Question
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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 ,
and those shares are now worth . David states that investors bought shares in his mutual fund 7
years ago for only , and they are now worth . 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 for the management period.
B. Martha has had the highest growth rate of for the management period.

Ask by Greene Campos. in the United States
Jan 22,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

David has had the highest growth rate of approximately 18.62% for his management period.

Solution

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:

2. Calculating CAGR for David’s Fund

  • Initial Investment: $2.30
  • Final Value: $7.60
  • Investment Period: 7 years

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 for the management period.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

Mind Expander

To find out which mutual fund manager had the highest growth rate, we can use the compound annual growth rate (CAGR) formula:
For Martha:
For David:
So, the best response is:
A. David has had the highest growth rate of for the management period.
Comparing growth rates over different time periods can be misleading because shorter periods may show more volatility, while longer periods can even out fluctuations. It’s essential to normalize and compare growth rates over equivalent time frames for a fair assessment of performance.
When examining mutual funds, it’s wise to consider the context of the market during the management periods. Variables like economic conditions, market cycles, and sector performance can all impact returns significantly, making it paramount to analyze them alongside growth rates for a comprehensive view.
In any investment journey, understanding the compound effect can be a game-changer! Small consistent returns can snowball over time, reminding us that patience could indeed be our greatest ally in wealth-building.

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