Example. In what time will $840 produce $57.40 interest at 5% ? $100 produces $5 int. in 1 yr. $840 produces $42 in 1 yr. It will take $840 as many years to produce $57.40 as the $42 which it produces in one year is contained times in $57.40. 57.4042=1=1 yr. 4 mo. 12 da. .. $840 produces $57.40 in 1 yr. 4 mo. 12 da. In what time will : EXERCISE 122 1. $1088.75 produce $87.10 interest at 8% ? Example. At what rate per cent will $720 produce $42.50 interest in 1 yr. 2 mo. 5 da.? Changing 1 yr. 2 mo. 5 da. to years gives yr. $720 produces $42.50 in 5 yr. In one year at the same rate $ 720 would produce $42.50 + $5 = 42.50 × 77. The interest on $720 for 1 yr. at 1 % is $7.20. The interest for 1 yr. at the given rate is as many times the interest at 1% as = 42.50 × 7.20 42.50 × 5 × .. the rate is 5 x 1% = 5%. 1 = 5. 7.20 EXERCISE 123 Find the rate per cent when the interest on 2. $928 for 1 yr. is $ 64.96. 4. $945 for 6 mo. is $37.80. 8. $2400 for 8 mo. is $64. 9. $2500 for 9 mo. 18 da. is $100. 10. $3000 for 7 mo. 12 da. is $90. Find the rate per cent when 15. $1080 amounts to $1123.20 in 8 mo. 16. $1200 amounts to $1270 in 10 mo. 17. $1600 amounts to $1640 in 6 mo. 18. $2460 amounts to $2574.80 in 9 mo. 10 da. 19. $92 amounts to $102.12 in 2 yr. 20. $324 amounts to $333.72 in 8 mo. Example. What principal will amount to $136.27 in 1 yr. 3 mo. 15 da. at 5%? The interest on $1 for 1 yr. 3 mo. 15 da. is $.06455. ... the amount of $1 for 1 yr. 3 mo. 15 da. is $1.06455. ... the number of dollars in principal = $136.27 ÷ $1.06455 = $128, nearly. EXERCISE 124 What principal will amount to 1. $840 in 1 yr. at 5%? 4. 5. 3. $645 in 1 yr. at 71%? 6. $903 in 1 yr. at 5 %? $414 in 3 yr. at 5%? $255.30 in 2 yr. at 51% ? 7. $12,540.45 in 2 yr. 3 mo. at 4% ? 8. $168.35 in 7 mo. 6 da. at 6%? 9. $618.67 in 1 yr. 4 mo. at 5% ? 10. $646.80 in 8 mo. at 4% ? 11. $776.07 in 1 yr. 1 mo. at 41%? 13. $432.55 in 11 mo. at 8% ? 14. $282.75 in 2 yr. 4 mo. 15 da. at 71% ? 15. $2090.07 in 1 yr. 1 mo. 15 da. at 8%? EXERCISE 125 REVIEW 1. Find the interest on $4000 for 13 mo. 2 da. at 9%. 2. Find the interest on $256.30 for 4 mo. 9 da. at 7%. 3. Find the interest on $30.85 for 11 mo. 6 da. at 5 %. 4. Find the interest on $653 for 2 mo. 16 da. at 4%. 5. Find the interest on $2105.60 for 84 da. at 5%. 6. Find the amount of $805 for 10 mo. at 8%. 7. Find the amount of $507 for 1 yr. 12 da. at 8%. 8. What principal will produce $20.83 interest in 5 mo. at 5%? 9. What principal will produce $17.50 interest in 9 da. at 5%? 10. Find the rate of interest when $ 500 produces $2.92 interest in 1 mo. 11. Find the rate of interest when $ 250 produces $7.30 in 5 mo. 12. How much must I invest at 5% interest to have an annual income of $1200 from my investment? 13. A man buys a house and lot and rents it for $40 a month. Taxes and insurance cost him $120 a year. If his net receipts gives him a profit of 6 % on his investment, find the cost of the house and lot. 14. For how long a time must $3000 be loaned at 5% to produce $20 interest? 15. For how long a time must $ 2400 be loaned at 7 % in order to have principal and interest amount to $ 2456 ? 16. For how long a time must a sum of money be loaned at simple interest at 8 % to produce in interest of itself? 17. For how long a time must a sum of money be loaned at simple interest at 6 % to produce in interest of itself? 18. Find the exact interest of $1200 for 292 da. at 5 %. 19. Find the exact interest of $7300 for 146 da. at 7 %. 20. The exact interest of $10,800 at 5 % is $324. the time. Find 21. In what time will $260 amount to $262.60 at 5 %? 22. What sum must be deposited in a savings bank which pays 3% interest to produce semiannually $8.75? 23. A man deposits his money in two banks. In one bank he has $572 which pays 33%. The other bank gives 4 % interest. If he receives as interest the same amount from both banks, how much money has he all together? 24. If I invest half my money at 6 % and the remainder at 4 %, and derive an income of $ 650 annually, how much money have I invested? REVIEW QUESTIONS 1. Define principal, rate, per cent, interest, amount. 2. How does exact interest differ from interest according to the common use of the term? |