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The question asks to find the **Effective Interest Rate (EIR)** for a loan compounded monthly at an annual nominal interest rate of 7.1%.

### Formula for Effective Interest Rate:
The formula to calculate the Effective Interest Rate (EIR) when compounded periodically is:

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

Where:
- \( r \) = Nominal interest rate (as a decimal) = 7.1% = 0.071
- \( n \) = Number of compounding periods per year = 12 (monthly)

### Calculation:

1. Convert the nominal interest rate to decimal: \( r = 7.1\% = 0.071 \).
2. Substitute \( r = 0.071 \) and \( n = 12 \) into the formula:

\[
EIR = \left(1 + \frac{0.071}{12}\right)^{12} - 1
\]

3. Compute:

\[
EIR = \left(1 + 0.0059167\right)^{12} - 1 = (1.0059167)^{12} - 1 \approx 1.07357 - 1 = 0.07357
\]

4. Convert the result back to a percentage:

\[
EIR \approx 7.357\%
\]

Thus, the **Effective Interest Rate** is approximately **7.357%** (rounded to three decimal places).

Would you like further details or clarification on any part of this? 

Here are 5 related questions you might find useful:
1. What is the difference between nominal and effective interest rates?
2. How does the compounding frequency affect the effective interest rate?
3. How would the effective interest rate change if the compounding was done quarterly instead of monthly?
4. What is the general use of the effective interest rate in financial calculations?
5. How would the effective interest rate change if the loan was compounded continuously?

**Tip**: Always remember to convert percentages to decimal form when plugging them into financial formulas.

Use your financial calculator to find the effective interest rate for a loan for four years compounded monthly at an annual rate of 7.1%.

Learn how to calculate the effective interest rate for a loan with monthly compounding at an annual rate of 7.1%. This problem involves key financial concepts, including the compounding of interest and exponential growth, and is suitable for high school students in Grades 10-12.

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