Exercise 67-Oral. 1. If we know that 1 year's interest on a certain principal at a certain rate per cent is $12.00, in what time would the same principal yield $6.00 at the same rate per cent? 2. In what time would the same principal yield $24.00? 3. What process did you use to find your answers to Question 1 and Question 2? 4. In what time will $100.00 yield $1.00 at 4%? 5. How do we find the time in which a given principal will yield a certain interest at a certain rate per cent? Show this by letters and signs. 6. If we know that the interest at 1% on a certain principal for a certain time is $8.00, at what rate per cent would the same principal yield $40.00 in the same time? 7. What process did you use to find your answer to Question 6? 8. At what rate per cent will $200.00 yield $6.00 in 1 year? 9. How do we find the rate per cent at which a certain principal will yield a certain interest in a certain time? Show this by letters and signs. 10. When finding the time or the rate per cent, what must be done when the amount due at maturity is known, but the interest is unknown? 11. Looking at Exercise 68, state how you will prove your answers for Examples #1 to #5. 12. Looking at Exercise 68, state how you will prove your answers for Examples #6 to #10. 13. Looking at Exercise 68, state how you will prove your answer for Example #11. 14. Looking at Exercise 68, state how you will prove your answer for Example #12. 15. Looking at Exercise 68, state how you will prove your answer for Example #13. State how you will prove your answer for Example #14. Exercise 68-Written.· Solve and prove: (Total interest rate; I (PX T) = R). At what rate per cent will: 1. $675.00 yield $6.75 in 3 months? 2. $420.00 yield $7.70 in 120 days? 3. $1,260.00 yield $170.10 in 2 years 3 months? 4. $808.00 yield $8.08 in 45 days? 5. $546.00 yield $11.83 in 6 months? At what rate per cent will: 6. $4,800.00 amount to $4,809.00 in 15 days? 7. $72.00 amount to $74.10 in 210 days? 8. $4,124.00 amount to $4,216.79 in 9 months? 9. $42.00 amount to $42.98 in 4 mo. 20 da.? 10. $98.80 amount to $106.21 in 1 yr. 8 mo.? Are you sure this is true each time: Total interest ÷ interest on $1 for full time, at full principal. rate = interest for 1 yr. on full principal at full rate = time. interest at 1% on full principal for 11. At what rate will $650. yield $97.50 interest in 2 yr. 6 mo.? 12. In what time will $922.50 yield $49.20 interest at 4%? 13. How much money loaned for 3 yr. 8 mo. at 5% will yield $112.20 interest? 14. In what time will $5,000. yield $5,000. interest at 4%? LESSON 32 Transposition in Figuring Interest EXAMPLE: Find the interest on $90.00 for 42 days at 5%. You will remember that in figuring wages we can transpose the hours worked and the rate per week to shorten the work, when the rate per week is an aliquot part of the weekly hour basis; as, 37 hours work at $16.00 per week on a 48-hour basis is the same as 16 hours at $37.25 per week, the answer being $12.42 (of $37.25). 16 48 37 18 of $37.25 is equal to of $16.00. 48 In the same manner, we can save much work in figuring interest by transposing the principal and the time when the principal is an aliquot part of 360, since 360 days is the basis on which commercial interest is figured; thus, in figuring the interest on $60.00 for 197 days at 6%, we can call the dollars "days" and the days dollars," and find the interest on $197.00 for 60 days at 6%, the answer being $1.97. 60 360 X 180 X $197. is equal to 387 × 180 × $60. Exercise 69—Oral. 1. The interest on $30.00 for 78 days is the same as the interest on $78.00 for how many days? 2. The interest on $90.00 for 56 days is the same as the interest for 90 days on how many dollars? 3. How can you find the interest on $60.00 for 273 days most quickly? 4. What is the interest on $60.00 for 273 days at 6%? 5. When can work be saved by transposing the time and the principal in figuring interest? 6. What must be done when the rate is more or less than 6%? 7. How would you find the interest on $120.00 for 18 days at 5%? See if you can give the answer. 8. How would you find the interest on $45.00 for 160 days at 7%? See if you can give the answer. 9. How would you find the interest on $180.00 for 411 days at 6%? 10. How would you find the interest on $90.00 for 544 days at 41%? Exercise 70-Written. Using transposition, find the interest on: 1. $75.00 for 148 days at 6%. 2. $15.00 for 312 days at 8%. 3. $120.00 for 188 days at 41%. 4. $150.00 for 78 days at 4%. 5. $80.00 for 96 days at 5%. 6. $40.00 for 318 days at 7%. 7. $180.00 for 1 day at 6%. 8. $50.00 for 84 days at 51%. 9. $30.00 for 488 days at 61%. 10. $210.00 for 22 days at 6%. LESSON 33 Compound Interest EXAMPLE: Find the compound interest on $500.00 for 3 years, at 6%, the interest being compounded annually. Original Principal. $30.00 Interest for 1st year; Amount $530.00; $31.80 Interest for 2d year; Amount $561.80; $33.71 Interest for 3d year; Amount $595.51; $95.51 Compound Interest for 3 years. or: $595.51 500.00 $95.51 Compound Interest for 3 years. When the interest for stated periods is added to the principal and the amount so found is used as the principal for the next interest period, the total interest so added to the several principals is called "compound interest." Savings banks usually allow compound interest, adding the interest to the principal quarterly or semiannually to form each new principal. Try to find out how the savings banks in your locality pay interest. |