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 8.5%, 4.1%, and 2.7% can be found by computing the geometric mean of 1.085, 1.041, and 1.027. Find that average growth factor, or geometric mean. What single percentage growth rateLOADING... would be the same as having three successive growth rates of 8.5%, 4.1%, and 2.7%? Is that result the same as the mean of 8.5%, 4.1%, and 2.7%?

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Dryomys Dryomys · Answer 1 · 2019-10-04T06:58:11+02:00

Answer:

(a) Average growth factor = [tex](Geometric\ mean)^{\frac{1}{3}}[/tex]

= [tex](1.085\times1.041\times1.027)^{\frac{1}{3}}[/tex]

= [tex](1.1599)^{\frac{1}{3}}[/tex]

= 1.05068

(b) Single percentage growth rate = (Average growth factor - 1) × 100

= (1.05068 - 1) × 100

= 5.068 %

(c) The mean of 8.5%, 4.1% and 2.7% = [tex]\frac{8.5 + 4.1 + 2.7}{3}[/tex]

= 5.1%

Therefore, the single percentage growth rate is not the same as the mean of 8.5%, 4.1%, and 2.7%.