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

Answer:

The average growth rate factor is 1.26    

Step-by-step explanation:

We are given the following in the question:

Geometric mean is given by:

$(x_1\times x_2\times ... \tyimes x_n)^{\frac{1}{n}}$

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

$=(1.34\times 1.26\times 1.24\times 1.22)^{\frac{1}{4}}\\= 1.26419\\\approx 1.26$

Hence, the average growth rate factor is 1.26