The geometric mean is often used in business and economics for finding average r

Question

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 14.2%, 5.2%, and 2.2% can be found by computing the geometric mean of 1.142, 1.052, and 1.022. Find that average growth factor, or geometric mean. What single percentage growth rate would be the same as having three successive growth rates of 14.2%, 5.2%, and 2.2%? Is that result the same as the mean of 14.2%. 5.2%, and 2.2%? The average growth factor is 1.0708. (Round to four decimal places as needed.) The single percentage growth rate that would be the same as having three successive growth rates of 14.2%, 5.2%, and 2.2% is %. (Round to two decimal places as needed.)

Explanation / Answer

the average geometricv mean = (1.142*1.052*1.022)^1/3 = 1.0708062

The single percentage growth rate that would be the same as having three successive growth rates of 14.2%,5.2%,and 2.2% is 8.062%

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