An agent is selling an investment that earns 4.755% compounded semiannually. What is the APY (in percent) of the investment? (Round your answer to the nearest hundredth of a percent.)




To calculate the Annual Percentage Yield (APY) for the investment, we use the same formula:

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

Where:
- \( r = 4.755\% = 0.04755 \) (annual nominal interest rate)
- \( n = 2 \) (compounded semiannually)

Substituting the values:

\[
APY = \left(1 + \frac{0.04755}{2}\right)^2 - 1
\]

\[
APY = \left(1 + 0.023775\right)^2 - 1
\]

\[
APY = (1.023775)^2 - 1
\]

\[
APY \approx 1.0483338 - 1
\]

\[
APY \approx 0.0483338 \text{ or } 4.83\%
\]

So, the APY for the investment is approximately **4.83%**.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:
1. What happens to the APY if the investment is compounded quarterly instead of semiannually?
2. How would the APY change if the nominal interest rate was 5% instead?
3. What is the difference between nominal interest rate and APY?
4. How does the frequency of compounding impact the overall yield of an investment?
5. Can the APY be used to compare different investments effectively?

**Tip:** APY is particularly useful when comparing investments with different compounding frequencies because it reflects the real rate of return.

Learn how to calculate the Annual Percentage Yield (APY) for an investment earning 4.755% compounded semiannually. Understand the formula and steps involved to find the APY, a key measure of investment return. Suitable for advanced high school students and anyone interested in financial calculations.

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