Concept explainers
Identify the mutual fund that performs better.
Answer to Problem 20E
The Mutual Fund T performs better.
Explanation of Solution
Calculation:
The investigator has invested $10,000 at the beginning of 2004 in mutual fund S and $5,000 in Mutual Fund T. The value of each investment at the end of each subsequent year is given.
The geometric mean is used to find the mean growth rate.
The general formula to obtain growth factor for a year is given below:
Denote the values of growth factors of Mutual Fund S for year 2004 to year 2011 as
The growth factor of Mutual Fund S for year 2004 is obtained as given below:
Denote the values of growth factors of Mutual Fund T for year 2004 to year 2011 as
The growth factor of Mutual Fund T for year 2004 is obtained as given below:
Similarly, growth factors of Mutual Fund S and Mutual Fund T for the remaining years are obtained in the table given below:
Year | Mutual Fund S | Mutual Fund T | ||
End of Year Value | Growth Factor | End of Year Value | Growth Factor | |
2004 | $11,000 | 1.100 | $5,600 | 1.120 |
2005 | $12,000 | 1.091 | $6,300 | 1.125 |
2006 | $13,000 | 1.083 | $6,900 | 1.095 |
2007 | $14,000 | 1.077 | $7,600 | 1.101 |
2008 | $15,000 | 1.071 | $8,500 | 1.118 |
2009 | $16,000 | 1.067 | $9,200 | 1.082 |
2010 | $17,000 | 1.063 | $9,900 | 1.076 |
2011 | $18,000 | 1.059 | $10,600 | 1.071 |
The general formula to obtain geometric mean is given below:
Mutual Fund S:
The mean growth factor of Mutual Fund S over the year 2004 to year 2011 is obtained below:
Thus, the mean growth factor of Mutual Fund S over the years 2004 to 2011 is 1.07624.
The mean annual return of Mutual Fund S over the years 2004 to 2011 is obtained below:
Thus, the mean annual return of Mutual Fund S over the years 2004 to 2011 is 7.624%.
For the Mutual Fund T:
The mean growth factor of Mutual Fund T over the years 2004 to 2011 is obtained below:
Thus, the mean growth factor of Mutual Fund T over the years 2004 to 2011 is 1.09848.
The mean annual return of Mutual Fund T over the years 2004 to 2011 is obtained below:
Thus, the mean annual return of Mutual Fund T over the years 2004 to 2011 is 9.848%.
The mean annual return or mean annual growth rate of Mutual Fund T is 9.848% and mean annual return or mean annual growth rate of Mutual Fund S is 7.624%.
Since
Hence, it can be concluded that Mutual Fund T performs better than Mutual Fund S.
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Chapter 3 Solutions
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