173. Method by Aliquot Parts. WRITTEN EXERCISES. 1. What is the interest of $1200 for 4 yr. 5 mo. 15 da. at 54%? 2. Of $1080 for 3 yr. 9 mo. at 5%. 3. Of $720 for 2 yr. 8 mo. at 51%. 4. Of $840 for 4 yr. 7 mo. at 6%. 5. Of $1600 for 2 yr. 6 mo. 15 da. at 7%. 6. Of $3600 for 3 yr. 10 mo. 18 da. at 8%. 7. Of $4200 for 2 yr. 5 mo. 25 da. at 41%. 8. Of $1800 for 1 yr. 1 mo. 11 da. at 61%. 9. Of $2100 for 6 yr. 6 mo. 6 da. at 6%. 10. Of $2400 for 2 yr. 2 mo. 12 da. at 5%. 174. Exact Interest. Exact Interest is interest obtained by reckoning 365 days to the year. Exact Interest is used by the United States government and by many business men. Common interest and exact interest for any number of years are the same. They differ only in periods of time less than a year. Find the interest of $100 for 1 yr. at 5%. the remainder will be exact interest. Hence off from common interest will give exact interest. WRITTEN EXERCISES. 1. Find the exact interest of $730 for 2 yr. 8 mo. 18 da. We find the common interest of $730 for 2 yr. by multiplying by .12, which is $87.60; and for 8 mo. 18 da. by multiplying by .043, which is $31.39. Since off from common interest gives exact interest, we deduct from $31.39, leaving $30.96, the exact interest for 8 mo. 18 da. Adding.$87.60 and $30.96, the result is $118.56. Find the exact interest of— 2. $850 for 10 mo. 24 da, at 6%. 4. $2400 for 3 yr. 9 mo. 15 da. at 7%. 5. $1560 from Mar. 1st to Nov. 25th at 8%. 6. $3330 from Jan. 4, 1888, to May 7, 1890, at 5%. 7. $960 from Mar. 12, 1890, to Dec. 20, 1890, at 51%. 8. $4080 from Dec. 11, 1892, to May 29, 1896, at 7%. PROBLEMS IN INTEREST. CASE I. 175. Given the time, rate, and interest, to find the principal. WRITTEN EXERCISES. 1. What principal will in 2 yr. 6 mo. 12 da. at 6% give $30.40 interest? Divide the given interest by the interest of $1 for the given time and rate. What principal at interest will gain— 2. $105.60 in 3 yr. 8 mo. at 6%? 3. $11.76 in 4 yr. 8 mo. at 6% ? 7. $97.20 in 2 yr. 8 mo. 12 da. at 5% ? What principal will amount to 9. $1710.58 in 28 da. at 6%? 10. $249.256 in 4 yr. 6 mo. at 31% ? 12. $32.82 in 7 yr. 7 mo. 21 da. at 5% ? CASE II. 176. Given the principal, the rate, and the interest, to find the time. WRITTEN EXERCISES. 1. In what time will $240 give $50.40 interest at 6%? Divide the given interest by the interest of the principal at the given rate for one year. In what time will 2. $940 at 6% give $432.40 interest? 3. $1450 at 6% give $217.50 interest? 4. $60 at 6% give $6 interest? 5. $120 at 7% give $37.10 interest? 6. $480 at 5% 7. $240 at 6% 8. $720 at 5% 9. $360 at 8% give $62 interest? give $16.92 interest? give $117.30 interest? give $312.80 interest? 10. $600 at 7% give $613.30 amount? 11. $960 at 5% give $984.80 amount? 12. $1200 at 41% give $1203.60 amount? 13. In what time will a principal double itself at 5%? At 8%? At 4%? 14. In what time will a principal treble itself at 6%? At 7%? At 51%? CASE III. 177. Given the principal, the time, and the interest, to find the rate. WRITTEN EXERCISES. 1. At what rate will $640 give $172.80 interest in 4 yr. 6 mo.? At what rate will 2. $900 gain $198 in 3 yr. 8 mo.? 8. $840 amount to $981.96 in 2 yr. 9 mo. 24 da.? 9. $18.20 amount to $28.43 in 9 yr. 9 mo. 9 da.? 10. $625 amount to $710.62 in 2 yr. 3 mo. 12 da.? 11. $192 amount to $200.928 in 9 mo. 9 da.? 12. $600 gain $3.525 in 47 da.? 13. $564 gain $64.108 in 11 mo. 11 da.? 14. $744 amount to $764.15 in 10 mo.? 15. At what per cent. will a principal double itself in 4 yr.? In 6 yr.? In 7 yr.? 16 At what per cent. will a principal treble itself in 10 yr.? In 30 yr.? In 5 yr.? |