Exam 9: Compound Interest: Further Topics and Applications

If a series of compound percent changes are all positive, is the overall percent change larger or smaller than the sum of the individual changes? Justify your answer.

Suppose the periodic rate for 6 months is 4%. Is the equivalent periodic rate for three months (pick one): (i) equal to ? (ii) less than 2%? (iii) greater than 2%? Answer the question without doing any calculations. Explain your choice.

Which interest rate would you prefer to pay on a loan: 9% compounded monthly, 9.1% compounded quarterly, 9.2% compounded semiannually, or 9.3% compounded annually?

For a five-year GIC investment, what monthly compounded nominal rate would put you in the same financial position as 8% compounded semiannually?

Norman is planning for his retirement. He initially deposits $25,000 in a retirement plan earning 4.4% compounded quarterly over 25 years. Three years later he begins another investment where he contributes $800 per quarter over 22 years. Based on monthly compounding, determine what the rate of interest will be on the final investment if he wishes to end up with $210,000.

Kristina can invest in a two-year GIC for 5.85% compounded monthly or 6% compounded annually. Which option pays the most interest? Support your answer with calculations.

Calculate the missing interest rate (to the nearest 0.01%)

Which of the following rates would you prefer for a loan: 7.6% compounded quarterly, 7.5% compounded monthly, or 7.7% compounded semiannually?

Calculate the missing interest rate (to the nearest 0.01%)

Over a five-year period, Hardip's $2,000 investment grew to $2675. At the same time, the CPI increased from 106.1 to 109.1. What was Hardip's real compound rate of return?

In the last year, the market value of the Muirs' bonds has declined from $1040.25 to $1020.75 each, and the coupons paid $30 in interest semi-annually. Calculate the following: a) Income yield. b) Capital gain yield. c) Rate of total return.

Three years ago Mikhail invested $7,000 in a three-year compound interest GIC. He has just received its maturity value of $7,867.34. What was the monthly compounded rate of interest on the GIC?

Is it possible for the capital gain yield to exceed 100%? Explain or give an example.

The proceeds from the sale of a $3500 four-year promissory note bearing interest at 5% compounded quarterly were $3612.31. The note was discounted to yield 6.8% compounded semiannually. When was the note sold?

A demand loan for $8,000 with interest at 16% compounded quarterly was repaid after two years and eight months. What was the amount of interest paid?

A $10,000 face value strip bond was purchased for $4188.77. At this price, the bond provided a return of 5.938% compounded semiannually until the maturity date. To the nearest day, how long before the maturity date was the bond purchased? Assume that each half year is exactly 182 days long.

You are offered a loan at a rate of 9% compounded monthly. What would a semiannually compounded nominal rate would a competing bank need to offer in order to provide an equivalent rate?

Philippe contributed $4,300 to an RRSP eight years and six months ago. The money was invested in a Canadian Equity mutual fund. The investment is now worth $5537.82. Over the entire period, what monthly compounded nominal rate of return has the investment delivered?

To be equivalent to 10% compounded monthly, what must be the nominal rate with: a. annual compounding? b. semiannual compounding? c. quarterly compounding?

Calculate the equivalent interest rate (to the nearest 0.01%)