1.8 Review Exercises

Chapter 1 Review Exercises

1. 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?
Solution

$FV = \21,524.50$, $I=\11,524.50$

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?
Solution

$PV = \67,313.13$

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?
Solution

$\5,450.83$

4. What is the effective rate of interest on your credit card if you are being charged $24.5\%$ compounded daily?
Solution

$27.7516\%$

5. Your $2$½-year investment of $\5,750$ just matured for $\6,364.09$. What weekly compounded rate of interest did you earn?
Solution

$4.0604\%$ 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)?
Solution

$18$ years, $6$ months

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?
Solution

$FV = \70,432.59$

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? How much interest did the investment earn?
Solution

$PV = \21,600$, $I=\4,578.21$

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 $2$½ 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 $2$½ years as the focal date.
Solution

$\3,817.05$

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?

$13.5131\%$ compounded annually

11. A sum of $\84,100$ was invested for $2$½ years and matured at $\101,268$ using quarterly compounding. What quarterly compounded interest rate was realized? What is this effectively?
Solution

$7.5\%$ compounded quarterly, $7.714\%$ effective

12. 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.
Solution

$\5,739.43$

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

$21$ years, $4$ months

14. 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.
Solution

$\67,978.25$

15. 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 $2$½ 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?
Solution

$PV = \4,957.60$

16. 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?
Solution

RBC: $5.925$ compounded quarterly, $6.0318\%$ effective; CIBC: $5.54\%$ compounded monthly, $5.6829\%$ effective