554. SYNOPSIS FOR REVIEW. 1. DEFINITIONS. 2. ELEMENTS. 1. Percentage. 2. Per Cent. 3. Sign of Per Cent. 4. Rate, or Rate %. 5. Base. 6. Percentage. 7. Amount. 8. Difference. 1. How many considered. 2. How many must be given. 3. 510. 1. Principle. 2. Rule. 3. Formula. 555. 1. When 5% is charged for the use of money, how many dollars should be paid for the use of $100 ? For the use of $200? Of $500? Of $50? 2. At 7% a year, what should be paid for the use of $100 for 2 years? Of $200 for 3 years? 3. If $500 is loaned for 3 years, what should be paid for its use, at 5% a year? At 6% a year? 4. If I borrow $250, and agree to pay 4% a year for its use, how much will be due the lender in 5 years? 5. If $7 is paid for the use of $100 for 1 year, what is the per cent.? 6. If $50 is paid for the use of $100 for 5 years, what is the per cent.? 7. If $14 is paid for the use of $200 for 1 year, what is the per cent.? 8. At 6%, what decimal part of the money borrowed is equal to the money paid for its use? At 7%? 8%? 9%? DEFINITIONS. 556. Interest is a sum paid for the use of money. 557. The Principal is the sum for the use of which interest is paid. 558. The Rate of Interest is the per cent., or number of hundredths, of the principal, paid for its use for one year. 559. The Amount is the sum of the principal and the interest. 560. Legal Interest is the interest according to the rate per cent. fixed by law. 561. Usury is a higher rate of interest than is allowed by law. 562. The legal rates of interest in the different States are as follows: 1. When the rate per cent. is not specified in accounts, notes, mortgages, contracts, etc., the legal rate is always understood. 2. Where two rates are specified, any rate above the lower, and not exceeding the higher, is allowed, if stipulated in writing. 3. In the States marked thus (*) the rate per cent. is unlimited il agreed upon by the parties in writing. 563. In the operations of interest there are five parts, or elements, namely: The Principal; the Rate per Cent. per Annum (for one year); the Interest; the Time for which the principal is lent; and the Amount, or sum of the Prin. and Int. 564. These terms correspond respectively to Base, Rate, Percentage, and Amount in Percen.age, excluding Time, which is an additional element in Interest. 565. 1. At 3% for 1 yr., what decimal part of the principal equals the interest? At 5%? At 8%? At 121% ? 2. What is the interest of $20 for 1 year at 5%? ANALYSIS. Since the interest of any sum at 5% for 1 yr. is .05 of the principal, the interest of $20 for 1 yr. at 5% is .05 of $20, or $1. 3. What is the interest of $50 for 1 yr. at 5%? 6%? 7%? 4. What is the interest of $80 for 1 yr. at 7%? 8%? 10%? 5. At 7% for 5 yr., what decimal part of the principal equals the interest ? ANALYSIS. Since the interest at 7% for 1 yr. is .07 of the principal, the interest for 5 yr. is 5 times .07, or .35 of the principal. Or, it is 5 times the interest for 1 year. 6. At 6% for 3 yr., what decimal the principal equals the interest? 5% for 5 yr.? At 61% for 2 yr.? or fractional part of At 7% for 6 yr.? At At 10% for 4 yr.? 7. Find the interest of $30 for 3 yr. at 5%. ANALYSIS. Since the interest of any sum at 5% for 1 yr. is .05 of the principal, for 3 yr. it is .15, and .15 of $30 is $4.50. Or, the interest for 1 yr. is .05 of $30, or $1.50, and for 3 yr. it is 3 times as much, or $4.50. 8. Find the int. at 6% of $20 for 2 yr. 9. Find the int. at 8% of $5 for 5 yr. Of $40 for 3 yr. Of $10 for 10 yr. 10. At 8% for 2 yr. 6 mo., what decimal part of the principal equals the interest? ANALYSIS. Since the interest of any sum for 1 yr. at 8% is .08 of the principal, the interest on the same for 2 yr. 6 mo. is 24 times .08, or .20 of the principal. Or, it is 2 times the interest for 1 yr. 11. At 6% for 3 yr. 3 mo., principal equals the interest? what decimal part of the At 9% for 3 yr. 3 mo.? 12. Find the int. of $9 for 2 yr. 4 mo. at 7%. At 8%. 13. What is the int. of $1000 for 2 yr. 3 mo. at 10%? For 4 yr. 6 mo.? For 5 yr. 3 mo.? For 8 mo.? 566. PRINCIPLE.-The interest is the product of three factors; namely, the principal, rate per annum, and time (expressed in years or parts of a year). 567. To find the interest or amount of any sum at any rate per cent., for years and months. 1. Find the amount of $97.50, at 7%, for 2 yr. 6 mo. |
