The Rate is the percentage paid per annum. The Amount is the sum of the principal and the interest. In computing interest 30 days are considered a month, and 12 months a year. GENERAL METHOD. 1. What is the yearly interest of $40 at 6% ? ANALYSIS.-At 6%, 18, or 3%, of the principal equals the interest. of $40 is $2.40; hence the interest of $40 for 1 year at 6% is $2.40. 2. What is the yearly interest of $300 at 6% ? 3. What is the yearly interest of $225 at 4% ? 4. What is the yearly interest of $50 at 8%? 5. What is the yearly interest of $60 at 5%? 6. What is the yearly interest of $40 at 7% ? 7. What is the yearly interest of $120 at 121% ? 8. What is the yearly interest of $500 at 5%? 9. What is the yearly interest of $140 at 3% 10. What is the yearly interest of $90.50 at 6%? 1. What is the interest of $500 for 3 yr. at 6%? SOLUTION.-At 6%, 185, or 3%, of the principal equals the interest for 1 year; and for 3 years, 3 times, or, of the principal equals the interest; of $500 is $90; hence the interest of $500 for 3 yr. at 6% is $90. 2. What is the interest of $40 for 2 yr. at 5% ? 10. What is the interest of $300 for 33 yr. at 5% ? 11. What is the interest of $300 for 3 yr. 4 mo. at 6% ? SOLUTION.-2 yr. 4 mo. equal 23 yr. If the interest for one year is 6%, for 23 yr. it is 23 times 6%, or 14%; 14% of $300 is $42. Therefore, etc. What is the interest 12. Of $200 for 2 yr. 8 mo. at 6% ? 13. Of $250 for 3 yr. 6 mo. at 4%? 14. Of $400 for 4 yr. 3 mo. at 5% ? 15. Of $120 for 6 yr. 3 mo. at 8% ? 16. Of $1000 for 3 yr. 7 mo. at 6%? 17. Of $450 for 2 yr. 5 mo. at 8% ? 18. Of $500 for 2 yr. 9 mo. at 5% ? 19. Of $20 for 1 yr. 6 mo. at 7% ? 20. Of $340 for 2 yr. 6 mo. at 6% ? 21. What is the interest of $300 for 2 at 5% ? yr. 3 mo. 18 days SOLUTION. 18 days equal 13, or 3, of a month; hence 3 months and 18 days equal 33 months, or 4 months. of a month equals of 11⁄2 of a year, or of a year, and 18 months equal 18 times, or %, of a year; hence 2 yr. 3 mo. and 18 days equal 2 years. If the interest for 1 year is 5%, for 2 years it is 2 times 5%, or 12% ; 121% of $300 is $37.50. Therefore, etc. What is the interest 22. Of $400 for 5 yr. 3 mo. 18 da. at 10% ? 23. Of $500 for 3 yr. 7 mo. 6 da. at 5% ? 24. Of $600 for 1 yr. 6 mo. 20 da. at 9% ? 25. Of $300 for 2 yr. 7 mo. 6 da. at 5% ? 26. Of $150 for 4 yr. 3 mo. 20 da. at 6% ? 27. What is the amount of $250 for 6 yr. at 5% ? NOTE. The amount is the sum of the principal and the interest. SOLUTION.-For 6 yr. at 5%, 30%, or %, of the principal equals the interest. of $250 is $75; $250 plus $75 are $325, the amount. What is the amount 28. Of $240 for 4 yr. at 10%? 31. Of $600 for 3 yr. 6 mo. at 6% ? 36. Of $200 for 2 yr. 7 mo. 6 da. at 5% ? 37. A has $400, which amount is of C's money; what is the interest on each one's money for 3 yr. at 6%? 38. I build a house for $4000 when money is worth 5%; what is the yearly interest on the value of the house? 39. If a house cost me $3000 when money is worth 6%, and my taxes and insurance amount to 3%, what does the use of the house cost me each year? INTEREST BY DAYS. When the number of days for which money draws interest does not exceed 123, a short method much used is that of moving the decimal point two places to the left in the principal to find the interest for 60 days at 6%. Thus, the interest of $200 for 60 days at 6% is $2.00. For 63 days it is $2.00 and of $2.00, or $2.10, because the 3 days is of 60 days. Find the interest of- 6. $200 for 93 da. at 6%. 7. $400 for 60 da. at 5%. 8. $600 for 60 da. at 10%. 9. $800 for 63 da. at 5%. 10. $200 for 93 da. at 5%. 11. $600 for 93 da. at 8%. 12. $100 for 63 da. at 8%. 13. $200 for 33 da. at 8%. 14. $600 for 60 da. at 7%. 15. $900 for 63 da. at 7%. 16. $1200 for 95 da. at 6%. 17. $840 for 63 da. at 6%. 18. $660 for 93 da. at 6%. 19. $330 for 93 da. at 8%. 20. $550 for 60 da. at 6%. 21. $600 for 45 da. at 6%. 22. $800 for 63 da. at 6%. 23. $500 for 63 da. at 5%. 24. $400 for 33 da. at 10%. GENERAL PROBLEMS IN INTEREST. 1. TO FIND THE RATE. 1. At what per cent. will $200 gain $36 in 3 years? SOLUTION 1.-The interest on $200 for 1 yr. at 1% is $2, and for 3 yr. it is 3 times $2, or $6. For $200 to gain $36 will therefore require a rate of as many per cent. as $6 is contained times in $36, or 6%. SOLUTION 2.-At 1% the interest on $1 for 3 years is 3 cents, and on $200 it is 200 times 3 cents, or $6; it will therefore require as many per cent. as $6 is contained times in $36, or 6%. 2. At what per cent. will $300 gain $30 in 2 yr. ? 9. At what per cent. will $90 amount to $108 in 4 yr.? 10. At what per cent. will $500 amount to $605 in 31 yr.? 11. At what per cent. will $30 in 4 yr. 2 mo. amount to $37.50? 12. At what per cent. will $300 in 5 yr. 3 mo. amount to 13. At what per cent. will a principal double itself in 10 yr.? 20 yr.? 4 yr.? 5 yr.? 25 yr.? 5 NOTE. In order to double itself it must gain 100%, or once itself. 14. At what per cent. will a principal treble itself in 4 yr.? yr. ? 10 yr.? 20 yr.? 25 yr.? 40 yr.? 15. At what per cent. will a principal quadruple itself in 4 yr.? 5 yr.? 10 yr.? 15 yr.? 30 yr.? 16. At what rate will the interest of $600 for 3 yr. 3 mo. 6 days be $102? 17. The amount of a certain principal for 5 years at a certain per cent. is $750, and for 3 years, $690; what are the principal and the rate per cent.? 18. The amount of a certain principal for 4 years at a certain per cent. is $650, and for 7 years, $710; what are the principal and the rate per cent.? 2. TO FIND THE TIME. 1. In what time will $300 at 6% give $54 interest? SOLUTION.-$300 in 1 year, at 6%, will yield $18 interest, hence to yield $54 will require as many years as 18 is contained times in 54, or 3 years. yield $15 interest? 2. In what time will $100 at 5% 3. In what time will $200 at 6% 4. In what time will $100 at 4% 5. In what time will $300 at 5% 6. In what time will $140 at 5% 7. In what time will $150 at 6% 8. In what time will $60 at 5% yield $7.50 interest? 9. In what time will $25 at 6% yield $7.50 interest? 10. In what time will $200 at 7% 11. In what time will $300 at 6% yield $42 interest? |