A bank advertises that it pays interest on saving accounts at the rate of 4.25% compounded daily. Find the effective rate if the bank uses 360 days in determining the daily rate. Round the answer to three decimal places.

To find the effective annual interest rate when the interest is compounded daily, we use the formula for effective annual rate (EAR):

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

Where:
- \(r\) is the nominal annual interest rate (4.25% in this case, or 0.0425 as a decimal),
- \(n\) is the number of compounding periods per year (360, since the bank uses 360 days in its calculation).

### Step-by-Step Calculation:

1. Convert the nominal interest rate to decimal: \( r = 0.0425 \).
2. The number of compounding periods per year is \( n = 360 \).
3. Apply the formula to calculate the effective annual rate (EAR):

\[
\text{Effective Rate} = \left(1 + \frac{0.0425}{360}\right)^{360} - 1
\]

Now let's calculate it:

\[
\text{Effective Rate} = \left(1 + \frac{0.0425}{360}\right)^{360} - 1
\]

I'll compute the final result.

It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can follow the steps I provided earlier to compute the effective rate manually using the formula.

Let me know if you'd like to go over any part of the process or if you have other questions!

Here are some related questions you might find useful:
1. How does compounding frequency affect interest rates?
2. What is the difference between nominal and effective interest rates?
3. How would the result change if interest were compounded monthly instead of daily?
4. What other financial scenarios use compounding daily interest rates?
5. How can you apply the concept of continuous compounding to calculate interest?

**Tip:** Always ensure that you convert percentage rates to decimals when performing interest rate calculations!

Learn how to calculate the effective interest rate for a savings account with a 4.25% nominal rate, compounded daily using 360 days. Follow the step-by-step process to apply the compound interest formula and determine the effective annual rate.

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