amount of £1 for 1 term in decimals of £1; raise this to a power equal to the number of terms, and multiply the principal by the result. II. TO FIND THE COMPOUND INTEREST ON A GIVEN PRINCIPAL. Rule. Find the amount (by preceding rule) and subtract the principal. EXAMPLE. Find the amount of £1066 : 13 : 4 for 3 years at 31 per cent. compound interest. 33 100 57301 1037500 1.076408 57301 1076408 1.116773 10663 6700638 6700638 11167730 744515 1191.224533 £. Ans. £1191 : 4:6 nearly. III. TO FIND THE PRINCIPAL, WHICH AT COMPOUND INTEREST FOR A GIVEN NUMBER OF TERMS WILL AMOUNT TO A GIVEN SUM. Rule. Find the amount of £1 for 1 term in decimals of £1; raise this to a power equal to the number of terms; and divide the given amount by the result. If the interest be given instead of the amount, add the principal, só obtaining the amount, and proceed as before. EXAMFLE. What sum lent out at compound interest at the rate of 4 per cent. will amount to £2050 : 10 : 8 in 3 years ? Amount of £1 for 1 year = 1.04£. Given amount = £2050 : 10:8 = £2050.53. 1.04 416 1.0816 1.04 43264 108160 1.1,2,4,8,6,4 ) 2050.533333(1822.916668£. 1124 864 9256693 2577813 3280853 1031125 18747 7498 749 75 Ans. £1822: 18:4. TO FIND THE TRUE DISCOUNT ON A DEBT DUE AT A GIVEN TIME. RU 1. Find the present worth of the debt, and subtract it from the debt; the difference is the discount. Rule 2. Find the interest on the debt for the given time, and also the amount of £1 for the given time; the ratio of the former to the latter is the discount in pounds. EXAMPLES 1. Find the discount on €845 : 16 : 4 due in 2 years, 8 months, at 44 per cent. per annum. 8 17 Amount of £1 for 2 yrs. 8 mo. = it Х £. 3 400 1.36 12 7793333331 £ = 1.113£. 2. The same example worked by Rule 2. Amount of £1 for 2 yrs. 8mo. = 1.113£. = 845.816 X.113£. 845816667 1.11333333)95.8592219(86.101097£. 890666666 67925553 66800000 1125553 12220 1087 1012 75 77 Ans. £86 : 2:0 nearly. 3. The same example worked by the exact method. £. d. £. 845 16 4 = Principal 4 5 0 = Int. of £100 for 1 year 44= Rate 3}= No. of years 3594 14 5 11 6 8 = Int. of £100 for 23 years 3-} = No. of yrs. 1000 0 Def. 1. Commission is an allowance of so much per cent made to an agent for buying or selling goods for his employer on the price of the goods sold. Def. 2. Brokerage is an allowance of so much per cent. made to brokers for assisting in the transference of property. Def. 3. Insurance is a contract by which one person, or company, undertakes to make good the loss of another person, on consideration of the latter paying a certain sum, called the premium, which is so much per cent. on the suin insured. When a third person is employed to effect the insurance, commission is charged; and in all cases a duty is payable to Government. I. TO FIND THE COMMISSION, OR BROKERAGE, ON A GIVEN SUM. Rule. Express the rate per cent. in terms of £1, multiply the given sum by it, and divide by 100. If the rate per cent. be less than £1, the multiplication may be effected by aliquot parts. |