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
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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