To convert the effective annual rate (EAR) to the annual percentage rate (APR) when compounding is quarterly, you can use the following formula:
\[ \text{EAR} = \left(1 + \frac{\text{APR}}{n}\right)^n - 1 \]
where:
- \( n \) is the number of compounding periods per year (in this case, \( n = 4 \) for quarterly compounding).
- \( \text{APR} \) is what we want to find.
We are given that the EAR is 5.60%, which we will convert to decimal form: \( \text{EAR} = 0.056 \).
Now we can rearrange the formula to solve for APR:
\[ 1 + \frac{\text{APR}}{4} = (1 + \text{EAR})^{1/4} \]
First, rearranging gives us:
\[ \frac{\text{APR}}{4} = (1 + 0.056)^{1/4} - 1 \]
Calculating \( (1 + 0.056)^{1/4} \):
\[ (1.056)^{1/4} \approx 1.013669 \]
Now substitute back into the equation:
\[ \frac{\text{APR}}{4} = 1.013669 - 1 \approx 0.013669 \]
Finally, multiplying by 4 to get APR:
\[ \text{APR} \approx 0.013669 \cdot 4 \approx 0.054676 \]
Now, convert this to a percentage:
\[ \text{APR} \approx 5.47% \]
Thus, the annual percentage rate (APR) is approximately 5.47%.