Review Exercises

1. If you invest $10,000 at 7.74% compounded quarterly for 10 years, what is the maturity value? (Answer: FV = $21,524.50)

2. Ford Motor Company is considering an early retirement buyout package for some employees. The package involves paying out today’s fair value of the employee’s final year of salary. Shelby is due to retire in one year. Her salary is at the company maximum of $72,000. If prevailing interest rates are 6.75% compounded monthly, what buyout amount should Ford offer to Shelby today? (Answer: PV = $67,313.13)

3. Polo Park Bowling Lanes owes the same supplier $3,000 today and $2,500 one year from now. The owner proposed to pay both bills with a single payment four months from now. If interest rates are 8.1% compounded monthly, what amount should the supplier be willing to accept? (Answer: x = $5,450.83)

4. What is the effective rate of interest on your credit card if you are being charged 24.5% compounded daily? (Answer: effective rate = 27.7516%)

5. Your 2½-year investment of $5,750 just matured for $6,364.09. What weekly compounded rate of interest did you earn? (Answer: 4.0604% compounded weekly)

6. Vienna just paid $9,567.31 for an investment earning 5.26% compounded semi-annually that will mature for $25,000. What is the term of the investment (in years and months)? (Answer: 18 years, 6 months)

Applications

7. Merryweather’s union just negotiated a new four-year contract with her employer. The terms of the contract provide for an immediate wage increase of 3.3%, followed by annual increases of 3.5%, 4.25%, and 2.75%. If she currently earns $61,500, what will her salary be in the final year of the contract? (Answer: FV = $70,432.59)

8. Bronco’s four-year investment just matured at $26,178.21. If the investment earned semi-annually compounded interest rates of 4.5% and 4.75% in the first two years, followed by monthly compounded interest rates of 5% and 5.1% in the last two years, how much money did Bronco initially invest? (Answer: PV = $21,600)

9. Jay’s Pharmacy owes the same creditor two debts of $6,000 due one year ago and $7,500 due in two years. Jay has proposed making two alternative payments of $10,000 due in three months and a final payment in 2½ years. If the creditor is agreeable to this proposal and wants an interest rate of 9% compounded quarterly, what is the amount of the final payment? Use 2½ years as the focal date. (Answer: x = $3,817.05)

10. Over a 10-year period, the Growth Fund of America had annual returns of 0.02%, 29.8%, 14.84%, 26.86%, 31.78%, 45.7%, 7.49%, −12.2%, −22.02%, and 32.9%. What fixed annually compounded rate of return did the fund realize over the 10 years? (Answer: 13.5131% compounded annually)

11. A sum of $84,100 was invested for 2½ years and matured at $101,268 using quarterly compounding. What quarterly compounded interest rate was realized? What is this effectively? (Answer: 7.5% compounded quarterly, 7.714% effectively)

12. A $10,000 loan at 8.15% compounded quarterly is to be repaid by two payments. The first payment is due in 9 months and the second payment, 1⅕ times the size of the first payment, is due in 33 months. Determine the amount of each payment. (Answer: x = $5,256.23 (first payment), 1.2x = 1.2($5,256.23) = $6,307.48 (second payment))

13. Exactly how long will it take for your money to quadruple at 6.54% compounded monthly? Express answer in years, months, days. (Answer: 21 years, 3 months, 2 days)

Challenge, Critical Thinking, & Other Applications

14. For the past four years, Darren has been saving up for a college fund for his oldest daughter. He deposited $5,000 initially, followed by annual deposits of $5,000, $4,000, $3,600, and $5,000. The money was initially invested at 5.75% compounded semi-annually for the first two years before increasing to 6% compounded quarterly for the balance of the investment. How much money is in the college fund today? (Answer: Final Balance Today = $25,596.53)

15. Six months ago Old Dutch Foods purchased some new machinery for a new product line that they just developed. The supplier agreed to three payments on the machinery of $40,000 due today, $85,000 due in six months, and $75,000 due in 15 months. The new product line has not been as successful as initially planned, so Old Dutch Foods has proposed an alternative agreement involving three payments, each due at 3 months, 9 months, and 21 months. The second payment is to be double the first payment, and the last payment is to be double the second payment. If the supplier is agreeable to this and wants an interest rate of 8.55% compounded monthly, determine the payments required in the proposed agreement. Use 3 months as the focal date. (Answer: x = $29,975.59 (first payment), 2x = 2($29,975.59) = $59,951.18 (second payment), 4x = 4($29,975.59) = $119,902.36 (third payment))

16. Louisa owns a furniture store and decided to help a friend out by allowing him to purchase $5,000 of furniture using her credit at 6.25% compounded semi-annually. The furniture loan is to be repaid in four years. However, after 2½ years Louisa can no longer have the loan outstanding and needs the money. Avco Financial has agreed to purchase the maturity amount of this loan from Louisa using a discount rate of 17.1% compounded monthly. If Louisa proceeds with selling the loan contract to Avco Financial, what sum of money can she expect to receive? (Answer: PV = $4,957.60)

17. Franklin owes the following amounts to the same person: $16,000 due today, $11,500 due in 1¼ years, $17,000 due in 2¾ years, and $15,000 due in 4¼ years. He wants to make a single payment of $56,500 instead. Using an interest rate of 8% compounded quarterly, when should this payment be made? Use today as the focal date. Express answer in years, months, days. (Answer: 1 year, 3 months, 70 days from today)