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To calculate the effective annual yield (EAY) given a nominal annual interest rate compounded quarterly, we can use the following formula:

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

where:
- \( r \) is the nominal annual interest rate (3.6% in this case, or 0.036 as a decimal),
- \( n \) is the number of compounding periods per year (quarterly compounding means \( n = 4 \)).

### Step-by-Step Solution

1. Substitute the values into the formula:
   \[
   \text{EAY} = \left(1 + \frac{0.036}{4}\right)^4 - 1
   \]

2. Calculate the quarterly interest rate:
   \[
   \frac{0.036}{4} = 0.009
   \]

3. Add 1 to this rate:
   \[
   1 + 0.009 = 1.009
   \]

4. Raise this to the power of 4 (for the four quarters):
   \[
   1.009^4 \approx 1.0364
   \]

5. Subtract 1 to find the effective annual yield:
   \[
   \text{EAY} = 1.0364 - 1 = 0.0364
   \]

6. Convert this to a percentage:
   \[
   \text{EAY} \approx 3.64\%
   \]

### Final Answer

The effective annual yield is approximately **3.64%**.

Would you like further details on this calculation, or do you have any questions?

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### Related Questions

1. How does the effective annual yield change if compounding is monthly instead of quarterly?
2. What would the effective annual yield be if the nominal rate were different, say 5%?
3. How does the formula for effective annual yield change if compounding is continuous?
4. Why does compounding increase the effective annual yield compared to the nominal rate?
5. How would you calculate the nominal rate if you know the effective annual yield?

### Tip

Always convert the nominal rate to a decimal form before using it in financial formulas to avoid calculation errors.

Suppose a savings and loan pays a nominal rate of 3.6% on savings deposits. Find the effective annual yield if interest is compounded quarterly.

Learn how to calculate the effective annual yield when given a nominal rate of 3.6% compounded quarterly. This problem involves understanding concepts of compound interest and the effective annual yield formula, suitable for college-level or advanced high school students.

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