the product the next inferiour denomination, and cut off as before, and so proceed till the work is finished. The several figures cut off at the left, will be the interest of the given sum for one year; then if it is required for a number of years, you may multiply the interest of 1 year by the number of years. 16. What is the interest of £155 for one year, at 6 per Ans. £9 6s. cent? 17. What is the interest of £300 for two years, at 7 per cent? Ans. £42. 18. What is the interest of £500 for five years, at 5 per -cent? Ans. £125. 19. What is the interest of £200 10s. 4d. for three years, at 7 per cent? £ S. d. 200 10 1403 12 4 4 3 £42)10 17 0 20 s. 2)17 12 d. 2)04 4 gr. 0)16 Ans. £42 2s. 2d. If we It is frequently the better way, after multiplying by the per cent, to multiply 7 by the time before the division is performed, because there be may some small loss by means of the remainder. first divide by 100, and then find the interest in the inferiour denominations, it is plain, if there is a loss on one year's interest, the same loss will be sustained on each year, where we first find the interest of one year, in all the inferiour denominations, before we multiply by the time. 20. What is the interest of £150 6 per cent? 8s. 3d. for 5 years, at Ans. £45 2s. 5d. 2qr. 21. What is the amount of 100 dollars for 1 year, at 7 per cent? $100 700 Ans. $107. DEM. It is plain, if a man lets out 100 dollars, at 7 per cent, for one year, that, at the end of the year, the interest due is seven dollars, and the principal or money lent is also due, which is 100 dollars, consequently the amount due is the interest and principal added together, which make 107 dollars due, at the year's end. 100 The principal added. NOTE. The learner may now discover, that casting interest on 100 dollars or any other sum for one year, does not differ from finding the value of so many yards of cloth. For, to find the value of 100 yards of N cloth, at 7 cents per yard, we may repeat 7 cents, the price of one yard, by 100, the number of yards, and the product will be the price of the whole quantity. So we may multiply 7 cents, the interest or price of one dollar for one year, by 100, the number of dollars, and the product will be the interest or price of one hundred dollars for one year; but, letting a certain number of dollars for a year or any other time, for so many cents on the dollar, differs from selling so many yards of cloth for the same number of cents per yard, because the buyer acquires a perfect right to the cloth purchased for the price which he pays, which is never to be returned; but he who receives money from the lender must not only return to the lender the per cent for the use of the money, but the principal or money recived, must be paid back to the lender. 22. What is the amount of 200 dollars for one year, at 7 per cent? Ans. $214. 23. What is the amount of 300 dollars for 3 years, at 7 Ans. $363. per cent ? Ans. $434. 24. What is the amount of 350 dollars for 4 years, at 6 per cent ? 25. What is the amount of $3,75 cents for 2 years, at 7 per cent ? Ans. $4,27cts. 5 mills. 26. What is the amount of $75,60cts. 5 mills, for 5 years, at 7 per cent? Ans. $102,06cts. 6,75 mills. 27. What is the interest of 1600 dollars for 1 month, at 6 $8, one month's interest. per cent ? $1600 6 Ans. 12)96,00 the interest for 1 year. $8,00 the interest for 1 month. 100 DEM.-Here, we find by multiplying the principal by the rate per cent, that the interest of 1600 dollars for 1 year, is 96 dollars; it is then evident, twelfth part of 96 dollars, a that one month's interest must be one year's interest, because 1 month is the twelfth part of a year, and it is plain, that by dividing 96 dollars by 12, the number of months in a year, the quotient, & dollars, must be the interest of one month. 6 28. What is the interest of 3600 dollars for 2 months, at per cent? $3600 6 12)216/00 $ 18/00 2 36 for 2 months. Ans. $36. DEM. We first obtain the interest for 1 month, as in the 27th example, we then multiply the interest of one month by 2, the number of months, which must give the interest for two months, because it is evident, that the interest for two months, must be twice as much as the interest for one month. Hence we derive the following RULE.-Divide the interest of one year by 12, and the quotientwill be the interest for one month; then multiply one month's interest by the number of months, and the product will be the interest for the number of months required. 29. What is the interest of 196 dollars for 3 months, at 7 per cent ? Ans. $3,43cts. 30. What is the interest of 396 dollars for 4 months, at 7 per cent? Ans. $9,24cts. 31. What is the amount of 396 dollars for 4 months, at 7 per cent? Ans. $405,24cts. 32. What is the amount of ,86 cents for 5 months, at 7 per cent ? Ans. 88 cents, 5 mills. 