Beth Chipman has money in a savings account that earns an annual interest rate of 8%, compounded quarterly. What is the APY on Beth's account? Round to the nearest hundredth of a percent

To calculate the Annual Percentage Yield (APY) for Beth's account, we can use the following formula:

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

Where:
- \( r \) is the annual nominal interest rate (expressed as a decimal).
- \( n \) is the number of compounding periods per year.

Given:
- \( r = 8\% = 0.08 \)
- \( n = 4 \) (since the interest is compounded quarterly)

Substituting the values into the formula:

\[
APY = \left(1 + \frac{0.08}{4}\right)^4 - 1
\]

\[
APY = \left(1 + 0.02\right)^4 - 1
\]

\[
APY = (1.02)^4 - 1
\]

\[
APY \approx 1.08243216 - 1
\]

\[
APY \approx 0.08243216 \text{ or } 8.24\%
\]

So, the APY on Beth's account is approximately **8.24%**.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. How does the number of compounding periods affect the APY?
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. Can APY be lower than the nominal interest rate?
5. How would the APY change if the interest rate increased to 10% with the same compounding frequency?

**Tip:** The APY is always higher than the nominal interest rate when interest is compounded more than once per year.

Learn how to calculate the Annual Percentage Yield (APY) on a savings account with an 8% annual interest rate, compounded quarterly. Follow our detailed step-by-step solution using the compound interest formula. Suitable for advanced high school students.

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