Interest rate. Two mutual fund managers, Martha and David, have been discussing whose fund is the top performer. Martha states that investors bought shares in her mutual fund 12 years ago for \( \$ 22.00 \), and those shares are now worth \( \$ 50.00 \). David states that investors bought shares in his mutual fund 7 years ago for only \( \$ 2.30 \), and they are now worth \( \$ 7.60 \). Which mutual fund manager had the higher growth rate for the management period? Should this comparison be made over different management periods? Why or why not? Which mutual fund manager has had the highest growth rate for the management period? (Select the best response.) A. David has had the highest growth rate of \( 18.62 \% \) for the management period. B. Martha has had the highest growth rate of \( 7.08 \% \) for the management period.

To determine which mutual fund manager, Martha or David, had the higher growth rate for their respective management periods, we'll calculate the Compound Annual Growth Rate (CAGR) for each fund. The CAGR provides a consistent measure of growth over multiple periods. ### **1. Calculating CAGR for Martha's Fund** - **Initial Investment:** \$22.00 - **Final Value:** \$50.00 - **Investment Period:** 12 years **CAGR Formula:** \[ \text{CAGR} = \left( \frac{\text{Final Value}}{\text{Initial Investment}} \right)^{\frac{1}{n}} - 1 \] \[ \text{CAGR} = \left( \frac{50}{22} \right)^{\frac{1}{12}} - 1 \approx 7.08\% \] ### **2. Calculating CAGR for David's Fund** - **Initial Investment:** \$2.30 - **Final Value:** \$7.60 - **Investment Period:** 7 years \[ \text{CAGR} = \left( \frac{7.60}{2.30} \right)^{\frac{1}{7}} - 1 \approx 18.62\% \] ### **3. Comparison and Considerations** - **Higher Growth Rate:** David's mutual fund achieved a higher CAGR of approximately **18.62%** compared to Martha's **7.08%**. - **Different Management Periods:** While CAGR accounts for different time periods by providing an annualized growth rate, it's essential to consider other factors such as risk, volatility, and investment strategies when comparing funds over different durations. However, for the purpose of evaluating pure growth rates, comparing CAGR across different periods is generally acceptable. ### **Conclusion** **Option A** is the correct answer. **Answer:** **A. David has had the highest growth rate of \( 18.62 \% \) for the management period.**