An account has a rate of 2.5%. Find the effective annual yield if the interest is compounded semiannually. Round your answer to the nearest hundredth as needed.

To calculate the **Effective Annual Yield (EAY)** with an interest rate of 2.5% compounded semiannually, we use the following formula:

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

Where:
- \( r \) is the nominal interest rate (2.5% or 0.025 in decimal),
- \( n \) is the number of compounding periods per year (semiannually means \( n = 2 \)).

Substitute the values into the formula:

\[
\text{EAY} = \left( 1 + \frac{0.025}{2} \right)^2 - 1
\]

Now, let's calculate that:

\[
\text{EAY} = \left( 1 + 0.0125 \right)^2 - 1 = \left( 1.0125 \right)^2 - 1
\]

\[
\text{EAY} = 1.02515625 - 1 = 0.02515625
\]

So, the effective annual yield is approximately **0.0252** or **2.52%** when rounded to the nearest hundredth.

### Final Answer:
\[
\text{Effective Annual Yield} = 2.52\%
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the effective annual yield if the interest is compounded quarterly?
2. How does the effective annual yield change with different compounding frequencies?
3. What would the EAY be if the nominal interest rate was 5% instead of 2.5%?
4. Can you explain the difference between nominal interest rate and effective interest rate?
5. What is continuous compounding, and how is it calculated?

**Tip:** The more frequently interest is compounded, the higher the effective annual yield will be!

Learn how to find the effective annual yield for an account with a 2.5% interest rate compounded semiannually. This step-by-step solution uses the effective annual yield formula and explains key concepts related to compounding interest. Suitable for high school students in Grades 9-12.

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