CMA Foundation · Fundamentals of Business Mathematics and Statistics · Measures of Central Tendency and Dispersion
An investment of a Chennai trader grew by 100% in the first year, by 300% in the second year and by 700% in the third year, each rate being on the previous year's value. What is the average compound growth rate per year?
The average compound growth rate is 300% per year. The growth factors are 2, 4 and 8, whose geometric mean is the cube root of 64, which is 4. Subtracting 1 gives 3, or 300%. The arithmetic mean of the rates ignores compounding.
- A300%Correct
- B400%
- C366.67%
- D250%
Explanation
The yearly growth factors are 2, 4 and 8. Their GM is (2 × 4 × 8)^(1/3) = 64^(1/3) = 4, so the average growth rate is 4 − 1 = 3, which is 300%. The 400% option forgets to subtract 1 from the factor. The 366.67% option is the arithmetic mean of the rates, which ignores compounding.
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