2. What is the interest of 2 dollars for one year, at 7 per cent? Ans. 14 cents. 82 DEM.--For convenience of the operation, we generally multiply the sum by the interest of 100 dollars for one year, and consequently Ans. ,14 cents. produce a product 100 times too much: for vur multiplier is 100 times greater than when we multiply by 7 cents, and our product being 100 times too great, We take one hundredth part by removing the decimal point two figures further to the left than its usual place, which is dividing the product by 100, for our true answer. Or the student may, if he choose, consider the multiplier to be 7 cents, that is, ,07 of a dollar; he will then discover that we point off two figures further to the left than the usual place of pointing off decimals, because the multiplier is, in fact, 7 cents, or → hundredths of a dollar, instead of 7 dollars, and may properly be considered as a contraction for the expression ,07. The same must be produced if we multiply the interest of $1, by the number of dollars, thus: ,07 cents. It is plain, if a man receives 7 cents for the use of $1, for a 2 year, he should receive 14cts. ,14 the answer as before. for the use of $2, 21 cents for $3, and 28 cents for $4, and so on. 3. What is the interest of $5 for one year, at 7 per cent ? Ans. ,35cts. 4. What is the interest of $6 for one year, at 7 per cent ? Ans. ,42cts. 5. What is the interest of $20 for one year, at 7 per cent ? Ans. $1,40cts. 6. What is the interest of $55 for one year, at 7 per cent ? Ans. $3,85cts. 7. What is the interest on $300 for 1 year, at 7 per cent ? Ans. $21. 8. What is the interest of $300 for 2 years, at 7 per cent ? Ans. $42: $300 Dem. First, it is plain, ny if $100 gain for the lender 7 dollars, that 300 dollars 21100 interest for one year. must #21 in the same time, 2 because $300 dollars must gain the lender three times $42 interest for two years. as much as $100, and three times 7 are 21, that is, $21, for one year. It is likewise evident, that 2 years must produce twice the interest of 1 year, and twice $21 are $42, the interest of $300 foi two years. Then we may draw from this the following rule: per cent ? RŪLE.-Multiply the interest of one year by the number of years, and the product will be the interest for the whole number of years; because if the interest of 100 dollars for one year is $7, for two years it must be 14 dollars, and for three years 21 dollars; and if 7 dollars be multiplied by two years the product will be 14 dollars, and if multiplied by three years the prodlict will he 21 dollars. 9. What is the interest of 400 dollars for three years, at 7 Ans. $84. 10. What must a man receive for the use of $500 for four years, at' 7 per cent ? Ans. $140. 11 W.ltat is the interest of 40 dollars for two years, at 6 per cent? Ans: $4,80cts $40 Here, it will seem that the use of 100 dol6 lars is considered to be only worth 6 dollars, consequently the principle is the same as in 2,40 the preceding examples; and whatever the 2 per cent may be we observe the same rule, to multiply by the rate per cent, and point off as Ans. $4,80 the rule directs. 12. What is the interest of $50,45 cents, at 6 per cent, for two years ? Ans. $6,05cts. 4m." 13. What is the interest of $49,50 cents for three years, at 6 perc Ans. $8,91 cents. 14. What is the interest of 350 dollars for two years, at 5 Anis. $35. 15. What is the interest of £150 10s. 6d. for two years, at 6 per cent? Ans. £18. 1s.* 3d. £" d. DEM.-Here, we first multiply as 150 10 6x6 in Conipound Multiplication, because the given sum is in pounds, shillings, £903 3 and pence, and we divide the pounds 20 by 100, because we have multiplied by the interest of £100, and consequently s. 0J63 the product is 100 tiines too much, till 12 we cut off the two right hand figures in pounds, which is dividing the prod.7156 duct by 100. Whatever stands at the 4 left of the line or mark which divides the product by 100, is units of the same kind of the units in the principal; £ d. I qr. consequently it is 9 0 7 2 interest for one year., pounds in this place. And then 2 to obtain the exAns. 18 1 3 O interest for two years. cess of interest, we multiply as in Reduction Descending, the figures cut off at the right, and adding the cent? per cent ? gr. 2/24 Rem. S. cent? 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 deft, 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. 