To calculate the effective annual interest rate $r$, given a nominal annual interest rate $i_{\text{nominal}}$ and the number of compounding periods per year $n$, we can use the following formula:

$r = \left(1 + \frac{i_{\text{nominal}}}{n}\right)^n - 1$

Where:

• $i_{\text{nominal}} = 0.14$ (14% nominal annual interest rate),
• $n = 12$ (since the interest is compounded monthly).

Let's plug in the values:

$r = \left(1 + \frac{0.14}{12}\right)^{12} - 1$

Now, let's calculate it step by step:

$r = \left(1 + \frac{0.14}{12}\right)^{12} - 1 = \left(1 + 0.01167\right)^{12} - 1$

$r = \left(1.01167\right)^{12} - 1$

$r \approx 1.14887 - 1$

$r \approx 0.14887$

To express $r$ as a percentage:

$r \approx 14.89\%$

Therefore, the effective annual interest rate is approximately 14.89%.

Would you like more details or have any questions?

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Here are 5 related questions:

1. What is the difference between nominal and effective interest rates?
2. How does the compounding frequency affect the effective annual rate?
3. Can you calculate the effective rate for quarterly compounding of a 14% interest rate?
4. What would happen to the effective rate if the nominal rate increased to 15% with monthly compounding?
5. How would the formula change for continuous compounding?

Tip: The higher the compounding frequency, the closer the effective rate gets to the nominal rate.