Find the effective annual interest rate r of the given nominal annual interest rate. Round your answer to the nearest 0.01%.
14% compounded monthly
r =

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.

Find the effective annual interest rate r of the given nominal annual interest rate. Round your answer to the nearest 0.01%. 14% compounded monthly.

Learn how to calculate the effective annual interest rate for a nominal interest rate of 14% compounded monthly. This problem covers key financial math concepts such as interest compounding and exponential growth, with step-by-step calculations. Suitable for students in Grades 10-12.

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