MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question

The mean of 13.8 percent, 5.3 percent, and 3.1 percent is?

The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. Given n values (all of which are positive), the geometric mean is the nth root of their product. The average growth factor for money compounded at annual interest rates of 13.8%, 5.3%, and 3.1% can be found by computing the geometric mean of 1.138, 1.053, and 1.031. Find that average growth factor, or geometric mean. What single percentage growth rate would be the same as having three successive growth rates of 13.8%, 5.3%, and 3.1%? Is that result the same as the mean of 13.8%, 5.3%, and 3.1%?
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Transcribed Image Text:The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. Given n values (all of which are positive), the geometric mean is the nth root of their product. The average growth factor for money compounded at annual interest rates of 13.8%, 5.3%, and 3.1% can be found by computing the geometric mean of 1.138, 1.053, and 1.031. Find that average growth factor, or geometric mean. What single percentage growth rate would be the same as having three successive growth rates of 13.8%, 5.3%, and 3.1%? Is that result the same as the mean of 13.8%, 5.3%, and 3.1%?
Expert Solution
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Step 1

First, we need to obtain the average growth factor or the geometric mean. It is calculated as follows:

Avearge growth factor=(1.138*1.053*1.031)13                                                                 = 1.073025

 

Hence, average growth factor=1.073025

 

The single percentage growth rate is obtained as follows;

Single percentage growth rate=(Avearge growth factor-1)*100                                                      =(1.073025-1)*100                                                      =0.073025*100                                                      =7.3025%

 

Thus, single percentage growth rate=7.3025%

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