SIMPLE INTEREST. Simple Interest is a profit allowed (or paid) for the use of money loaned, or for forbearance of payment. The allowance for £100, or 100 dolls. for one year is called the ratio, or rate per cent; sometimes distinguished by r. The sum loaned, or that for which payment is forborne, is called the principal; sometimes distinguished by p. The years and parts of a year, &c. for which interest is paid, is called the time; sometimes distinguished by t. The principal and interest added into one sum, is called the amount; sometimes distinguished by a. Various methods have been given by authors, to find the interest of a given sum; some of those methods are not so general, as might be wished; for instance, multiplying the principal by half the number of months, and dividing the product by 100, will give the interest for the time when the rate is 6 per cent; but in no other case, or at any other rate per cent. The best general rule for calculating interest (which holds good not only in finding the interest of any sum proposed, but also in calculating commissions, ensurance, discount, &c. at any rate per cent) is the following. CASE I. When the interest of any sum is required. for one year. 1. If the given principal is dollars. Multiply by the rate per cent, and divide by 100, which division is made by pointing off the two right hand figures; those at the left of the point will be dollars, those pointed off, decimals of a dollar, for cents ) 2. If there are cents, or cents and mills, or mills only given in the principal. Multiply by the rate as before, and if cents were piven, point off four, if mills were given, point off five places* of right hand figures; those at the left of the point (if any) are doilars; the next two places of figures. are cents, the next one mills; if any are at the right of the mills, it is a decimal of a mill * If there are not so many places as required, to be pointed supply them by prefixing ciphers. 7 NOTE. The questions in this case may be proved by division, when dollars are given. 6 EXAMPLES. 1. What is the interest of 537 dolls. for one year, at per cent. per annum ? dolls. 32,22 Ans. 2. Required the interest of $ 43,21, for a year, at 5 per cent. 43,21 dolls. 2,16,0,5 Ans. Or 2 dollars, 16 cents, O mills, 5 tenths of a mill. 3. Required the interest of 93 cents for a year, at & per cent. per annum. 4. What is the interest of 9 mills for a year, at 4 per cent ? ,00,0,36 Ans. ,36 of a mill, or thirty six hundredth parts of a mill. 3. If the given principal is sterling money, or any currency in pounds, shillings, pence, &c. Multiply the whole of the principal, by the rate per cent, (as in Compound Multiplication) and point off the two right hand figures in the pounds of the product, (which is dividing by 100) those at the left of the point, will be pounds interest, Reduce those two figures pointed off, to shillings, taking in or adding the figures in the shilling's place of the product if any; then point off two figures from the right of this product, those at the left of the point will be shillings interest; then reduce the last figures pointed off to pence, taking in the pence in the product, if any, and point off as above, for pence of interest, &c. NOTE 1. The best method is, instead of points, to draw a line downward, so as to cut of the two right hand figures of the pounds in the product; then in reducing to shillings, pence, &c. set two figures of each product on the right of this line, those at the left (if any) will be shillings, pence, &c. NOTE 2. To prove these examples, multiply the interest by 100, and divide by the rate per cent, the quotient will be equal to the principal; if there is a remainder in the interest, add it to the product. EXAMPLES. 1. What is the interest of £936 18 7, for a year, at 6 per cent. per annum ? 986 187 principal. 2. What is the amount of a note of £738 9 4 for a year, at 6 per cent. per annum? Principal at 738 9 4 Rate 6 per cent. per annum ? TOO 3. What is the interest of £163 18 41, for a year, at Ans. £9 15 102 32 4. What is the amount of 7s. 34d. for a year, at 6 per cent. per annum? Ans. 7s. 84d. cent. per Peri Ans. 793 16. 5. What is the amount of £756, at 5 | annum, for one year? Miscellaneous Questions. I. What is the interest of 736 dolls. for a year, at 5 per cent. per annum ? ? Ans. dolls, 36,80. 2. What is the interest of 11 13 4, for a year, at 4 per cent. per annum Ans, 9s. 4d... 3. What is the amount of dolls. 936,22, at 5 per cent. per annum? Ans, dolls. 983,03,1. 4. What is the interest of dolls. 7365,27, for a year, per cent. per annum? Ans. dolls. 441,91,6%. at 6 5. What sum will dolls. 593,12 amount to in a year, at 5 per cent. per annum ? Ans. dolls, 622,77,6. 6. What sum will £436 2 14 amount to in a year, at 6 per cent. per annum ? Ans. £462 5 54 376 CASE II. When the given time is several years. 100 Multiply the principal by the number of years, and that product by the ratio, (or rate per cent) and then point off, &c as in Case I. NOTE. To prove these examples, divide by the number of years, after dividing by the rate per cent.* EXAMPLES 1. What is the interest of 936 dolls. for 7 years, at 6 per cent. per annum ? * This Case may also be proved by Case VII. 2. What is the interest of $736,21,3 for 3 years, at 7 per cent. per annum ? Ans. 154,60,473. 3. What is the amount of £936 11 8 for 5 years, at 5 per cent. per annum? Ans. 1170.14 74. 4. What is the amount of $936,21, for 9 years, at 4 per cent. per annum ? Ans. $1273,24,5-5. 1136 18 4, amount to in 18 years, at Ans. £2364 15 8200. CASE III. When the given time is years, and parts of a year. Multiply the principal by the years, and take parts for the parts of a year, and add the several sums together; then multiply this sum of the several parts, by the rate, and point off, &c. as in the preceding cases.* EXAMPLES. 1. What is the interest of $936,40, for 3 years, at 6 per cent. per annum? 2. What is the amount of $437,21 for 6 years, 8 months, at 6 per cent. per annum ? * To prove these examples after dividing by the rate per cent, multiply the quotient by so many as the parts of a year are, and divide the product by so many as the years, and parts will make of such parts, the quotient will be equal to the principal. |