If a value grows from 100 to 150 over 3 years, what is the CAGR?

If a value grows from 100 to 150 over 3 years, what is the CAGR?

• A. 10%
• B. 12.5%
• C. 14.47% per year
• D. 16%

Answer: (C)

CAGR measures the constant annual growth rate that would turn the initial value into the final value over the given period, assuming growth compounds annually. The formula is CAGR = (final/initial)^(1/n) - 1. Here final/initial is 1.5 and n is 3, so CAGR = 1.5^(1/3) - 1. The cube root of 1.5 is about 1.1447, minus 1 gives approximately 0.1447, or 14.47% per year. This rate, when applied each year for three years, grows 100 to 150 exactly. Other rates yield different end values over three years (for example, 10% would reach roughly 133.1, 12.5% about 142.5, and 16% about 156.1), so the 14.47% figure is the one that fits.

CAGR measures the constant annual growth rate that would turn the initial value into the final value over the given period, assuming growth compounds annually. The formula is CAGR = (final/initial)^(1/n) - 1. Here final/initial is 1.5 and n is 3, so CAGR = 1.5^(1/3) - 1. The cube root of 1.5 is about 1.1447, minus 1 gives approximately 0.1447, or 14.47% per year. This rate, when applied each year for three years, grows 100 to 150 exactly. Other rates yield different end values over three years (for example, 10% would reach roughly 133.1, 12.5% about 142.5, and 16% about 156.1), so the 14.47% figure is the one that fits.