[41] Your Credit Card charges you a nominal interest rate of 18.6% per year. If they compound interest monthly, what effective rate of interest do they charge?
[42] You are offered two options for your mortgage.
- A Canadian bank offers you a rate of j2 = 8.40%
- A US bank offers you j12 = 8.30%.
Which rate is better? Convert both rates to effective rates to compare them.
[43] What is the effective rate of interest earned on an investment of $10,652,952,497,853.65 that earns 15% compounded quarterly?
[44] What nominal rate, compounded semi-annually, is equivalent to 8% compounded quarterly?
[45] What nominal rate, compounded quarterly, is equivalent to 8% compounded monthly?
[46] What is the effective interest rate of 8% compounded monthly?
[47] Canada Premium Bonds are a new kind of Canada Savings Bond. They were available for sale until November 1, 2022. They proposed to pay the following interest rates, compounded annually.
| Year 1 | 2.50% |
| Year2 | 3.00% |
| Year3 | 4.00% |
| Year4 | 4.85% |
| Year 5 | 6.00% |
What effective interest rate would a Canada Premium Bond purchaser average over the five years? Hint: use the formula to find the FV. Do not round the FV.
[48] What nominal rate, compounded monthly, is equivalent to 10% compounded semi-annually?
[49] What is the effective interest rate of 20% compounded quarterly?
[50] You have $5,000 saved. You are considering two investments:
- Canada Savings Bonds (CSB) which pay 5.25% in the first year, 6% in the second year, and 6.75% in the third year, compounded semi-annually.
- A 3-year “Bond-Beater” Guaranteed Investment Certificate (GIC) offered by a bank that pays 5.75%, 6.5%, and 7.25% compounded annually in the three successive years.
(a) How much would you have at the end of 3 years if· you bought a $5,000 CSB and how much if you bought a $5,000 GIC?
(b) Find the average effective interest rate earned for the entire 3-year period for both the CSB and the GIC.
[51] You invest $6,000 in a mutual fund. Your investment of $6,000 earns the following returns.
| Year | Return |
| Year 1 | j2 = 10% |
| Year 2 | j12 = 6% |
| Year 3 | j4 = 8% |
| Year 4 | j1 = 7% |
(a) How much would your $6,000 investment be worth at the end of the fourth year?
(b) How much did you earn (in dollars) during those four years?
(c) In the fifth year the mutual fund loses money and the value of your investment decreases by $400. Calculate the average annual rate of return, compounded semi-annually, for the five years you have held your investment.
(d) A friend has invested in a different mutual fund and says she doubled her money in seven years. What effective interest rate did she average over the seven years?
[52] A Canada Savings Bond pays j2 = 5% in the first year, j2 = 8% in the second year, and j2 = 10% in the third year. What nominal interest rate, compounded quarterly, would provide the same return? Do not round the FV.
[53] An investment earned 12%, compounded quarterly, for two years and 10% compounded annually for the next three years. Calculate the average annual rate of return, compounded monthly, for the five years. Do not round the FV.
[54] An investment earned 20%, 15%, -10%, 25%, and -5% in 5 successive years. What average annual rate of return, compounded annually, was earned for the entire 5-year period? Hint: use the formula to find the FV. Do not round the FV.
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