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 positive), the geometric mean is the nth root of their product. The average growth factor for money compounded at annual interest rates of 34%, 26%, 24%, and 22% can be found by computing the geometric mean of 1.34, 1.26, 1.24, and 1.22. Find that average growth factor.

Answer 1

The average growth rate factor is 1.26

Explanation:

We are given the following in the question:

Geometric mean is given by:

`(x_1* x_2* ... \tyimes x_n)^{(1)/(n)}`

The average growth factor for money compounded at annual interest rates of 34%, 26%, 24%, and 22% can be found by computing the geometric mean of 1.34, 1.26, 1.24, and 1.22.

We have to find the average growth factor.

Average growth factor = Geometric mean of 1.34, 1.26, 1.24, 1.22

`=(1.34* 1.26* 1.24* 1.22)^{(1)/(4)}\\= 1.26419\\\approx 1.26`

Hence, the average growth rate factor is 1.26