How do you calculate compound annual growth rate (CAGR)?

• A. CAGR = (Ending value / Beginning value)^(1/n) − 1
• B. CAGR = (Ending value - Beginning value) / Beginning value
• C. CAGR = (Ending value / Beginning value) − 1
• D. CAGR = (Ending value - Beginning value)^(1/n) - 1

Answer: (A)

Compound annual growth rate represents the constant yearly growth rate that would take you from the starting value to the ending value if the investment grew with compounding each year. The correct formula first forms the overall growth factor by dividing the ending value by the beginning value. Then it converts that total growth into an annual rate by taking the nth root (the 1/n power), and finally subtracts 1 to express it as a rate rather than a factor. This 1/n root is what accounts for compounding over n years.

For example, growing from 1,000 to 1,728 over 3 years gives a growth factor of 1.728. The cube root of 1.728 is 1.20, and subtracting 1 gives 0.20, or a 20% CAGR.

The other forms aren’t correct for CAGR because they represent simple return, not annualized compound growth (Ending minus Beginning, divided by Beginning), or they mix subtraction with a root in a way that doesn’t reflect how compounding works.