Question

When data consist of percentages, ratios, compounded growth rates, or other rates of change, the geometric mean is a useful measure of central tendency. For n data values, the geometric mean, assuming all data values are positive, is as follows. To find the average growth factor over 5 years of an investment in a mutual fund with growth rates of 10.5% the first year, 12.1% the second year, 13.5% the third year, 3.5% the fourth year, and 7.3% the fifth year, take the geometric mean of 1.105, 1.121, 1.135, 1.035, and 1.073. Find the average growth factor of this investment. (Round your answer to four decimal places.)

Answer 1

Answer: 1.09

Step-by-step explanation:

Given the following :

Year__growth rate ___growth factor

1 ______10.5% _____ 100%+10.5%

2______12.1%______ 100%+12. 1%

3______13.5%______ 100%+13.5%

4______3.5%_______ 100%+3.5%

5______7.3%_______ 100%+7.3%

The geometric mean:

(Product of the n data values)^(1/n)

Where n = number of data values

For the data above, the average growth factor :

n = 5

(1.105×1.121×1.135×1.035×1.073)^(1/5)

= (1.561362785497125)^(1/5)

= 1.0932028

= 1.09

Hence, average growth factor = 1.09