INTEREST DEFINITIONS. 556. Interest is a sum paid for the use of money. Thus, I owe Wm. Henry $200, which he allows me to use for one year after it is due. At the end of the year I pay him the $200 and $14 for its use. The $14 is called the Interest and the $200 the Principal. 55%. Principal is a sum of money for the use of which interest is paid. 558. Rate of Interest is the number of units of any denomination of money paid for the use of 100 units of the same denomination for one year or some given interval of time. 559. The Amount is the sum of the principal and interest. 560. Simple Interest is interest which falls due when the principal is paid, or when a partial payment is made. 561. Legal Interest is interest reckoned at the rate per cent fixed by law. 562. Usury is interest reckoned at a higher rate than is allowed by law. 563. The following table gives the legal rates of interest in the different States. Where two rates are given, any rate between these limits is allowed, if specified in writing. When no rate is named in a paper involving interest, the legal or lowest rate is always understood. The legal rate for England and France is 5%; for Canada and Ireland, 6%. 564. PROB. I.-To find the simple interest of any given sum for one or more years. 1. Find the interest on $384 for 5 years, at 7%. SOLUTION.-1. Since the interest of $100 for one year is $7, the interest of $1 for one year is $.07. Hence the interest of $1 for 5 years is $.07 × 5 = $.35. 2. Since the interest of $1 for 5 yr. is $.35, the interest of $384 for the same time must be 384 times $.35, or $134.40. Hence the following 565. RULE.-I. Find the interest of $1 at the given rate for the given time, and multiply this result by the number of dollars in the given principal. II. To find the amount add the interest and principal. 566. Find the interest on the following orally: 1. $800 for 2 years at 4%. 7. $400 for 8 years at 5%. 9. $600 for 7 years at 10%. 10. $1000 for 5 years at 8%. 11. $20 for 3 years at 9%. 12. $500 for 5 years at 5%. 22. Find the interest on the following: 13. $245.36 for 3 years at 7%. 14. $784.25 for 9 years at 4%. 15. $836.95 for 2 years at 1%. 16. $795.86 for 7 years at %. 17. $896.84 for 3 years at 24%. 18. $28.95 for 1 years at 4%. 19. $414.14 for 4 years at 4%. 23. 20. $375.84 for 3 years at 91%. 21. $293.50 for 6 years at 45%. $899.00 for 12 years at 73%. $600.80 for 9 years at 85%. 24. $50.84 for 5 years at 13%. 25. $95.60 for # of a yr. at 71%. 26. $262.62 for 6 years at 61%. METHOD BY ALIQUOT PARTS. 567. PROB. II.-To find the interest on any sum at any rate for years, months, and days by aliquot parts. 1. In business transactions involving interest, 30 days are usually considered one month, and 12 months 1 year. Hence the interest for days and months may be found according to (499), by regarding the time as a compound number; thus, Find the interest and amount of $840 for 2 yr. 7 mo. 20 da., at 7%. $840 Principal. 6 mo. of 1 yr., hence 2) 58.80 Interest for 1 yr. = $995.16 Amount for 2 yr. 7 mo. 20 da 568. The interest, by the method of aliquot parts, is usually found by finding first the interest of $1 for the given time, and multiplying the given principal by the decimal expressing the interest of $1; thus, Find the interest of $680 for 4 yr. 9 mo. 15 da. at 8%. 1. We first find the interest of $1 for the given time thus: 8 ct. = Int. of $1 for 1 yr., 8 ct. x 4 = Int. for 4 yr. = 32 ct. 2. The decimal .3831 expresses the part of $1 which is the interest of $1 for the given time at the given rate. Hence, $680 ×.3831-$260.66, is the interest of $680 for 4 yr. 9 mo. 15 da., at 8%; hence the following 569. RULE.-I. Find by aliquot parts the interest of $1 for the given rate and time. II. Multiply the principal by the decimal expressing the interest for $1, and the product will be the required interest. III. To find the Amount, add the interest to the principal. EXAMPLES FOR PRACTICE. 570. Find the interest 1. Of $284 for 3 yr. 8 mo. 12 da. at 6%; at 81%. 2. Of $560.40 for 2 yr. 10 mo. 18 da. at 7%; at 9%. 3. Of $296.85 for 4 yr. 11 mo. 24 da. at 8%; at 5%. 4. Of $860 for 1 yr. 7 mo. 27 da. at 41%; at 71%. 5. Of $2940.75 for 3 yr. 11 mo. 17 da. at 7%; at 91%. 6. Find the amount of $250.70 for 2 yr. 28 da. at 8%. 7. Find the amount of $38.90 for 3 yr. 13 da. at 9%. 8. A man invested $795 at 8% for 4 yr. 8 mo. 13 da. How much was the amount of principal and interest? 9. Paid a debt of $384.60, which was upon interest for 11 mo. 16 da. at 7%. What was the amount of the payment? 10. Find the amount of $1000 for 9 yr. 11 mo. 29 da. at 7%. 571. STEP I.—To find the interest for any number of months at 6%. 1. Since the interest of $1 for 12 months, or 1 yr., at 6%, is 6 cents, the interest for two months, which is of 12 months, must be 1 cent, or part of the principal. 2. Since the interest for 2 months is of the principal, the interest for any number of months will be as many times To of the principal as 2 is contained times in the given number of months. Hence the following 572. RULE.-I. Move the decimal point in the principal TWO PLACES to the left (470), prefixing ciphers, if necessary. II. Multiply this result by one-half the number of months. Or, Multiply To of the principal by the number of months and divide the result by 2. 574. STEP II.—To find the interest for any number of days at 6%. 1. Since the interest of $1 for 2 months at 6% is 1 cent, the interest for 1 month, or 30 days, must be cent or 5 mills. And since 6 days are of 30 days, the interest for 6 days must be of 5 mills, or 1 mill, which is Too of the principal. |
