# 2.9 Review Exercises

## Chapter 2 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?
Solution

$\110.36$

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?
Solution

$\652.42$

3. 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?
Solution

$\429.84$

4. Consider an investment of $\225,000$ earning $5\%$ annually. How long could it sustain annual withdrawals of $\20,000$ starting immediately?
Solution

$16$ years

5. The advertised month-end financing payments on a $\28,757.72$ car are $\699$ for a four-year term. What semi-annual interest rate is being used in the calculation?
Solution

$7.9\%$

6. 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?
Solution

$1$ year, $2$ months

7. 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?
Solution

$\19,695.13$

8. 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?
Solution

$2.9\%$

9. 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?
Solution

$\19,894.24$

10. 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?
Solution

$\394.14$

11. 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 $\100$?
Solution

$8$ years

12. 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?
Solution

$\1799.23, \2,196.92$

13. 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?
Solution

$9$ years

14. Being able to start an RRSP with a lump-sum investment can reduce your end-of-month contributions. For any $35-$year term RRSP earning $8.7\%$ compounded annually, calculate the monthly contribution necessary to have a maturity value of $\1,000,000$ if the starting lump sums are $\5,000, \10,000, \15,000$, and $\20,000$. What do you observe from your calculations?
Solution

$\360.92, \324.06, \287.19, \250.31$

15. An annuity needs to pay out $\1,000$ at the end of every quarter for three years. Using an interest rate of $5\%$ quarterly throughout, what amount of money must be invested today to fund the investment if the first payment is paid out in four years?
Solution

$\9,195.75$

16. Red Deer College wants to set up a scholarship for students in its business programs such that at the end of every year it could distribute a total of $\50,000$. If the perpetuity fund can earn $4.85\%$ compounded semiannually, how much money will need to be raised to fund the scholarship?
Solution

$\1,019,577.58$

17. Procter and Gamble shares are valued at $\61.00$ with perpetual year-end dividends of $3.1639\%$. What dividend payment would a holder of $750$ shares receive in perpetuity assuming the share price and dividend rate remain unchanged?
Solution

$\1447.48$

18. The common shares of The Coca-Cola Company are forecast to pay $\1.55$ per share at the end of the next four years, and then $\2.05$ annually in perpetuity. If the market rate of return on such shares is $2.89\%$, what price should an investor be willing to pay today?
Solution

$\69.07$

19. A Canadian college plans to implement a new business major in five years. To support the new program, it wants to offer $15$ annual $\2,500$ scholarships at the beginning of each school year in perpetuity. If the scholarship fund can earn $4.65\%$ compounded annually, what amount of money does the college need to raise today to fund the program?
Solution

$\672,390.21$

20. AVCO Financial is under contract with a national retail chain to purchase its loan contracts on its date of sale. Under a special promotion, the retail chain allows a customer to defer her payments. If AVCO purchases the contract for $\5,276.83$ at its contractual rate of $21\%$ compounded monthly and the consumer is required to make $30$ month-end payments of $\425$, in how many months will AVCO receive its first payment?
Solution

$37$ months

21. Jacques Cousteau just won the $\10$ million Powerball lottery. He has been offered the following choices on how to collect his winnings.
• Option 1: A one-time lump-sum payment of $\4,289,771.59$ today.
• Option 2: Year-end payments of $\400,000$ for $25$ years at $5\%$ effective with the first payment received in five years.
• Option 3: Annual payments of $\207,150$ in perpetuity starting today earning $5\%$ compounded annually.

Which option is the best financial choice?

Solution

PV of Option $1$: $\4,289,771.59$, PV of Option $2$: $\4,638,049.33$, PV of Option $3$: $\4,350,150$; Option #$2$ is best