# Compound Annual Growth Rate

The compound annual growth rate is the year on year percentage growth rate of an investment over a given period of time. It is found by calculating the nth root of the total percentage return over the period where n is the number of years. Suppose, for example, that an investment of $100 grew 50 percent in the first year to $150, 25 percent in the second year to $187.5 then lost 10 percent in the third year to $168.75. The total percentage return over the three years is 68.75 percent. The cube root of 68.75 is 4.0965. The compound annual growth rate is 4.0965 percent.