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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
BuyFind

STATISTICS F/BUSINESS+ECONOMICS-TE...

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:

YearStiversTrippi
End of Year ValueGrowth FactorEnd of Year ValueGrowth Factor
2004$11,0001.100$5,6001.120
2005$12,0001.091$6,3001.125
2006$13,0001.083$6,9001.095
2007$14,0001.077$7,6001.101
2008$15,0001.071$8,5001.118
2009$16,0001.067$9,2001.082
2010$17,0001.063$9,9001.076
2011$18,0001.059$10,6001.071

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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Chapter 3 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT
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