91Ó°ÊÓ

: To convert the nominal annual interest rate from a percentage to a decimal, divide by 100. This gives us: Nominal Rate (decimal form) = \(\frac{9}{100} = 0.09\)

: We'll now use the formula for effective annual interest rate with various values of n: 1. Annually (n = 1): Effective Annual Rate = \((1 + \frac{0.09}{1})^1 - 1\) 2. Semiannually (n = 2): Effective Annual Rate = \((1 + \frac{0.09}{2})^2 - 1\) 3. Quarterly (n = 4): Effective Annual Rate = \((1 + \frac{0.09}{4})^4 - 1\) 4. Monthly (n = 12): Effective Annual Rate = \((1 + \frac{0.09}{12})^{12} - 1\)

: Solve each of the expressions in step 2 to find the effective annual rates for each compounding frequency: 1. Annually: Effective Annual Rate = \((1 + 0.09)^1 - 1 = 1.09 - 1 = 0.09 = 9\% \) 2. Semiannually: Effective Annual Rate = \((1 + 0.045)^2 - 1 = 1.045^2 - 1 ≈ 0.092025 = 9.2025\%\) 3. Quarterly: Effective Annual Rate = \((1 + 0.0225)^4 - 1 ≈ 1.0225^4 - 1 ≈ 0.0938076 = 9.38076\%\) 4. Monthly: Effective Annual Rate = \((1 + 0.0075)^{12} - 1 ≈ 1.0075^{12} - 1 ≈ 0.0941848 = 9.41848\%\) Once the calculations are complete, we find that the effective rate of interest for each compounding frequency is as follows: - Annually: 9% - Semiannually: 9.2025% - Quarterly: 9.38076% - Monthly: 9.41848% These results demonstrate that the effective rate of interest increases as the compounding frequency increases.