SIMPLE INTEREST. 308. Interest is money charged for the use of money. It is estimated at a certain rate per cent. per annum. 309. The Principal is the sum on which interest is reckoned. 310. The Rate of interest is the interest on 100 for one year. 311. The Time is how long the money is on interest. 312. The Amount is the sum of the principal and interest. 313. Simple Interest is interest upon the principal only. Compound Interest is interest upon the principal and interest. 314. Legal Interest is the rate established by law. Usury is a rate greater than the legal rate. The taking of usury is prohibited by law. The legal rate in Alabama, Georgia, Mississippi, and Florida is 8 per cent.; in New York, Michigan, Iowa, Wisconsin, and South Carolina, 7 per cent.; in Louisiana, 5 per cent.; in Texas, 10 per cent.; in the rest of the States, the Territories, the District of Columbia, and United States Courts, 6 per cent. 315. The quantities considered in Simple Interest are the Principal, Rate, Time, Interest, and Amount. There are four cases. CASE I. 316. Given the principal, rate per cent., and time, to find the interest or amount. FIRST METHOD. 1. What is the interest of $2400, for 6yr. 7mo. 15da., at 7%? SOLUTION. By reduction we find that 6yr. 7mo. 15da. equals 6ğyr. If the interest of $1 for lyr. is 7ct., the interest of $2400 for lyr. is 2400 times 7ct., which is $168, and for 6ğyr. it is 6 times $168, which by multiplying we find is $1113. Hence the following OPERATION. $2400 .07 168.00 63 RULE.-Multiply the principal by the rate per cent., expressed decimally, and that product by the time expressed in years. Required the interest 2. Of $360 for 3yr. 6mo. at 7%. 3. Of $940 for 7yr. 8mo. at 6%. 4. Of $860 for 5yr. 9mo. at 5%. Ans. $88.20. Ans. $432.40. 5. Of $780 for 8yr. 4mo. at 7%. 7. Of $1296 for 5yr. 10mo. 15da. at 6%. SECOND METHOD. Ans. $455. Ans. $180.93. Ans. $456.84. Ans. $668.10. Ans. $1290.78+. Ans. $3038.58.. Ans. $5510.808. Ans. $3931.11-. 317. The second method, called the six per cent. method, may be briefly stated by the following RULE.-I. Call ONE-HALF the number of months cents, and ONE-SIXTH of the number of days mills, and their sum will be the interest of one dollar for the given time at 6 per cent. II. Multiply this by the principal, and the product will be the entire interest at 6 per cent. For any other rate take as many sixths of it as that rate is of six. DEMONSTRATION.-The interest of $1 for 12mo. is 6ct., and since 6 is of 12, hence of the number of months equals the number of cents interest of $1 for the given number of months. Again, the interest of $1 for 12mo. is 6ct., and for 1mo., or 30 days, the interest is of 6ct., which is 5 mills, and since 5 is of 30, hence of the number of days equals the number of mills interest of $1 for the given number of days. 1. What is the interest of $240 for 6yr. SOLUTION.-6yr. and 8mo. equals 80mo. Calling of the number of months cents, and of the number of days mills, and taking the sum, we have $0.403, the interest of $1 for the given time. If the interest of $1 is $0.403, the interest of $240 is 240 times $0.403, which is $96.72. 7mo. 18da. at 6%? OPERATION. 6yr. 8m0.80mo. of 18 $0.403 $96.720 NOTE. Had it been for any other per cent. we would have divided the interest at 6 per cent. by 6, and thus found the interest at 1 per cent, and then multiplied by the given rate. Required the interest 2. Of $380 for 3yr. 4mo. 12da. at 6% Ans. $76.76. Ans. $322.721. Ans. $494.141. 6. Of $23.75 for 7yr. 7mo. 21da. at 5%. 7. Of $0.325 for 9yr. 5mo. 14da. at 8%. 8. Of $147.37 for 4yr. 11mo. 13da. at 7%. 9. Of $635.62 for 9yr. 9mo. 11da. at 9% 10. Of $387.18 for 10yr. 7mo. 7da. at 10%. 11. Of $570.05 for 3yr. 5mo. 5da. at 61%. 12. Of $980.81 for 5yr. 9mo. 17da. at 73%. THIRD METHOD. Ans. $9.07+. Ans. $0.241+. Ans. $51.094. Ans. $410.52+. 318. A method of computing interest by taking aliquot parts. 1. What is the interest of $2400 for 6yr. 7mo. 15da. at 7%? RULE.