§ 4 Interest. INTEREST is the allowance given for the use of money, by the Borrower to the Lender. It is computed at so many dollars for each hundred lent for a year, (per annum) and a like proportion for a greater or less time. The highest rate is limited by our laws to 6 per. Cent. that is 6 dollars for a hundred dollars, 6 cents for a hundred cents, 6 for a £100, &c. This is called legal interest, and is always understood when no other rate is mentioned. THERE are three things to be noticed in Interest. 1. THE PRINCIPAL; or, money lent. 2. THE RATE; or, sum per cent, agreed on. 3. THE AMOUNT; or, Principal and Interest added together. INTEREST is of two sorts, simple and compound. 1. SIMPLE INTEREST is that which is allowed for the principal only. 2. COMPOUND INTEREST is that which arises from the interest being added to the principal and (continuing in the hands of the lender) becomes a part of the principal, at the end of each stated time of payment. GENERAL RULE. 1. For one year, multiply the principal by the rate, from the product cut off the two right hand figures of the dollars, which will be cents, those to the left hand will be dollars; or, which is the same thing, remove the separatrix, from its natural place two figures towards the left hand, then all those figures to the left hand will be dollars, and those to the right hand will be cents, mills, and parts of a mill. In the same way is calculated the interest on any sum of money in pounds, shillings, pence, and farthings, with this difference only, that the two figures cut off to the right hand of pounds, must be reduced to the lowest denomination, each time cutting off as at first. 2. For two or more years, multiply the interest of one year by the number of years. 3. For months, take proportional or aliquot parts of the interest for 1 year that is, for 6 monhts,; for 4 months,; for 3 months, &c. 4. FOR days, take proportional or aliquot parts of the interest for 1 month, allowing 30 days to a month. EXAMPLES. 1. WHAT is the interest of Dolls. 86,446 for one year, at 6 per cent? OPERATION. Dolls. cts. m. 86, 44 6 principal. 518, 67 6 Interest. IN the product of the principal multiplied by the rate is found the answer. Thus, cutting off the two right hand figures from the dollars leaves 5 on the left hand which is dollars; the two figures cut off (18) are cents, the next figure (6) is mills, all the figures which may chance to be at the right hand of milis, are parts of a mill, hence we collect the Answer, 5 Dolls. 18 cts. 678 m. 2. WHAT is the interest of Dolls. 365 14cts. 6mills, for 3 years, 7 months and 6 days? OPERATION. 3 65, 146 principal. 7 8,87 1 5 3 interest for 3 years, 7 months, and 6 days; that is 78 dolls. 87 cts. 1-53 m. BECAUSE 7 months is not an even part of a year, take two such numbers as are even parts and which added together will make 7 (6 and 1,) 6 months is of a year, therefore, for 6 months, divided the interest of 1 year by 2; again, 1 month is of 6 months, therefore, for 1 month, divide the interest of 6 months by 6. For the days, because 6 days is of a month, or of 30 days, therefore, for 6 days, divide the interest of 1 month by 5. Lastly add the interest of all the parts of the time together, the sum is the answer. WHEN the rate is 6 PER CENT, there is not, perhaps, a more concise and easy way of casting Interest, on any sum of money in Dollars, Cents, and Mills, than by the following METHOD. WRITE down half the greatest even number of months for a multiplier; if there be an odd month it must be reckoned 30 days, for which and the given days, if any, seek how many times you can have 6 in the sum of them, place the figure for a decimal at the right hand of half the even number of months, already found, by which multiply the principal; observing in pointing off the product, to remove the decimal point or separatrix two figures from its natural place towards the left hand, that is point off two more places for decimals in the product, than there are decimal places in the multiplicand and multiplier counted together; then all the figures to the left hand of the point, will be dollars, and those to the right hand, dimes, cents, mills, &c. which will be the interest required. SHOULD there be a remainder in taking one sixth of the days, reduce it to a vulgar fraction, for which take aliquot parts of the multiplicand. Thus, Ir the remainder be 1, divide the multiplicand by 6 .by 3 by 3 twice. 5 and by 2 and 3. The quotients which in this way occur, must be added to the product of the principal multiplied by half the months, &c. the sum thus produced, will be the interest required. WHEN there are days, but a less number than 6, so that 6 cannot be contained in them, put a cypher in place of the decimal at the right hand of the months' then proceed in all respects as above directed. NOTE. IN casting interest, each month is reckoned 30 days. EXAMPLES. 1. WHAT is the interest of Dolls. 76,54 for 1 year, 7 months, and 11 days? OPERATION. 7 6,5 4 4 59 2 4 38 2 7 Ans. 7,4 1 162 THE number of months being 19, the greatest even number is 18, half of which is 9, which I write down; then seeking how often 6 is contained in 41, (the sum of the days in the odd month and the given days) I find it will be 6 times, which I also set down at the right hand of half the even number of months for a decimal, by which together I multiply the principal. In taking one sixth of the days (41) there will be a remainder of 5 and for which I take, first 1-3 one half the multiplicand, that is, divide the multiplicand by 2, then by 3 and these quetients added, with the products of half the even number of months &c. the sum of them will shew the interest required, observing to count off two more figures for decimals in the product than there are decimal figures in both the multiplier and multiplicand, counted together. Dols. cts. For the conciseness and simplicity of the above METHOD, it is conceived, that Enstructors will recommend it to their Pupils in preference to any other WHEN the rate is any other than 6 PER CENT, first find the interest at 6 per cent, then divide the interest so found by such parts as the interest at the rate required, exceeds or falls short of the interest at 6 per cent, and the quotient added to or subtracted from the interest at 6 per cent, as the case may be, will give the interest at the rate required. 6. WHAT is the interest of Dolls. 137,84 for 2 years and 6 months at 5 per cent ? Ans. Dolls. 17,23 7. WHAT is the interest of Dolls. 79,07 for 10 months at 8 per cent ? Ans. Dolls, 5,271. |