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? Ans. £42 2s. 2d. £ S. d. It is frequently the better way, after 200 10 4 multiplying by the per cent, to multiply 7 by the time before the division is per1403 12 4 formed, because there may be some small 3 loss by means of the remainder. If we first divide by 100, and then find the £42) 10 17 0 interest in the inferiour denominations, 20' it is plain, if there is a loss on one year's interest; the same loss will be sustained 12 on each year, first find the d. 2)04 interest of one year, in all the inferiour 4 denominations, before we multiply by the time. 20. What is the interest of £150 8s. 3d. for 5 years, at 6 Ans. £45 2s. 5d. 2qr. 21. What is the amount of 100 dollars for 1 year, at 7 Ans. $107. 100 DEM. It is plain, if a man 17 lets out 100 dollars, at 7 per cent, for one year, that, at the 7100 end of the year, the interest 100 The principal added. due is seven dollars, and the principat or money lent is also 107 Ans. que, which is 100 dollars, con sequently the amount due is he interest and principal added together, which make 107 dollars due, at the year's end. 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 s. 2) 17 97. 0)16 per cent? per cent ? per cent ? per cent? per cent ? per cent ? 1 cloth, at 9 cents per yard, we may repeat y 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 certs, 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 received, must be paid back to the lender. 22. What is the amount of 200 dollars for one year, at 7 Ans. $214. 23. What is the amount of 300 dollars for 3 years, at 7 Ans. $363. 24. What is the amount of 350 dollars for 4 years, at 6 Ans. $434. 25. What is the amount of $3,75 cents for 2 years, at 7 Ans. $4,27 cts. 5 mills. 26. What is the amount of $75,60cts. 5 mills, for 5 years, at 7 per cent ? Ans. $102,06cts. 6-7,5 mills. 27. What is the interest of 1600 dollars for 1 month, at 6 Ans. $8, one month's interest. 81600 Dem.--Here, we find by Ő multiplying the principal by the rate per cent, that 12)96,00 the interest for 1 year. the interest of 1600 dollars $8,00 'the interest for 1 month. for 1 year, 'is 96 dollars; it is then evident, that one month's interest must be one twelfth part of 96 dollars, a 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, 8 dollars, must be the interest of one month. 28. What is the interest of 3600 dollars for 2 months, at 6 Ans. $36. per cent? $3600 DEM.–We first obtain the interest 6 for 1 month, as in the 27th example, we then multiply the interest of one month 12)21600 hy 2, the number of months, which must give the interest for two months, be18|00 cause it is evident, that the interest for 2 iwo months, must be twice as much as the interest for one month. Hence we 36 for 2 months. derive the following. per cent? per cent? per cent ? per cent ? per cent? per cent? per cent? RULE.-Divide the interest of one year wy 12, and the quotient will 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 Ans. $3,43cts. 30. What is the interest of 396 dollars for 4 months, at 7 Ans. $9,24cts. 31. What is the amount of 396 dollars for 4 months, at 7 Ans. $405,24cts. 32. What is the amount of ,86 cents for 5 months, at 7 Ans. 88 cents, 5 mills, 33. What is the amount of 25 dollars and fifty cents for 10 months, at 7 per Ans. $26,98cts. 7 Fom. 34. What is the interest of 79 dollars for 15 months, at 7 Ans. $6,91 cts. 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. $1,89cts. $360 DEM.--The interest for one 7 month, is obtained the same as in the preceding examples; we 12)25,20 then divide the interest of one 30)2,100,07 one day's int. month by 30, to obtain one day's interest. We divide by 30, be2,10 27 cause one day is considered to 0 49 be the one thirtieth part of a month;. We then multiply 7 14 cents, one day's interest, by 27, Ans. $1,89 in. for 27 days. 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 interest 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 muliiplied by 27, would give the interest for 27 days. Note.-In obtaining the interest for one day by dividing by 12 and by 30, 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 yeai; consequently our divisors being oo small, it follows that the quotient must be too great, because our quotient is one three hundred and sixieth part of a year's interest, which is a little too much, and the it's verest of 27 days thus obtained, must consequently be too much, alhough it is sufficient y accurate for common business. |