-I. Find the interest for the number of years, as by the first method. II. Find the interest for the number of months by taking convenient fractional parts of one year's interest. III. Find the interest for the number of days by taking fractional parts of one month's interest. Required the interest 2. Of $780 for 4yr. 8mo. at 6% 3. Of $960 for 7yr. 9mo. at 7%. 4. Of $1260 for 3yr. 6mo. 15da. at 8%. 5. Of $2480 for 5yr. 5mo. 10da. at 5%. Ans. $218.40. Ans. $520.80. Ans. $357. Ans. $675.11. NOTE. Let the pupil solve by this method the problems under the first method. OTHER METHODS. 319. FOURTH METHOD.-Reduce the days to the fraction of a month, find the interest for the number of years, divide the interest of one year by 12, and multiply by the number of months. 320. FIFTH METHOD.-Reduce the months to days, divide the interest of one year by 360, and multiply by the number of days. 321. SIXTH METHOD. When very exact interest is required, find the exact number of days, divide the interest of one year by 365, and multiply by the number of days. NOTE. In the solution of problems, sometimes one method is preferable and sometimes another. In solving the following examples, let the pupils exercise their ingenuity in selecting the method best adapted to the problem. Required the amount EXAMPLES. 1. Of $87.50 for 3yr. 3mo. at 7%. 2. Of $18.28 for 5yr. 9da. at 5%. Ans. $107.406. Ans. $22.872. Ans. $0.2224. Ans. $.08. Ans. $153.21+. 3. Of 12 ct. for 12yr. 12mo. 12da. at 6%. 4. Of one cent for 100 years, at 7%. 5. Of $100 for 7yr. 7mo. 7da. at 7%. 6. Of 9 dimes for 9yr. 9mo. 9da. at 9%. Ans. $1.691+. 7. What is the interest, at 7%, of $327.25 from January 5th, 1860, to July 12th, 1862? Ans. $57.71-. 8. What is the amount of $480, on interest at 6%, from Ans. $750.24. 9. A had $1200 on interest from May 20th, 1856, to September 5th, 1861; what was the interest, at 51%? Ans. $349.25. April 7th, 1851, to August 25th, 1860? 10. B gives his note, August. 6th, 1857, for $670, interest at 7 per cent.; he pays the note and interest May 17th, 1861; how much did he pay 7? Ans. $847.30. 11. Required the amount of $1900 on interest at 5% from June 9th, 1850, to January 14th, 1860? Ans. $2812.44. 12. Required the amount of a debt of $875.48, on interest at 6 per cent., from December 19th, 1845, to February 29th, 1860. Ans. $1621.09. 13. What would have been the amount, at 6 per cent., of $1 on interest from the birth of Christ to the present time?. 14. What would have been the interest of $100 at 7 per cent. from the 4th of July, 1776, until the present time? CASE II. 322. Given the principal, rate, and interest or amount, to find the time. 1. In what time will $234 give $49.14 interest, at 6%? SOLUTION. The interest of $234, at 6 per cent., for one year, is $14.04. If in one year the principal gives $14.04 interest, to give $49.14 interest it will require as many times lyr. as $14.04 is contained times in $49.14, which is 3 yr., or 3yr. 6mo. Hence we have the following OPERATION. $234 14.04 Int. lyr. 49.14 3 yr. 14.04 =3yr. 6mo. RULE. Divide the given interest by the interest of the principal, at the given rate, for ONE year. NOTE. When the amount is given, divide it by the amount of the principal for one year, or subtract the principal from the amount to find the interest, and then proceed as before. 2. In what time will $750, at 6 per cent., give $105 interest? Ans. 2yr. 4mo. 3. In what time will $480, at 7 per cent., give $210 interest? Ans. 6yr. 3mo. 4. In what time will $960, at 5 per cent., give $54.40 interest? Ans. 1yr. 1mo. 18da. 5. In what time will $720, at 6 per cent., give $957.60 amount? Ans. 5yr. 6mo. 6. In what time will $712, at 8 per cent., give $1094.106} amount? Ans. 6yr. 8mo. 15da. 7. In what time will $13.50, at 9 per cent, give $26.56 amount? Ans. 10yr. 8mo. 29da. 8. In what time will $1800, at 4 per cent., give $3047.40 amount? Ans. 15yr. 4mo. 24da. 9. In what time will $26.50, at 7 per cent., give $17.46 interest? Ans. 8yr. 9mo. 12da. |