Question

17.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 14.9​%, 7.9​%, and 3.7​% can be found by computing the geometric mean of 1.149​, 1.079​, and 1.037. Find that average growth​ factor, or geometric mean. What single percentage growth rate single percentage growth rate would be the same as having three successive growth rates of 14.9​%, 7.9​%, and 3.7​%? Is that result the same as the mean of 14.9​%, 7.9​%, and 3.7​%?

The average growth factor is___

(Round to four decimal place as needed)

Answer 1

here as we know that average growth factor =

r =$\sqrt[n]{(1+r1)(1+r2)(1+r3)...(1+rn))}-1$

=$\sqrt[3]{1.149*1.079*1.037)}-1$ =0.087360 ~8.7360%