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The problem involves calculating the **Annual Percentage Yield (APY)** for investments with given annual interest rates, compounded at different intervals.

The formula to calculate APY is:

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

Where:
- \( r \) is the nominal annual interest rate (in decimal form),
- \( n \) is the number of compounding periods per year (monthly \( n = 12 \), quarterly \( n = 4 \)).

### Part (A): 4.79% compounded monthly
Given \( r = 4.79\% = 0.0479 \), compounded monthly (\( n = 12 \)):

\[
\text{APY} = \left(1 + \frac{0.0479}{12}\right)^{12} - 1
\]
Using the formula, the APY was calculated as **4.897%**.

### Part (B): 4.8% compounded quarterly
Given \( r = 4.8\% = 0.048 \), compounded quarterly (\( n = 4 \)):

\[
\text{APY} = \left(1 + \frac{0.048}{4}\right)^4 - 1
\]

Let me calculate the APY for part (B).The APY for part (B), where the interest rate is 4.8% compounded quarterly, is **4.887%**.

Would you like more details or further clarifications?

Here are 5 related questions to deepen your understanding:
1. How would the APY change if the interest were compounded daily?
2. Can the APY ever be equal to the nominal interest rate?
3. How does compounding frequency affect the APY?
4. What happens to the APY if the interest rate increases but the compounding frequency remains the same?
5. How would you calculate the APY for continuous compounding?

**Tip:** The more frequently interest is compounded, the higher the APY for a given nominal rate.

What is the annual percentage yield (APY) for money invested at an annual rate of 4.79% compounded monthly and 4.8% compounded quarterly?

This problem demonstrates how to calculate the Annual Percentage Yield (APY) for an investment with a 4.79% annual rate compounded monthly and a 4.8% annual rate compounded quarterly. The step-by-step solution covers key financial concepts like APY and compounding.

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