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An investment grows from 10,000 to 22,000 over five years. What is the average rate of return per year?
AIt is about 12 percent
BIt is about 24 percent
CIt is about 44 percent
DIt is about 17 percent
Answer & Solution
Correct answer: D. It is about 17 percent
1. The growth rate over the whole period is the ending value divided by the starting value.
2. That ratio is 22,000 divided by 10,000, which is 2.2.
3. The average multiplier for one year is the fifth root of 2.2, because there are five periods.
4. The fifth root of 2.2 is about 1.17.
5. Subtracting 1 leaves about 0.17, so the average rate of return is about 17 percent a year.
6. Answering 24 percent divides the total gain of 120 percent by five, which ignores compounding altogether.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.5 Geometric Mean_
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