The Investment Company Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 410 in 1985 to 857 in 1995. What is the geometric mean annual percent increase in the number of funds?
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There are 11 years involved. The geometric mean = [(1 + 857/410)^1/10]-1. In words, it is the 10th square root of (1 + 857/410) minus 1. So we have GM = (1 +
2.09)^(1/10) - 1 = 0.0765 = 7.65%
To calculate the geometric mean annual percent increase in the number of funds, we need to use the following formula:
Geometric mean annual percent increase = [(Ending value / Beginning value)^(1 / Number of years)] - 1
Given data: Beginning value (1985) = 410 mutual funds Ending value (1995) = 857 mutual funds Number of years = 1995 - 1985 = 10 years
Let's calculate the geometric mean annual percent increase step by step:
Step 1: Calculate the growth rate from the beginning value to the ending value: Growth rate = (Ending value / Beginning value) - 1 = (857 / 410) - 1 = 1.09024 - 1 = 0.09024
Step 2: Calculate the annualized growth rate: Annualized growth rate = (1 + growth rate)^(1 / Number of years) - 1 = (1 + 0.09024)^(1 / 10) - 1 = (1.09024)^(0.1) - 1 = 1.0199 - 1 = 0.0199
Step 3: Convert the annualized growth rate to a percentage: Geometric mean annual percent increase = Annualized growth rate * 100 = 0.0199 * 100 = 1.99%
Therefore, the geometric mean annual percent increase in the number of funds is approximately 1.99%.
However, none of the provided answer choices matches this result. It seems there may be an error in the available answer choices, or the calculations may have been done incorrectly.