INTEREST. 684. Interest is a compensation paid for the use of money. 685. The Principal is the money for the use of which interest is paid. 686. The Amount is the sum of the principal and interest. 687. The Time is the period during which the principal bears interest. 688. Interest is reckoned at a certain per cent. of the principal. It is therefore a Per Cent. of which the Base is the Principal. 689. The Rate of Interest is the annual rate per cent. 690. Interest differs from the preceding applications of Percentage only by introducing time as an element, in connection with the rate per cent. The Principal = the Base. The Per Cent. per Annum = the Rate. The Interest the Percentage. The Sum of the Principal and Interest = the Amount. 691. Legal Interest is interest according to the maximum rate fixed by law. 692. Usury is interest taken at a rate higher than the law allows. 693. Simple Interest is interest on the principal only, for the whole time. of the loan or credit; and this is generally understood by the term interest. 694. Annual, Semi-Annual, or other Periodic Interest, is interest computed at a specified rate for a year, half-year or other designated period. 695. Compound Interest is interest computed on the amount at regular intervals. REMARKS.-1. The payment of periodic interest, if specified in a contract, may usually be enforced; and if not paid when due, becomes simple interest bearing, and is not usury. 2. Neither the paying nor the receiving of compound interest is usury; but its payment cannot ordinarily be enforced, even though it is mentioned in the contract. 696. Accrued Interest is interest accumulated on account of any obligation, due or not due. 697. Common Interest is interest computed on a basis of 360 days for a year. REMARKS.-1. This method is generally employed by business men, and in some states has received the sanction of law. 2. In reckoning interest by this method, it is customary to consider a year to be 12 months. and a month to be 30 days. STATEMENT.-July 22, 1887, at the annual convention of the Business Educators' Associa tion of America, then in session at Milwaukee, Wis., the following resolution was unanimously adopted: Resolved, That, as business educators, we uniformly teach interest and discount on a 360-day basis, finding time by compound subtraction, and calling each month thirty days, except where the day of the minuend time be thirty-one, when it shall be so counted. REMARK.—In computing interest for short periods of time, it is customary to take the exact number of days. 698. Exact Interest is interest computed for the exact time in days, and regarding the days as 365ths of a year. This method is used by the United States Government and by some merchants and bankers; but as it is inconvenient unless interest tables are used, it is not generally adopted. REMARKS.-1. Exact interest, for any period of time expressed in days, may be obtained by subtracting part from the common interest for that period of time. 2. Common interest may be obtained from exact interest by adding thereto part of itself. 699. For convenience, the rate of interest should always be expressed decimally; the rules governing the multiplication and division of decimals may then be applied to any product or quotient arising from the use of the decimal rate. REMARKS.—1. In many of the States a legal rate of interest is established, to save dispute and contention in cases of contracts in which no rate of interest is agreed upon by the parties; still the laws sanction an interest rate higher than the fixed legal rate, if such rate be agreed upon by the parties; in a few of the States, any rate, if agreed upon, is thus made legal. 66 2. When no particular rate of interest is named in a contract containing a general interest clause, as with interest," or "with use," the legal rate of the place where the contract is made is understood. 3. Debts of all kinds bear interest after they become due, but not before, unless specified. SIX PER CENT. METHOD. 700. The following method of computing interest is based upon time as usually reckoned; i. e., 12 months of 30 days each, or 360 days for a year, and is called the Six Per Cent. Method. It is convenient for use in all cases where time is not given in days, as for years and months, or for years, months, and days, and where exact interest is not required. Should the rate be any other than six per cent., the change can be easily made. It is a common method of computing interest. Six Per Cent. Method. $1.00 in 1 yr., at 6%, will produce $.06 interest. $1.00 in yr., or 2 mo., at 6%, will produce $.01 interest. 701. To find the Interest on Any Sum of Money, at Other Rates than 6 per cent.: 1. To find the interest at 7%. RULE.-To the interest at 6% add one-sixth of itself. 2. To find the interest at 74%. RULE.-To the interest at 6% add one-fourth of itself. 3. To find the interest at 8%. RULE.-To the interest at 6% add one-third of itself. 4. To find the interest at 9%. RULE.-To the interest at 6% add one-half of itself. 5. To find the interest at 10%. RULE.-Divide the interest at 6% by 6, and remove the decimal point one place to the right. 6. To find the interest at 12%. RULE.-Multiply the interest at 6% by 2. 7. To find the interest at 5%. one-twelfth of itself. 8. To find the interest at 5%. one-sixth of itself. RULE.-From the interest at 6%, subtract RULE.-From the interest at 6%, subtract 9. To find the interest at 41%. RULE.