# Suppose that at the beginning of 2004 you invested $10,000 in the Stivers mutual fund and$5000 in the Trippi mutual fund. The value of each investment at the end of each subsequent year is provided in the table below. Which mutual fund performed better? Year Stivers Trippi 2004 11,000 5,600 2005 12,000 6,300 2006 13,000 6,900 2007 14,000 7,600 2008 15,000 8,500 2009 16,000 9,200 2010 17,000 9,900 2011 18,000 10,600

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section
Chapter 3.1, Problem 20E
Textbook Problem

## Suppose that at the beginning of 2004 you invested $10,000 in the Stivers mutual fund and$5000 in the Trippi mutual fund. The value of each investment at the end of each subsequent year is provided in the table below. Which mutual fund performed better? Year Stivers Trippi 2004 11,000 5,600 2005 12,000 6,300 2006 13,000 6,900 2007 14,000 7,600 2008 15,000 8,500 2009 16,000 9,200 2010 17,000 9,900 2011 18,000 10,600

Expert Solution
To determine

Identify the mutual fund that performs better.

### Explanation of Solution

Calculation:

In the Stivers mutual fund, $10,000 is invested at the beginning of 2004 and in Trippi mutual fund,$5,000 is invested at the beginning of 2004. The given table represents the value of each investment at the end of each subsequent year.

The geometric mean is often used for finding the mean growth rate.

The mean growth factor over these eight periods is:

x¯g=(x1)(x2)(x3)(x4)(x5)(x6)(x7)(x8)8

The growing factor of each year can be obtained by dividing the end of year by the previous year value.

The growth factor of the year 2004 can be obtained as follows:

Growth rate of x1=11,00010,000=1.100

Similarly the growth actor for remaining years can be obtained as shown in the table given below:

 Year Stivers Trippi 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

For the Stivers mutual fund:

The balance at the end of the year 2011 is the initial investment times the product of all 8 growth factors.

18,000=10,000[(x1)(x2)...(x8)]

That is,

[(x1)(x2)...(x8)]=18,00010,000=1

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