QuestionDecember 16, 2025

What is the EAR if the APR is 5% and compounding is quarterly?

What is the EAR if the APR is 5% and compounding is quarterly?
What is the EAR if the APR is 5%  and compounding is quarterly?

Solution
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Answer

5.09\% Explanation 1. Write the EAR formula The effective annual rate (EAR) is calculated using: ** EAR = (1 + \frac{r_{APR}}{m})^m - 1 **, where r_{APR} = 0.05 and m = 4 (quarterly compounding). 2. Substitute values EAR = (1 + \frac{0.05}{4})^4 - 1 = (1 + 0.0125)^4 - 1 = 1.050945 - 1 = 0.050945 3. Convert to percentage EAR = 5.0945\%

Explanation

1. Write the EAR formula<br /> The effective annual rate (EAR) is calculated using: <br />**$ EAR = (1 + \frac{r_{APR}}{m})^m - 1 $**, <br />where $r_{APR} = 0.05$ and $m = 4$ (quarterly compounding). <br /><br />2. Substitute values<br /> $ EAR = (1 + \frac{0.05}{4})^4 - 1 = (1 + 0.0125)^4 - 1 = 1.050945 - 1 = 0.050945 $<br /><br />3. Convert to percentage<br /> $ EAR = 5.0945\% $
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