-From the interest at 6%, subtract one-fourth of itself. 10. To find the interest at 4%. one-third of itself. RULE. From the interest at 6%, subtract 11. To find the interest at 3%. RULE.-Divide the interest at 6% by 2. 702. To find the Interest, the Principal, Rate, and Time being given. -What is the interest on $550, at 6%, for 3 yr. 8 mo. 12 da.? OPERATION. EXAMPLE. EXPLANATION.-Since the interest on $1 for 1 year is $.06, for 3 years it will be $.18; since the interest on $1 for 2 months is $.01, for 8 months it will be $.04; since the interest on $1 for 6 da. is $.001, for 12 days it will be $.002; therefore the interest on $1, at 6 per cent., for the full time, is $,222; and the interest on $550 will be 550 times the interest on $1, or the product of the principal and the rate for the given time, which is $122.10. Rule.-Multiply the principal by the decimal expressing the interest of one dollar for the full time. EXAMPLES FOR PRACTICE. 703. 1. Find the interest on $900, for 4 yr. 1. mo. 6 da., at 7%. 4. Compute the interest on $1200, for 3 yr. 4 mo. 15 da., at 9%. EXPLANATION.-To the interest at 6% add one-half of itself. 5. Find the interest, at 10%, on $840, for 5 yr. 5 mo. 9 da. EXPLANATION.-Divide the interest at 6% by 6, to obtain the interest at 1%, and remove the decimal point 1 place to the right. 6. What is the interest, at 12%, on $366, for 2 yr. 11 mo. 27 da.? EXPLANATION.—Multiply the interest at 6% by 2%. 7. Find the interest on $1800, for 6 yr. 9 mo. 25 da., at 51%. EXPLANATION.-From the interest at 6% subtract one-twelfth of itself. 8. Compute the interest, at 5%, on $1000, for 11 yr. 4 mo. 24 da. EXPLANATION.- From the interest at 6% subtract one-sixth of itself. 9. What is the interest, at 41%, on $1100, for 6 yr. 6 mo. 6 da.? EXPLANATION.-From the interest at 6% subtract one-fourth of itself. 10. What is the interest, at 4%, on $1350, for 9 yr. 8 mo. 12 da.? EXPLANATION.-From the interest at 6% subtract one-third of itself. 11. Find the interest, on $546, for 6 yr. 2 mo. 24 da., at 3%. EXPLANATION.-Divide the interest at 6% by 2. REMARKS.-1. Interest at any other rate, entire or fractional, can be found by a general application of the methods above explained. 2. When the mills of a result are 5 or more, add 1 cent; if less than 5, reject them. 12. Compute the interest on $752.50, for 4 yr. 11 mo. 9 da., at 6%. 19. Compute the interest on $2400, for 7 yr. 1 mo. 19 da., at 10%. 22. Find the amount due after 1 yr. 10 mo. 20 da., on a 6% loan of $1941.50. 23. On the 16th of September, 1884, I borrowed $3500, at 8% interest. How much will settle the loan Jan. 1, 1890? 24. My note, given 2 yrs. 9 mo. 27 da. ago, for $875.25, and bearing 4% interest, is due to-day. What is the amount due? A manufacturer marks a carriage with two prices; the one for a credit of 6 months on sales, and the other for cash. If the cash price was $750, and money was worth 8%, what should be the credit price? 26. Borrowed $2750 July 16, 1887, at 5% interest, and on the same day loaned it at 71% interest. If full settlement is made Jan. 4, 1889, how much will be gained? 27. On goods bought for $4500, on 6 months credit, I was offered 5% off for cash. If money was worth 6%, how much did I lose by accepting the credit? 28. A man sold his farm for $16000; the terms were, $4000 cash on delivery, $5000 in 9 months, $3000 in 1 year and six months, and the remainder in 2 years from date of purchase, with 6% interest on all deferred payments. What was the total amount paid? 29. May 16th I bought 300 barrels of flour, at $7 per barrel; July 28th I sold 50 barrels, at $8 per barrel; Oct. 30th, 100 barrels, at $6.75 per barrel; and Feb. 13th following, the remainder, at $7.80 per barrel. Allowing interest at 6%, what was my gain? 30. John Doe bought bills of dry goods as follows: May 3, $250; July 1, $1125; Sept. 14, $450; Oct. 31, $150; Dec. 1st. $680; and on Dec. 21st, he paid in full, with 6% interest. What was the amount of his payment ? 31. On March 25, I sold five bills of goods, for amounts as follows: $1046.81, $952.40, $173.50, $1250, and $718.25; and on the first day of the following December I received payment in full, with interest at 6%. What was the amount received? 32. A firm bought goods on credit, and agreed to pay 7% interest on each purchase from its date; Oct. 6, 1887, goods were bought to the amount of $268; Dec. 31, 1887, to the amount of $165.80; Feb. 29, 1888, to the amount of $600; Apr. 1, 1888, to the amount of $325.25. If full settlement was made Aug. 25, 1888, how much cash was paid. REMARK.-In the following examples, given for teacher's use in class drill, the interest on each separate principal should be computed to its nearest cent; the sum of the results so obtained will be the answer sought. 33. Find the amount of interest at 6%, by the six per cent. method, On $680, for 2 yr. 6 mo. 10 da. On $468, for 5 yr. 5 mo. 1 da. On $500, for 3 yr. 1 mo. 27 da. On $1650, for 1 yr. 10 mo. 23 da. On $1463, for 9 yr. 1 mo. 9 da. 34. Find the amount of interest, by the six per cent. method, On $350, for 3 yr. 7 mo. 18 da., at 6%. | On $538, for 6 yr. 6 mo. 6 da., at 9%. On $586.50, for 2 yr. 9 mo. 15 da., at 7%. 35. Find the amount of interest, by 36. Find the amount of interest, by On $1200, for 7 yr. 4 mo. 27 da., at 10%. the six per cent. method, On $675, for 5 yr. 5 mo. 25 da., at 10%. On $3546.81, for 5 yr. 0 mo. 5 da., at 3%. |