A bank features a savings account that has an annual percentage rate of 5.2 % with interest compounded quarterly. Kylie deposits $10,000 into the account.

What is the annual percentage yield (APY) for the savings account?

The Annual Percentage Yield (APY) represents the effective interest rate, taking into account the effect of compounding. To calculate the APY for an account with interest compounded quarterly, we use the following formula:

\[
APY = \left(1 + \frac{r}{n}\right)^n - 1
\]

Where:
- $ r $ is the annual interest rate (as a decimal).
- $ n $ is the number of times the interest is compounded per year.

Given:
- $ r = 5.2\% = 0.052 $
- $ n = 4 $ (since the interest is compounded quarterly)

Now, plug in the values:

\[
APY = \left(1 + \frac{0.052}{4}\right)^4 - 1
\]

\[
APY = \left(1 + 0.013\right)^4 - 1
\]

\[
APY = (1.013)^4 - 1
\]

\[
APY \approx 1.0531 - 1
\]

\[
APY \approx 0.0531 \text{ or } 5.31\%
\]

The Annual Percentage Yield (APY) for the savings account is **5.31%**.

Would you like further details or have any questions?

Here are some related questions:
1. How much money will Kylie have in the account after 1 year?
2. What would be the APY if the interest were compounded monthly instead?
3. How does the APY compare to the nominal interest rate?
4. What would the APY be if the interest rate were 6% compounded quarterly?
5. How does changing the compounding frequency affect the APY?

**Tip:** The APY provides a more accurate reflection of the interest you’ll earn over a year because it accounts for the effects of compounding.

Learn how to calculate the Annual Percentage Yield (APY) for a savings account with a 5.2% Annual Percentage Rate (APR) compounded quarterly. Get a detailed explanation and formula for APY calculation.

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