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The question asks to convert a nominal interest rate of 4.75% compounded quarterly into its effective annual rate (EAR), and round the answer to four decimal places. To do this, we can use the following formula for effective interest rate:

\[
\text{Effective Annual Rate (EAR)} = \left(1 + \frac{r}{n}\right)^n - 1
\]

Where:
- \( r \) is the nominal annual interest rate (expressed as a decimal, so 4.75% becomes 0.0475),
- \( n \) is the number of compounding periods per year (since the interest is compounded quarterly, \( n = 4 \)).

Now, let me calculate that for you.The effective annual rate (EAR) for a nominal interest rate of 4.75% compounded quarterly is **4.8353%**.

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

Here are five related questions to further explore this topic:
1. How would the effective rate change if the interest were compounded monthly instead of quarterly?
2. What is the difference between nominal and effective interest rates?
3. How can this formula be applied to different compounding frequencies, like daily or semi-annually?
4. What happens to the effective rate if the nominal rate is increased to 5% but compounded quarterly?
5. How do continuous compounding and quarterly compounding compare in terms of the effective rate?

**Tip:** The more frequent the compounding periods (e.g., monthly or daily), the higher the effective annual rate will be for a given nominal interest rate.

Convert the nominal interest rate 4.75% compounded quarterly to its effective rate. Report your final answer as a percentage rounded to 4 decimal places.

Learn how to convert a nominal interest rate of 4.75% compounded quarterly into its effective annual rate (EAR). This problem explains key concepts in compound interest and demonstrates how to apply the EAR formula to calculate the correct answer, rounded to 4 decimal places.

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