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 for money for money compounded at annual interest rates of 12.2%,5.5%,and 1.9% can be found by computing the geometric mean of1.122,1.055,and1.019.Find that average growth factor,geometric mean.What single percentage growth rate would be the same as having three successive growth rates of 12.2%,5.5%,and1.9%?Is that result the same as the mean of 12.2%,5.5%,and1.9%

Explanation / Answer

Given,

three annual interest rates 12.2%, 5.5% and 1.9%

to find,

Average Growth factor

Average Growth factor=12.2+5.5+1.9/3

Average Growth factor=19.6/3=6.53%

hence Average Growth factor=6.53%

Geometric mean= (0.122*0.055*0.019)^1/3

=0.050 or 5%

hence Geometric mean =5%

the single percentage which would have same impact is?

assume an amount of 100 is invested

with the 3 percentages, the returns are

100

12.20%

112.2

5.50%

118.371

1.90%

120.62

hence the final return after 3 years is 120.62

now to calculate the compounded rate(r) for similar returns

120.62=100*(1+r)^3

solving, we get r=6.45%

r=6.45%

Average rate=6.53%

hence this result is not similar to the mean of the 3 percentages

100

12.20%

112.2

5.50%

118.371

1.90%

120.62

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.