Find the effective annual interest rate r (as a percent) of the given nominal annual interest rate. Round your answer to the nearest 0.01%.
13% compounded daily (assume 365 days per year)
r =

The effective annual interest rate (EAR) can be calculated from the nominal interest rate using the following formula:

\[
r_{\text{eff}} = \left(1 + \frac{r_{\text{nominal}}}{n}\right)^n - 1
\]

Where:
- \(r_{\text{eff}}\) is the effective annual interest rate
- \(r_{\text{nominal}} = 0.13\) (since 13% is the nominal rate)
- \(n = 365\) (since interest is compounded daily)

Now, let's plug in the values and compute the effective annual interest rate.

\[
r_{\text{eff}} = \left(1 + \frac{0.13}{365}\right)^{365} - 1
\]

I'll calculate this next.The effective annual interest rate for a nominal interest rate of 13% compounded daily is **13.88%**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does the compounding frequency affect the effective interest rate?
2. What is the effective interest rate if compounded quarterly instead of daily?
3. How would you calculate the nominal interest rate if given the effective rate?
4. What is the difference between nominal and effective interest rates?
5. How can this formula be applied in real-world financial decisions?

**Tip:** The more frequently interest is compounded, the higher the effective annual interest rate becomes compared to the nominal rate.

Find the effective annual interest rate r (as a percent) of the given nominal annual interest rate. Round your answer to the nearest 0.01%. 13% compounded daily (assume 365 days per year) r =

Find out how to calculate the effective annual interest rate for a nominal rate of 13% compounded daily. This solution involves the use of compounding interest formulas and exponential growth, suitable for high school and finance students. Learn how the compounding frequency impacts the final rate.

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