10. Reduce $141 to pounds, &e. New England currency. Ans. 42 £. 6 s. 11. Reduce $250 to pounds, &c. Canada currency. Ans. 62 £. 10 s. 12. Reduce $121.60 to pounds, &c. New Jersey currency. Ans. 45 £. 12 s. 13. Reduce $475.75 to pounds, &c. New York currency. Ans. 190 £. 6 s. 14. Reduce $89.54 to South Carolina currency. Ans. 20£. 17 s. 10 d. 15. Reduce $75 to pounds, &c. New England currency. Ans. 22 £. 10 s. 16. Reduce $384 to pounds, &c. Nova Scotia currency. Ans. 96 £. QUESTIONS.-What was the original currency of the United States? When this was abolished, what currency was substituted? What are the denominations of federal money? What is the value of the dollar, New England currency? What fraction of a dollar does the pound of that currency equal? What fraction of a pound does the dollar equal? Similar questions should be asked relative to the currencies of the other states. The scholar may explain why it is that the dollar is composed of a different number of shillings and pence in the different states. What note precedes the rule? What is the rule for bringing pounds, &c. into dollars? How are the terms arranged for canceling? What is the rule for bringing dollars into pounds, &c.? What is the rule for canceling? SIMPLE INTEREST. Interest is an allowance made for the use of money. It is computed at a certain rate per cent.; that is, at a certain number of dollars for the use of a hundred for one year. If the sum on interest be more or less than $100, or the time during which it draws interest, more or less than one year, the sums paid as interest must be in proportion both to the time and the sum lent. For illustration: if $100 be borrowed for one year, and if the interest allowed be 6 per cent., the interest for one year will be $6. Now, if twice that sum, viz. $200, be borrowed for the same time, or if the same sum be borrowed for twice that time, viz. for two years, the interest will in either case be twice that sum, viz. $12. Again, if twice the sum be borrowed for twice the time, that is, if $200 be borrowed for two years, the sum to be paid as interest will be increased four-fold; or it would be 6×4=$24. The scholar will carefully notice the following particulars : 1st. The principal is the money lent, or the sum on which interest is paid. 2d. The interest is the money paid for the use of the principal. Legal interest is that established by law. In the New England states, it is fixed at 6 per cent.; in New York, at 7, and in Louisiana, at 8 per cent. 3d. The amount is the sum obtained by adding the interest to the principal. 4th. The rate per cent. is always a decimal of two places, when expressed by cents, and of three, when expressed by cents and mills. CASE 1st.-To CAST INTEREST ON ANY SUM FOR ONE OR MORE YEARS. RULE.-Multiply the principal by the rate per cent. written as a decimal, the product will be the interest for one year; which, being repeated as many times as there are years given, will be the required interest. Note 1st.-In all cases where no rate per cent. is mentioned, six per cent. is always implied. Ex. 1. What is the interest of $215 for one year, at 6 per cent.? It is obvious that the required interest will be 6 times 215 cents, for it is 6 cents on each dollar. Therefore, 215 1 2 9 0 cents=$12.90, Ans. On a note of $215, which had been on interest two years, there would then be due $227.90; that is, $215 principal + $12.90 interest $227.90, the amount. Therefore, the amount is found by adding the principal and interest together. 2. What is the interest of $47.86 for 3 years, at 6 per cent. per annum? To understand why 4 figures are cut off in this sum, the scholar should remember, that 1 cent is of a dollar; and consequently, 6 cents are of a dollar, which is the same as .06. (See introductory remarks to Decimal Fractions.) 3. What is the interest of $72.72 for 4 years, at 6 per cent. ? Ans. $17.45.+ 4. What is the amount of $456 for two years? Ans. $510.72. 5. What is the interest of $146.31 for five years, at 6 per cent.? Ans. 43.893. 6. What is the interest of $24.91 for 6 years, at 5 per cent.? Ans. $7.473. 7. What is the interest of $222.46 for three years, at 3 per cent.? Ans. $26.695.+ 8. What is the amount of $42 for six years, at 3 per cent.? Ans. $49.56. 9. What is the amount of $566.33 for one year, at 5 per cent.? Ans. $594.646.+ 10. What is the amount of $1567 for 9 years, at 2 per cent.? Ans. $1849.06. CASE 2d.-WHEN THE TIME CONSISTS OF YEARS AND MONTHS. Lawful interest in the New England states is 6 per cent. per annum; that is, it is 6 cents for 12 months, or cent per month on a single dollar. Therefore, RULE.-Reduce the given years to months, and add the given months; then with half this number of months as a multiplier, multiply the given sum. The product will be the interest for the whole time. Note 2d.-It is obvious that half the whole number of months in the given time, is the same as the number of cents on a dollar for the whole time, when the interest is at 6 per cent.; for, from the above remark, the interest of one dollar for one month is evidently per cent., therefore, the whole number of months divided by 2, must determine the number of cents on each dollar for the whole time. If, in taking half the number of months, there be an odd one, the interest for that odd month will becent, or 5 mills. Ex. 1. What is the interest of $220 for 2 years and 6 months, at 6 per cent. ? 2 yr. 6 months 30 months, and 30÷2=15. The interest on each dollar for the whole time is, therefore, 15 cents. sequently, $33 is the interest of the given sum. 220 .15 Con 1100 220 $33.00 Ans. 2. What is the interest of $756.20 for 1 year and 3 months, at 6 per cent.? 1 yr. 3 mo. 15 months; therefore, 7 cents, or 7 cents, 5 mills, is the interest on each dollar for the whole time. Therefore, 756.20 3781 00 529340 5 6.7 15 00 Ans. $56.715. Note 3d.—If the interest be required at some other than 6 per cent., first cast it at 6 per cent. by the preceding rule. Then divide the interest so found by 6, and the quotient will be the interest of the given sum at one per cent. for the time specified; and this multiplied by the given per cent., will be the required interest. 3. What is the interest of $656 at 8 per cent. per annum, 17 4.9 3 2 8 interest at 8 per cent., viz. $174.932.+ 4. What is the interest of $37.50 for 3 years and 6 months, at 6 per cent.? Ans. $7.875. 5. What is the interest of $672 for 3 years and 8 months, at 6 per cent.? Ans. 147.84. 6. What is the interest of $372 for 2 years and 11 months, at 5 per cent.? Ans. $54.25. 7. What is the interest of $215.34 for 4 years and 6 months, at 3 per cent.? Ans. 33.916.+ 8. What is the interest of $350 for 2 years and 6 months, at 6 per cent.? Ans. $52.50. CASE 3d.-WHEN THE GIVEN TIME CONSISTS OF YEARS, MONTHS, AND DAYS. It was shown in the preceding case, that the interest of $1 for one month was cent=5 mills, whenever the rate is 6 per cent. Now since 30 days are always allowed for a month in computing interest, 5 mills also equals the interest for 30 days; and 30÷5=6, the number of days required for one dollar at 6 per cent. per annum, to gain one mill. If, therefore, the number of days given, be divided by 6, the quotient will be the number of mills to which the interest of one dollar will amount during that time. Therefore, RULE. Find the interest of one dollar for the given time, by allowing half a cent for every month, and one mill for every six days; the sum thus obtained will be the per cent. for the whole time. Multiply the principal by this, and the product will be the interest. |