9. Of $840 for 3 mo. 28 da. at 6%. exact time. EXACT TIME. OPERATION. Int. for 60 da. "30 da. 60 66 $54.60 16. On a 3 mo. note for $2400, dated Feb. 20, 1887, at 6%, exact time? Ans. $35.60. 17. Of $750, for May 12 to Oct. 20, at 6%, exact number of days? Ans. $20.125. 18. Of $480, from June 16 to Nov. 10, at 7%, exact number of days? Ans. $13.72. 19. On a note for $570, dated Nov. 24, 1887, and due Feb. 10, 1888, at 6%, allowing 3 da. of grace ? Ans. $7.595. 20. On a note for $1050, dated Oct. 16, 1887, and due Mar. 25, 1888, at 6%, allowing 3 da. of grace? Ans. $28.70. METHOD BY CANCELLATION. 474. The following Six Per Cent. Method by Cancellation will be found convenient and practical: Rule for Months.-Point off two places in the principal, di vide by 2, and multiply by the number of months. For the Int. for 2 mo. is of the principal, and for 1 mo. it is of r of the principal; hence the above rule. Rule for Days.-Point off three places in the principal, di vide by 6, and multiply by the number of days. For the int. for 2 mo. or 60 days is of the principal, and for a. it is of it, or ro of the principal, and for 1 da. it is of 100 of the principal; hence the above rule. 1. What is the Int. of $2400 for 38 mo. at 6%? at 7%? SOLUTION.-We point off two places in $2400 to divide by 100, then divide by 2, and multiply by 38; cancelling and multiplying, we have $456. OPERATION. $24.00X38 -$456. 2. What is the Int. of $4800 for 63 da. at 6%? at 4%? SOLUTION.-The Int. for 1 da. is of r of the Prin.; hence we point off three places in $4800, divide by 6 to find the Int. for 1 da., and multiply by 63 to find the Int. for 63 days; cancelling and multiplying we have $50.40. OPERATION. .800 $4.899×63-$50.40, Ans NOTE.-To find the Int. at 4%, divide by 6 and multiply by 4%, expres ing the work and cancelling. WRITTEN EXERCISES. Required the interest 3. Of $120 for 2 yr. 9 mo. at 6%. 4. Of $245 for 3 yr. 4 mo. at 6%. 5. Of $1360 for 75 days at 6%. 6. Of $2240 for 2 mo. 12 da. at 6%. 7. Of $2520 for 3 mo. 14 da. at 7%. 8. Of $126.50 for 4 mo. 24 da. at 5%. 9. Of $5000 for 5 mo. 12 da. at 44%. 10. Of $3600 for 3 mo. 3 da. at 4%. METHOD OF EXACT INTEREST. Ans. $19.80. Ans. $49.00. Ans. $17.00. Ans. $26.88. Ans. $50.96. Ans. $2.53. Ans. $101.25, Ans. $41.85. 475. Exact Interest is that which is obtained by reckoning 365 days to the year. 475. Exact Interest is reckoned by the United States Government, and is growing in favor with business men. Bankers and business men often use Interest Tables, which are sometimes calculated to exact interest. 1. What is the exact interest of $785 from July 20 to December 1st, at 7% ? SOLUTION. From July 20 to December 1 there are 134 days; the interest of $785 for 1 year of 365 days, at 7%, is $54.95, and for 134 days it is } of $54.95, which is $20.17+. OPERATION. $785 .07 54.95 134 365)7363.30 $20.17} Rule.-Multiply the principal by the rate, and that pro duct by the integral number of years; then multiply the in terest for one year by the exact number of days, and divide by 365; and take the sum of the two results. NOTE. The exact interest for an, number of days less than 1 year. may also be found by deducting from the cominon interest of itself. WRITTEN EXERCISES. 2. What is the interest, at 7%, of $327.25 from January 5th, 1860, to July 12th, 1862? Ans. $57.613. 3. What is the amount of $480, on interest at 6%, from Apr. 7th, 1851, to Aug. 25th, 1860? Ans. $750.25 →. 4. A had $1200 on interest from May 20th, 1856, to Sept. 5th, 1861; what was the int. at 51% ? Ans. $349.53—. 5. Required the amount of $19003 on int. at 5% from June 9th, 1850, to Jan. 14th, 1860. Ans. $2813.11. 6. B gives his note, August 6th, 1857, for $670, interest at 7%; he pays the note and interest May 17th, 1861; how much did he pay? Ans. $847.19. 7. Required the amount of $875.48, on interest at 6%, from Dec. 19th, 1845, to Feb. 29th, 1860. Ans. $1621.24. 