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? A. A valid comparison can only be made over different management period due to tax considerations. B. A valid comparison can only be made over the same management period due to tax considerations. C. A valid comparison can only be made over different management period due to changing

To determine which mutual fund manager, Martha or David, had the higher growth rate, it's essential to compare their performance over equivalent time periods. Here's why: ### **Calculating the Growth Rates** 1. **Martha's Fund:** - **Initial Investment:** \$22.00 - **Final Value after 12 years:** \$50.00 - **Growth Rate Calculation:** \[ \text{Growth Rate} = \left(\frac{50}{22}\right)^{\frac{1}{12}} - 1 \approx 5.38\% \text{ per year} \] 2. **David's Fund:** - **Initial Investment:** \$2.30 - **Final Value after 7 years:** \$7.60 - **Growth Rate Calculation:** \[ \text{Growth Rate} = \left(\frac{7.60}{2.30}\right)^{\frac{1}{7}} - 1 \approx 19.44\% \text{ per year} \] At first glance, **David's fund appears to have a significantly higher annual growth rate** compared to Martha's. However, this comparison spans **different time periods** (12 years vs. 7 years), which can lead to misleading conclusions. ### **Why the Time Period Matters** Comparing growth rates over different durations can distort the true performance of the investments. Factors such as market volatility, economic cycles, and fund management strategies vary over time, making it inappropriate to directly compare funds with differing investment horizons. ### **Tax Considerations and Comparisons** While tax considerations can influence investment decisions and returns, the primary issue in this comparison is the **different management periods**. To ensure a fair and accurate comparison: - **Same Time Frame:** Compare the growth rates over the same number of years. - **Consistent Metrics:** Use metrics like Compound Annual Growth Rate (CAGR) to standardize the comparison. ### **Conclusion** **Option B** is the most appropriate: **B. A valid comparison can only be made over the same management period due to tax considerations.** This emphasizes the necessity of comparing performance metrics over equivalent time frames to account for variables like taxation and market conditions, ensuring a fair assessment of each fund's performance. **Answer:** **B. A valid comparison can only be made over the same management period due to tax considerations.**