[14] North Credit Union advertises that it will pay 7% compounded annually on money on deposit for periods longer than one year and that the money may be taken out, with interest, at any time after the first year. A depositor placed $20,000 on deposit at the above rate for four years, but decided to withdraw it after 2.5 years.
(a) How much should the depositor receive?
(b) Show that, if this amount were deposited at the same rate for the remaining 1.5 years, the result would be the same as if it had never been withdrawn.
[15] A loan of $17,000 for three years resulted in a future value of $21,560.11. Use your calculator functions to find the nominal interest rate if the loan was compounded:
(a) quarterly
(b) semi-annually.
[16] Use your calculator functions to find the FV of a principal of $1.00 invested for one year at 16% compounded quarterly, and leave the results in your calculator. Then find the nominal monthly rate that will give the same FV – the rate compounded monthly that is equivalent to 16% compounded quarterly. Check your answer by finding the future value of a principal of $10,000 invested for two years at each rate. You should get the same answer in each case.
[17] Complete the following table of equivalent nominal rates, giving answers in percent to six decimals. Each row will contain equivalent rates.
| Effective Rate, j1 | j2 | j4 | j12 |
| ? | ? | ? | j12 = 16% |
| ? | ? | j4 = 12% | ? |
| ? | j2 = 9% | ? | ? |
[18] Use your results in Row 1 in the previous problem to find the future value of a loan of $4,000 for 18 months by doing the compounding:
(a) monthly.
(b) quarterly.
(c) semi-annually.
(d) annually.
[19] Your first child was born this year and you decide to save for her education. You deposit $2,000 into an RESP (registered education savings plan) that pays 4.5% compounded annually (j1=0.045). How much will your child have in 18 years? Use both the formula and the TVM Keys.
[20] You borrow $5,000 from a private loan company and agree to pay it back with interest calculated at 10% compounded quarterly. How much will you owe in 30 months? Use both the formula and the TVM Keys.
[21] You are expecting a tax refund of $3,000 six months from now. You take your T4 slips to H&P Square Tax preparation service and they agree to give you the money now if you sign over the refund to them. How much money will you receive today if interest is calculated at j12 = 9%. Use both the formula and the TVM Keys.
[22] You go to purchase a brand new motorcycle and the dealer quotes you a price of $14,000 to be paid as a single payment in 30 months. You would like to pay cash today for the motorcycle. How much should you offer if interest is calculated at 8% compounded semi annually? Use the formula and the TVM Keys.
[23] You have $75,000 and decide to purchase a 30 year Government of Canada strip bond with an interest rate of 7.0% compounded semi-annually. How much will the bond be worth in 30 years? (i.e., what is the maturity value of the strip bond?)
[24] Financial planners predict you will need one million dollars to retire.
(a) You would like to buy a 30-year strip bond with an interest rate of 7% compounded semi-annually that has a maturity value of one million dollars. How much will you need to pay for this strip bond today?
(b) Unfortunately, you only have $75,000 available to buy a bond. You are considering buying a junk bond (risky bond) because you know that the interest rates are much. higher than for a Government of Canada bond. What nominal interest rate, compounded semi-annually, do you require so that the bond will have a maturity value of $1,000,000 in 30 years?
(c) Your friend convinces you that junk bonds are too risky to be used as a retirement investment. If instead, you buy the Government of Canada bond (with your $75,000) that pays 7% compounded semi-annually, how many years will it take you to reach your goal of having $1,000,000?
[25] If an investment grows from $10,000 to $16,000 in 27 months, what was the nominal rate of interest, compounded quarterly?
[26] If an investment grows from $4,000 to $6,000 in 48 months, what was the nominal rate of interest:
(a) compounded monthly?
(b) compounded quarterly?
(c) compounded semi-annually?
(d) compounded annually?
[27] 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 grows to at least $6,000. If you make no more contributions, how many years will it take you to reach your goal?
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