8. Which is the greater, exact interest or common interest, and why? Prove that off from common interest will give exact interest. CASE II. 476. Given, the time, the rate, and the interest or the amount, to find the principal. MENTAL EXERCISES. 1. What principal will in 3 yr. 4 mo., at 6%, give $80 interest? SOLUTION. We find that of the principal equals the interest, which is $80; if of the principal is $80, £, or the principal, equals 5 times $80, or $100. What principal will give an interest of 2. $60 in 8 yr. at 5%? 5. $18 in 7 yr. 6 mo. at 6% ? 3 $70 in 7 yr. at 4%? 6. $54 in 2 yr. 3 mo. at 8%? 4. $12 in 8 yr. at 6%? 7. $106 in 8 yr. 10 mo. at 6%? 8. How much money must a person borrow that he must pay an annual interest of $180 at 6%? 9. How much money has Howard on interest, supposing he re ceives $320 for 5 yr. 4 mo. at 6 per cent.? 10. The interest on A's money for 4 years at 5% is $200, and A's money is of B's; how much money has each? WRITTEN EXERCISES. 1. What principal will in 4 yr. S mo., at 6%, give $151.20 interest? SOLUTION.-We find the interest of $1 for 4 yr. 8 mo., at 6%, is $.28. If $1 gives an interest of $.28, to give $151.20 interest it will require as many dollars as $.28 are contained times in $151.20, which is $540. Hence the following Rule. Divide the given interest by the interest of $1 for the given rate and time; or divide the amount by the amount of $1. 2. What principal will in 3 yr. 8 mo., at 6%, give $462 interest? Ans. $2100. 3. What principal will in 12 yr. 9 mo., at 7%, give $64.26 interest? Ans. $72. 4. What principal will in 7 yr. 4 mo., at 8%, amount to $749.70? Ans. $472.50. 5. What principal will in 5 yr. 8 mo. 15 da., at 5%, give $575.40 interest? Ans. $2016. 6. What principal will in 7 yr. 7 mo. 13 da., at 7%, amount to $2400? Ans. $1565.19. 7. What principal will in 4 yr. 11 mo. 17 da., at 7%, amount to $3363.79? Ans. $2496.37+. 8. The sum of A's and B's money on interest for 4 yr. 6 mo., at 6%, gives $5400 interest; how much money has each, if 3 times B's equals A's? Ans. $15000; $5000. CASE III. 477. Given, the principal, the rate, and the interest or the amount, to find the time. MENTAL EXERCISES. 1. In what time will $200 at 5% give $60 interest? SOLUTION.-At 5 per cent. for one year, of the principal equals the interest; of $200 is $10; if it require one year for $200 to gain $10, to gain $60 it will require as many years as $10 are contained times in $650, which are 6. 8. In what time will a principal gain 2 times, 3 times, or 4 times itself at 10%? 9. In what time will a principal double itself at 5%? at 6%? at8%! at 124 %? 10. In what time will a principal treble itself at 5% at 10%? at 20%? at 25%? 11. The amount of a principal for a certain time at 5% is $250, and for the same time at 8% is $280; required the principal and the time. WRITTEN EXERCISES. 1. In what time will $234 give $49.14 interest, at 6%? Rule.-Divide the given interest by the interest of the principal at the given rate for ONE year. NOTE. When the amount is given, 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 interAns. 2 yr. 4 mo. est? 3. In what time will $720, at 6 per cent., give $957.60 amount? Ans. 5 yr. 6 mo. 4. In what time will $960, at 5 per cent., give $54.40 interest? Ans. 1 yr. 1 mo. 18 da. 5. In what time will $1800, at 41 per cent., give $3047.40 amount? Ans. 15 yr. 4 mo. 24 da. 6. In what time will $26.50, at 7 per cent., give $17.46 interest? yr. 9 mo. 12 da. 7. In what time will $18.20, at 5 per cent., give $10.23 interest? Ans. 9 yr. 9 mo. 9 da. 8. The amount of a certain principal, in a certain time, at 5 per cent., is $833, and the amount for the same time at 12 per cent. is $1047.20; required the principal and time. Ans. 8 Ans. Prin. $680; Time, 4 yr. 6 mo. SUG.-The difference of the amounts equals the interest at 7% |