[31] You would like to save to return to school. You deposit $4,000 into a GIC that pays j4 = 7.44%. You have decided to return to school when your savings grow to at least $6,000. If you make no more contributions, how many years will it take you to reach your goal?
[32] An investment of $2,000 made 30 months ago is now worth $2,676.45. What nominal rate of interest, compounded semiannually, did the investment earn?
[33] What nominal rate, compounded semiannually, is equivalent to 12% compounded quarterly?
[34] Debts of $800 due today and $900 due in 27 months are to be repaid with 2 equal payments, 1 year and 2 years from today. If the interest rate is 9% compounded quarterly, find the size of the payments. Use 2 years as the focal date.
[35] You are searching for a mutual fund.
- Fund 1 offers a rate of return of 6.4% compounded quarterly.
- Fund 2 offers a rate of return of 6.6% compounded semi-annually.
Convert all rates to effective rates. Which fund is the better investment?
[36] You purchase a new car. The dealer offers you terms of 20% down and the remainder financed over three years at an interest rate of 9% compounded quarterly. The cost of the car is $21,640.79.
(a) Find the size of your monthly payment if your first payment is due one month after you purchase the car.
(b) What is the cost of financing (i.e., how much interest will you pay)?
[37] A TV set may be purchased on these terms: a down payment of 20% of the selling price is to be made on the date of purchase, followed by 18 monthly payments of $40 each, with the first payment one month after the date of purchase. If the interest rate charged is 10% compounded monthly, what is the cash price (selling price) of the TV set?
[38] A used car that sells for $15,000 may be purchased by making payments of $500 per month for 3 years with the first payment due the day the car is purchased.
(a) What nominal rate of interest, compounded quarterly, is charged?
(b) What effective rate of interest is charged?
[39] You take out a loan for $12,000 with quarterly payments of $806.59 at the end of each quarter. If the interest rate on the loan is 12% compounded quarterly, how many years will it take you to pay off the loan?
[40] John will purchase an annuity that will pay him $5,000 per quarter for 10 years beginning when he turns 60 years of age. If John’s current age is 45 years and the invested funds will earn 7.0% compounded quarterly, what amount must he invest in the annuity today so he can collect $5,000 per quarter for 10 years with the first payment on his 60th birthday?
[41] A bursary fund for BCIT honour students is to be funded by a perpetual fund. The fund earns interest at 8% compounded semi-annually and is to pay $2,000 every six months, with the first scholarship paid in six months. Find the size of the initial funding that is required.
[42] A friend has invested in a bond fund and says she doubled her money in five years. What rate of interest, compounded semi annually, did she earn?
[43] A person can buy a piece of land for $130,000 now or $60,000 now and $100,000 in 5 years. Which option is better if money can be invested at:
(a) 6% compounded quarterly?
(b) 10% compounded quarterly?
[44] Meryl just turned 50 years old. She put $50,002 into her RRSP today. She will leave the money in her RRSP until her 65th birthday. She will then purchase a 10-year annuity with the first withdrawal one month later. Use
(a) What will be the size of the monthly withdrawals?
(b) How much interest did Meryl earn over the 25 years?
(c) Meryl has determined that she requires a larger monthly payment than that found in part (a). She would like to receive $2,000 per month. How much additional money must she transfer to her RRSP today so she can collect $2,000 per month instead?
[45] You invest $4,000 in a mutual fund. Your investment of $4,000 earns the following returns.
| Year | Return |
| Year 1 | j1 = 9% |
| Year 2 | j2=12% |
| Year 3 | j4 = 10% |
What average nominal rate of return, compounded semiannually, did you earn?
(source)