Review Exercises

1. Sangarwe will deposit $300 every quarter into an investment annuity earning 4.5% compounded quarterly for seven years. What is the difference in the amount of money that she will have after seven years if payments are made at the beginning of the quarter instead of at the end? (Answer: $110.36)

2. Canseco wants to have enough money so that he could receive payments of $1,500 every month for the next nine-and-a half years. If the annuity can earn 6.1% compounded semi-annually, how much less money does he need if he takes his payments at the end of the month instead of at the beginning?
   (Answer: $652.42)

3. Kevin wants to save up $30,000 in an annuity earning 4.75% compounded annually so that he can pay cash for a new car that he will buy in three years’ time. What is the difference in his monthly contributions if he starts today instead of one month from now? (Answer: $3.00)

4. Brianne has a $21,000 loan being charged 8.4% compounded monthly. What are the month-end payments on her loan if the debt will be extinguished in five years? (Answer: $429.84)

5. Consider an investment of $225,000 earning 5% annually. How long could it sustain annual withdrawals of $20,000 (including the smaller final payment) starting immediately? (Answer: 16 years)

6. The advertised month-end financing payments on a $28,757.72 car are $699 for a four-year term. What semi-annual and effective interest rate is being used in the calculation? (Answer: 7.9% semi-annually; 8.056% annually)

Applications

7. Kubb Bakery estimates it will need $198,000 at a future point to expand its production plant. At the end of each month, the profits of Kubb Bakery average $20,000, of which the owner will commit 70% toward the expansion. If the savings annuity can earn 7.3% compounded quarterly, how long will it take to raise the necessary funds? (Answer: 1 year, 2 months)

8. An investment fund has $7,500 in it today and is receiving contributions of $795 at the beginning of every quarter. If the fund can earn 3.8% compounded semi-annually for the first one-and-a-half years, followed by 4.35% compounded monthly for another one-and-three-quarter years, what will be the maturity value of the fund? (Answer: $19,695.13)

9. A $17,475 Toyota Matrix is advertised with month-end payments of $264.73 for six years. What monthly compounded rate of return (rounded to one decimal) is being charged on the vehicle financing? (Answer: 2.9% monthly)

10. A variable rate loan has a balance remaining of $17,000 after two years of fixed end-of-month payments of $655. If the monthly compounded interest rate on the loan was 5.8% for the first 10 months followed by 6.05% for 14 months, what was the initial amount of the loan? (Answer: $29,894.24)

11. Hank has already saved $68,000 in his RRSP. Suppose he needs to have $220,000 saved by the end of 10 years. What are his monthly payments starting today if the RRSP can earn 8.1% compounded annually? (Answer: $394.14)

12. Many companies keep a “slush fund” available to cover unexpected expenses. Suppose that a $15,000 fund earning 6.4% compounded semi-annually continues to receive month-end contributions of $1,000 for the next five years, and that a withdrawal of $12,000 is made two-and-a-half years from today along with a second withdrawal of $23,000 four years from today. What is the maturity value of the fund? (Answer: $52,351.32)

13. Many consumers carry a balance each month on their credit cards and make minimal payments toward their debt. If a consumer owes $5,000 on a credit card being charged 18.3% compounded daily interest, how long will it take him to pay off his debt with month-end payments of $100? (Answer: 8 years)

14. You have a loan for $20,000 on which you are charged 6% compounded quarterly. What payment amount at the end of every six months would reduce the loan to $15,000 after two years? What is the interest portion of the total payments made? (Answer: PMT = $1,799.23; I = $2,196.92)

Challenge, Critical Thinking, & Other Applications

15. Stan and Kendra’s children are currently four and two years old. When their older child turns 18, they want to have saved up enough money so that at the beginning of each year they can withdraw $20,000 for the first two years, $40,000 for the next two years, and $20,000 for a final two years to subsidize their children’s cost of postsecondary education. The annuity earns 4.75% compounded semi-annually when paying out and 6.5% compounded monthly when they are contributing toward it. Starting today, what beginning-of-quarter payments must they deposit until their oldest reaches 18 years of age in order to accumulate the needed funds? (Answer: $1,551.14)

16. Karen is saving $1,500 at the end of every six months into an investment that earns 9.4% compounded monthly for the next 20 years. The maturity value will then be rolled into an investment earning 5.85% compounded annually, from which she plans on withdrawing $23,800 at the beginning of each year. How long will the annuity sustain the withdrawals (including the smaller final payment)? (Answer: 9 years)

17. In an effort to clear out last year’s vehicle inventory, Northside Ford advertises a vehicle at $46,500 with 0% financing for five years of end-of-month payments. Alternatively, consumers can pay cash and receive a $6,000 rebate. What is the maximum monthly compounded interest rate that a bank could charge that would result in equal or lower monthly payments? (Answer: 5.575% monthly)

18. Delaney is 18 years old and wants to sustain an annual income of $30,000 in today’s dollars for 17 years at the end of every year when she retires at age 65 (the amount will remain fixed once set at age 65). If the annually compounded annuity can earn 4.65% in retirement and 9.5% during contributions, how much does she need to invest at the end of every month? Assume the annual rate of inflation is 2.7%. (Answer: $131.36)