A bank features a savings account that has an annual percentage rate of
3.5% with interest compounded semi-annually. Serena deposits $4,500 into the account.

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

To calculate the **Annual Percentage Yield (APY)**, we use the formula:

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

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

For this problem:
- $ r = 3.5\% = 0.035 $,
- The interest is compounded **semi-annually**, so $ n = 2 $.

Now, substituting the values into the APY formula:

\[
APY = \left( 1 + \frac{0.035}{2} \right)^2 - 1
\]

Let me calculate this for you.The Annual Percentage Yield (APY) for the savings account is approximately **3.53%**.

Would you like more details on how this was calculated or have any other questions?

Here are five related questions:
1. How does the compounding frequency affect the APY?
2. What would the APY be if the interest was compounded quarterly?
3. How does APY differ from the nominal interest rate?
4. What is the future value of Serena's deposit after one year with this APY?
5. How does inflation impact the real return of this savings account?

**Tip:** Increasing the compounding frequency (e.g., quarterly or monthly) will slightly increase the APY, even if the nominal interest rate stays the same.

A bank features a savings account that has an annual percentage rate of 3.5% with interest compounded semi-annually. Serena deposits $4,500 into the account. What is the annual percentage yield (APY) for the savings account?

Learn how to calculate the Annual Percentage Yield (APY) for a savings account with a 3.5% annual percentage rate compounded semi-annually. Understand the key mathematical concepts of interest rates and compounding. Suitable for high school students in Grades 10-12.

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