# 4.8 Review Exercises

- If you invest $10,000 at 7.74% compounded quarterly for 10 years, what is the maturity value? How much interest did the investment earn?

**Click to see Answer**FV = $21,524.50, I=$11,524.50

- 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?

**Click to see Answer**PV = $67,313.13

- 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?

**Click to see Answer**$5,450.83

- What is the effective rate of interest on your credit card if you are being charged 24.5% compounded daily?

**Click to see Answer**27.7516%

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

**Click to see Answer**4.0604% compounded weekly

- 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)?

**Click to see Answer**18 years, 6 months

- 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?

**Click to see Answer**FV = $70,432.59

- 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? How much interest did the investment earn?

**Click to see Answer**PV = $21,600, I=$4,578.21

- 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.

**Click to see Answer**$3,817.05

- 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?

**Click to see Answer**13.5131% compounded annually

- 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?

**Click to see Answer**7.5% compounded quarterly, 7.714% effective

- A $10,000 loan at 8.15% compounded quarterly is to be repaid by two equal payments due in 9 months and in 33 months. Determine the size of the payments.

**Click to see Answer**$5,739.43

- Exactly how long will it take for your money to quadruple at 6.54% compounded monthly? Express answer in years, months, days.

**Click to see Answer**21 years, 4 months

- 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 equal payments, each due at 3 months, 9 months, and 21 months. 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.

**Click to see Answer**$67,978.25

- 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?

**Click to see Answer**PV = $4,957.60

- Jack is considering alternative three-year investment proposals from different banks for his $20,000 principal. RBC says that if he invests his money with them, he will have $23,841.78 using quarterly compounding. CIBC indicates that he would have $23,607.15 using monthly compounding. What nominal and effective rates are being offered by each bank?

**Click to see Answer**RBC: 5.925 compounded quarterly, 6.0318% effective; CIBC: 5.54% compounded monthly, 5.6829% effective

#### Attribution

“Chapter 9 Review Exercises” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.