DECIMAL PROPORTION. Rule. Arrange the given terms according to the directions of the Rule of Three, and reduce, if necessary, the first and third terms into similar decimal quantities. Then, for Direct Proportion, multiply the second term by the number of the third, and divide the product by the number of the first. Or, for Inverse Proportion, multiply the second term by the number of the first, and divide the product by the number of the third. Observe. When the second term is a compound quantity, it will in general be best to reduce the lower denominations into the decimal of the highest integer; but when either the second or third terms of a direct Proportion is a fractional number, it may be used as a multiplier without being reduced into a decimal. Ex. 1. To find the amount of 13 per cent. upon £ 837 16 2. £837 16 2 = £837.808 The 16 S. 2 d. is valued as a decimal by the Rule to Case 6. Page 155. The three terms being similar, we make use of the third as the producing term, and multiplying it by the number of the second, viz. 131, we divide the product by 100, by cutting off two more places of decimals. See Ex. 1. page 163. Then valuing the result by the Rule to Case 5, page 153, and reckoning the 9-1000 ths as 10 on account of the remainder, we obtain the amount to the nearest farthing; but as farthings are for such purposes not generally used, the proper result is, in pence, only 2 d. Example 2. To find the per centage profit produced by a gain of £ 64 13 3 upon £ 382 16 0. £ 64 13 3 = £ 64.662 £ If 382.8 £382 16 £382.8 3828) 64662 (16.892 = 16 17 10. 26382 3414 352 We value the given shillings and pence, and also the decimal in the result, by the rules quoted in the last page. To multiply by 100 we remove the decimal place in the 2 nd term 2 places to the right, and to correct for 1 place in the divisor, we remove it another place, in all 3 places, to the right, which makes the dividend a whole number. After the first two quotient figures are obtained, we contract the division, because we want only 5 figures in the quotient, and there are 4 in the divisor. Example 3. In order to include £ 90 6 6, it is required to insure £100, how much must be insured to include £ 835 17 2? Both the first and third terms containing the same number of decimal places, they may be both considered as whole numbers. EXERCISES. Ex. 1. What is the amount of 173 per cent. upon £ 456 7 8? Answer £79 5 11. Ex. 2. What is the amount of 234 per cent upon £ 527 11 9? Answer £ 122 13 31. Ex. 3. What is the amount of £ 629 14 5 Stock at 92 per cent.? Answer £581 14 1. Ex. 4. What is the amount of £ 1343 18 7 Stock at 931 per cent.? Answer £1253 4 3. Ex. 5. If 91g in money will buy £ 100 Stock, how much Stock may be bought with £ 1138 14 5? Answer £1242 16 1. N. B. After the third term has been expressed as a decimal, both the 1 st and 3 rd terms may be multiplied by 8 to get rid of the fraction. Ex. 6. If £100 produce a profit of £ 16 5 8, what will be the profit upon £ 520 17 11? Answer £84 16 4. Ex. 7. If goods which cost £ 1711 14 4 produce a profit of £ 273 17 7, what is the rate of this gain per cent.? Answer £16 0 0.. Ex. 8. If goods which cost £ 821 15 9 had been sold for £ 784 16 2, what is the rate of this loss per cent. ? Answer £4 10 0. Ex. 9. What is the rate per Pound at which the distribution of effects must be made, when the amount of the claims is £ 37634 16 0, and the assets are only £ 8316 14 2? Answer £0 4 5. Ex. 10. What is the rate per Pound at which the distribution of effects must be made, when the amount of the claims is £ 11208 4 4 and the assets are only £ 2603 8 1? Answer £ 0 4 8. FORMULA FOR THE CALCULATION OF SIMPLE INTEREST. To find the amount of the Interest on £ 864 12 6 for 35 days at 5 per cent. per annum. As it is not usual to calculate the Interest upon the shillings and pence in the Principal, the above calculation would commonly be worked as for £ 865; (see page 104 ;) but it is sometimes required to calculate for the lower denominations, and then the best method is to value them decimally. The third, tenth, and tenth of the 10.000 th is an approximation for the division by 7300, as shown page 171. The valuation is made upon £ 4.1457 reckoned £ 4.146. EXERCISES. Ex. 1. What is the amount of the Interest upon £ 348 13 6 for 101 days at 5 per cent. per annum. Answer £4 16 6. Ex. 2. What is the amount of the Interest upon £ 654 for 234 days at 5 per cent. per annuin. Answer £ 20 19 4. Ex. 3. What is the amount of the Interest on £ 1635 17 4 for 29 days at 3 per cent. per annum. Answer £ 4 11 0. FORMULA OF THE CALCULATION OF COMPOUND INTEREST BY DECIMALS. To find the amount of the Compound Interest on £ 6781 11 4 half yearly for 2 years at 4 per cent. per annum. £ At 4 per cent. per annum the half yearly Interest is 2 per cent., which is calculated for, either by multiplying by 2, and placing the figures 2 places to the right of their regular situation, or by dividing by 50. Another method of calculating Compound Interest, is, to take the amount of £1 for 1 period of Interest, and involve it as many times, less one, as the compound Interest is to be taken; then to multiply the given sum by this product, and subtract the original sum from the product. thus 1.02 X 1.02 x 1.02 X 1.02 1.08243216 £ 6781.566 x 1.08243216 Subtract the Principal Compound Interest £ 7340.585 6781.566 £559.019 = £ 559 0 5 In general, however, it will be found that the common way is best. N. B. The Exercises given page 111 may be recalculated by decimals. |