Suppose that your bank account pays an 8% APR. The interest is compounded quarterly. Which of the following statements is correct?a.The periodic rate of interest is 2% and the effective annual rate is greater than 8%.b.The periodic rate of interest is 4% and the effective annual rate is less than 8%.c.The periodic rate of interest is 8% and the effective annual rate is greater than 8%.d.None of them.e.The periodic rate of interest is 2% and the effective annual rate is 4%.
Question
Suppose that your bank account pays an 8% APR. The interest is compounded quarterly. Which of the following statements is correct?a.The periodic rate of interest is 2% and the effective annual rate is greater than 8%.b.The periodic rate of interest is 4% and the effective annual rate is less than 8%.c.The periodic rate of interest is 8% and the effective annual rate is greater than 8%.d.None of them.e.The periodic rate of interest is 2% and the effective annual rate is 4%.
Solution
The correct answer is a. The periodic rate of interest is 2% and the effective annual rate is greater than 8%.
Here's the step-by-step explanation:
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The Annual Percentage Rate (APR) is 8%, and the interest is compounded quarterly. This means the interest is calculated and added to the account four times a year.
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To find the periodic rate, we divide the APR by the number of compounding periods in a year. In this case, 8% divided by 4 equals 2%. So, the periodic rate of interest is 2%.
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The Effective Annual Rate (EAR) takes into account the effects of compounding, so it is usually higher than the APR when there are multiple compounding periods in a year. In this case, the EAR would be greater than 8%.
Similar Questions
Which of the following statements is NOT correct?A term deposit with an interest rate with a quarterly compounding would A.would be accessible without penalty after 2 years. B.would generate larger amount of interest each quarter.C.pay the interests quarterly in the transaction account. D.would calculate the interests using the interest rate .
Which of the following statements is FALSE?a.The annual percentage rate indicates the amount of simple interest earned in one year.b.Because interest rates may be quoted for different time intervals, it is often necessary to adjust the interest rate to a time period that matches that of our cash flows.c.The effective annual rate indicates the amount of interest that will be earned at the end of one year.d.None of them.e.The annual percentage rate indicates the amount of interest including the effect of compounding.
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