Question

When the interest is compounded monthly, the effective interest rate will be:

• A. 26.8%
• B. 24.8%
• C. 12.6%
• D. 40.8%

Hint:

To calculate the effective interest rate when interest is compounded monthly, use the formula \( \left( 1 + \frac{r_{\text{nom}}}{n} \right)^n - 1 \), where \( n = 12 \).

Answer 1

The Correct Option is B

Step 1: Understanding the formula for effective interest rate.
When interest is compounded monthly, the effective interest rate can be calculated using the formula: \[ r_{\text{eff}} = \left( 1 + \frac{r_{\text{nom}}}{n} \right)^n - 1 \] Where: - \( r_{\text{eff}} \) is the effective interest rate, - \( r_{\text{nom}} \) is the nominal interest rate, - \( n \) is the number of compounding periods (monthly, so \( n = 12 \)).

Step 2: Apply the formula.
If the nominal interest rate is 24%, then: \[ r_{\text{eff}} = \left( 1 + \frac{0.24}{12} \right)^{12} - 1 = \left( 1 + 0.02 \right)^{12} - 1 = (1.02)^{12} - 1 \approx 0.2483 = 24.8% \]

Final Answer: \[ \boxed{24.8%} \]