33. What is the amount of 25 dollars, and fifty cents for 10 months, at 7 per cent? Ans. $26,98cts. 7m. 34. What is the interest of 79 dollars for 15 months, at 7 per cent ? Ans. $6,91cts. 2m. 35. What is the amount of fifty four dollars for 9 months, at 7 per cent? Ans. $56,83cts. 5m. 36. What is the interest of 360 dollars for 27 days, at 7 Ans. $1,89ets. per cent? $360 12)25,20 30)2,10(,07 one day's int. interest. 0 49 DEM. The interest for one month, is obtained the same as in the preceding examples; we then divide the interest of one month by 30, to obtain one day's We divide by 30, because one day is considered to be the one thirtieth part of a month; we then multiply 7 cents, one day's interest, by 27, the number of days, which gives us the interest for 27 days, because the interest for 27 days must be 27 times more than the interset for one day. Or, which would come nearer the true interest, we might divide the interest of a year, by 365, the number of days in a year, and the quotient would be the interest for one day, and that multiplied by 27, would give the interest for 27 days. Ans. $1,89 in. for 27 days. NOTE. In obtaining the interest for one day by dividing by 12 and. by 80, we go on the supposition, that 12 and 30, the divisors, form the component parts of a year in days, which is not strictly true; they only form the component parts of 360, which is 5 days less than a year; consequently our divisors being too small, it follows that the quotient must be too great, because our quotient is one three hundred and sixtieth part of a year's interest, which is a little too much, and the interest of 27 days thus obtained, must consequently be too much, al though it is sufficiently accurate for common business. 38. 37. What is the interest of 150 dollars for 19 days, at 7 per cent ? Ans. $0,55cts. 4m. What is the amount of 200 dollars for 20 days, at 7 per cent? Ans. $200,77cts. 7m. 39. What is the amount of 96 dollars for 21 days, at 7 per cent? Ans. $96,39cts. 2m. When there are certain parts of a year in the time, as quarters; months, or days, the interest may be obtained by taking the aliquot parts of the interest of a year, for the months, and the aliquot parts of a month, for the days, and add the several quotients together, and the sum will be the interest for the whole time. NOTE.-By taking aliquot parts, is perhaps the better way of casting interest; the whole work is then together, and by a little practice the learner will find no difficulty in taking parts. The teacher should frequently exercise his students in taking parts from 1 month up to 12 months, and from 1 day to 30 days. 40. What is the interest of $372 for 1 year, 10 months, and 15 days, at 7 per cent? $372 )26,04 one year's int. 3 =)13,02 int. for 6 mo. 6,51 int. for 3 mo. 15ds.) 2,17 int. for 1 mo. 1,08,5 int.. for 15d. ... 10m. 15ds. Ans. $48,82cts. 5m. NOTE. Where it is more convenient, the student can take parts of parts, as in this example; and in taking parts for days, he should reckon the month thirty days. It only wants a little exercise of the Ans. $48,82,5 in. for 1yr. 10m. 15d. of of a year; 2 months. a year; 4 months the of a year; 6 months of a year; 8 months mind to determine that one month is the of a year; three months the of a year; 5 months the and the the of a year; 7 months the and the and the of a year; 9 months the and the of a year; 10 months the and the of a year; 11 months the , the and the of a year. And so of days, take the parts of 30 days or one month, thus, 1 day is of a month two days; 3 days; 5 days; 6 days; 10 days; 15 days, &c.; but where it is more convenient, take parts of parts. 41. What is the interest of 960 dollars for 7 months and 12 days, at 7 per cent? Ans. $41,43cts. 9m.. or 30 days, and 2 day's interest is part of the interest for 10 days; it is then evident, when these sums are added, the total sum must be the interest for the whole time. 42. What is the interest of $221,75 cents for 3 years, months, and 6 days, at 7 per cent? $221,75 7 6mo....=)15,5225 I .... 3 46,5675 int. for 3 years. 6ds. =}) 1,2935 int. for Imo. Ans. $55,88,09 in. for 3y. 7m. 6ds. 43. What is the amount of 950 dollars, 3 years and 6 months? 10 months, at 7 per cent? Ans. $55,88cts. NOTE.-The shortest method of casting interest for days, at 7 per cent, is to multiply the principal by the number of days and divide the product by 52, the quotient will be the interest of the given number of days. at 7 per cent forAns. $1182,75cts. 44. What is the amount of 950 dollars, at 6 per cent for 3 years and 6 months? Ans. 1149,50cts. 45. What is the amount of $350,50 cents for 2 years and Ans. $420,01ct. 5m. 46. What is the amount of $35,12 cents for 4 years, 11 months and 10 days, at 7 47. What is the amount of $1000 for 3 years, 101 mo., at 7 per cent? Ans. $1271,25cts. When there is a fraction, as, 1, 1, 4, &c. in the rate per cent: per cent ? Ans. $47,27ets. 5m. RULE.-Multiply the principal by the rate per cent, then to the product add 4, 4, or of the principal, and divide the summ by 100, as in the preceding examples, and the quotient will be the interest for 'one year. |