Concept explainers
To Give:An example of two interest rates −one that is compounded monthly and one that is compounded annually-such that the effective monthly interest rates are approximately equal. Justify your answer.
Answer to Problem 8HP
0.25% compounded monthly and 3% compounded annually.
Explanation of Solution
Given information:Effective monthly interest rates are approximately equal.
Calculation:
If the interest is compounded annually, then n =1 so the compound interest formula simplifies to ,
Choose P =1 and any value of r and then rewrite the formula to have a power of 12t to find its effective monthly interest rate. I have choose to use
The effective monthly interest rate is then 1.0025-1=0.0025=0.25%.
If an interest rate is compounded monthly, then its effective monthly rate is equal to itself. Choosing an interest rate of 0.25% that compounded monthly and an interest rate of 3% that compounded annually will then give two interest rate that have approximately equal effective monthly interest rate.
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