EXAMPLE. What principal put to interest at 5 per cent. per annum for 7 months will make the interest 17s. Od.? Here 17s. Od. =204 d. 7) £204 3s. 4d. Answer, £29 3s. 4d. The above is a proof to the first question in multiplication, when I multiplied by 7; or, which is the same thing, 7; but here the multiplier is inverted, and I multiply by, that is, divide by 7. What principal put to interest at 5 per cent. per annum for 11 months will make the interest 19s. 7 d.? Answer, £21 8s. 7 The principal and interest being given at find the time, d. per cent, to Rule. Divide the pence in the interest by the units of the pounds sterling in the principal, and the quotient will be the number of months.* EXAMPLES. In what time will £76 gain £2 4s. 4d. at 5 per cent. per annum? Here £2 4s. 4d.=532; this divided by 76-7. Answer, 7 months. In what time will £56 gain £2 10s. at 5 per cent. per Answer, 10 months. annum? NOTE CONTINUED. What principal put to interest for 5 months at 7 per cent. will gain £1 10s. ? First. 5 2 73' ,which shows that a third part of the shil lings in the gain must be deducted. And £1 10s.=360d. 360 120 Number of month 5) 2403 of the gain. £483 of the gain, divided by 5; or, of the pence in the whole gain; so that 360 divided by 15, and taken twice, is equal to 48. *If it were required to give the answer in days instead of months, (which is by far the best,) it is only necessary after finding the months, to multiply them by 30; but by this process the answer would be greater than the true one; It may be as well to give a few rules for finding the principal, &c. at 6 per cent. The interest and time given to find the principal. Rule. Muliply the shillings in the interest by 10, and divide by the number of months, and the principal is found. Note. Perhaps it would be better to remember the rule thus, the m being put as a denominator, is the first letter for months, and will be the easiest to be retained in the memory; and also, should the number of months be the same as the numerator, no division is wanting for 365 divided by 12, is equal to 30, and is less than 30, or 30, by; so that, by adopting the latter method, we have an error of too much by of a day for every month; which, in the way of business, is not worth noticing, and may easily be remedied by dropping half a day when the months are more than 5. EXAMPLE. Reduce 5 months to days. less than Here 30×5=152; now here it would be near enough to say 152 days; but the real answer is 5 times 152, or 152 days. When the number of months is more than 6, more than must be deducted, (because is,) and therefore the difference between the number of and should be taken and deducted out of the unit's place of the days. EXAMPLE. In 7 months how many days? and First. 30×7=213; but the difference between is, and therefore the true answer is of an unit less than 213, or 212+ days. I recommend the above plan; for when there are fractional parts of a month the answer may the more readily be obtained, without using figures, near enough to the truth. Should it appear by the gain that it would require years, in that case reduce the gain to shillings only, instead of pence, and divide by the principal. EXAMPLE. In what time will £85 gain £10 7s. 6d. at 5 per cent per for the answer will be as many pounds as there are shillings in the interest; but even should that not be the case, it may be capable of being reduced, and by this means the answer obtained the more readily. The following question is taken from a Tutor's Assistant: the operation is there done by the double rule of three in vulgar fractions; the superiority of the author's method will be made manifest by a comparison of the two operations. EXAMPLE. What principal put to interest will gain £4 158. in 9 months at 6 per cent. per annum? What principal put to interest will gain £5 17s. 6d. in 10 months at 6 per cent. per annum? Here in a moment I know it to be £117 10s,, because £5 17s. 6d. is 117 shillings. If the rate per cent. be more than 5, the time will be less. If less than 5, the time will be more; in either of those cases, observe the following Rule. Place 5 as a numerator, and the given rate per cent. a denominator, multiply the gain by it, and proceed as before directed. EXAMPLE. In what time will £84 gain £17 8s. at 7 per cent. per annum ? First, 348 X=10, And 10=145÷7=4=2 years 1145 months. In what time will £184 gain £13 4s. at 3 per cent. per annum ? Answer, 2years 44 months. D What principal put to interest will gain £7 13s. in 16 months at 6 per cent. ? Answer, £95 12s. 6d. the multiplier, and 153 X5_765_ £95 12s. 6d. answer. 8 8 = The interest and time given at any rate per cent. to find the principal. The principal at 6 per cent. for 10 months having been proved to consist of as many pounds as there are shillings in the interest or money gained, it follows that if a sum is put to interest for 8 months at 7 per cent., or for 12 months at 5 per cent., the principal must be the same, because the product of the months and rate per cent. are all equal to 60, that is, 10×6=8×7=12×5, &c. Hence we may find the principal for any time at any rate per cent. by the following very simple rule. Place 60 as a numerator, and the product of the rate per cent. and months as a denominator, which reduce to its lowest terms, then multiply the shillings in the gain by this fraction, and the result considered as pounds will be the answer.* NOTE. The above rule for months is better retained in the memory by placing the first letter for time and rate as a 60 60 denominator, thus, -or ; for in case we are desirous to txr tr make additional rules for either years, weeks, or days, it can easily be done in manner following. It is required to find a rule for years. Here, as there are 12 months to a year, we must divide E the rule required. the above rule by 12, thus, 60÷12 5 tr EXAMPLE. What principal put to interest for 6 years at 4 per cent. will gain £3 6s.? Here, as there are 52 weeks in a yeer, the above rule must be multiplied by 52, and we have it, thus, EXAMPLES. What principal put to interest for 2 years (30 months) at 7 per cent. will gain £3 10s. ? Here 2 and 70x2=£20, the principal required. 60 7 What principal put to interest will gain £2 8s. 6d. in 5 months at 5 per cent. per annum ? Here 12 60 and 48-52-£116 8s. answer. What principal put to interest will gain £3 7s. 6d, in 11 years at 7 per cent. per annum? Answer, £38 11s. 54d. What principal put to interest will gain £5 10s. in 14 years at 8 per cent. per annum? Answer. £45 16s. 8d. Given the principal and interest at any rate per cent. to find the time. Rule. Multiply the shillings in the gain by 60, this divided by the product of the principal (in pounds sterling) and rate will give the time required in months. NOTE CONTINUED. EXAMPLE. What principal put to interest for 16 weeks at 5 per cent. will gain £7 4s.? There being 365 days in a year, multiply the rule above 5 X 365 1825 found for a year by it, thus, the rule required. What principal put to interest for 25 days at 6 per cent. per annum will gain 7s. ? |