An initial investment of $25,000 forty years ago is worth $1,533,913 today. What is the geometric average return on this investment?

a) 9.47%

b) 11.47%

c) 10.84%

d) 11.23%

e) 12.08%

Question

High School

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Answer :

ArturEkert ArturEkert · Answer 1 · 2024-10-11T08:16:53-04:00

The geometric average return on this investment is e) 12.08%. So, option e is the correct answer.

The geometric average return on the investment that had an initial investment of $25,000 forty years ago and is worth $1,533,913.

Step 1: Compute the rate of return per year

R = (End value/Start value)^(1/n) - 1

Where, End value = $1,533,913

Start value = $25,000

n = 40 years

R = ($1,533,913/$25,000)^(1/40) - 1= 0.1037797 or 10.378%

Step 2: Calculate the geometric average return

GAR = (1 + R1) * (1 + R2) * ... * (1 + Rn)^(1/n) - 1

GAR = (1 + 10.378%)^40 - 1= (1.10378)^40 - 1= 12.0762 or 12.08%

Therefore, the geometric average return on this investment is e) 12.08%. So, option e is the correct answer.

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