# How to Calculate Average Annual Growth

by Bryan Keythman

An average annual growth rate measures the average percentage by which a certain value grew annually over a certain period of time. You can use the average annual growth rate formula to calculate the growth rate of different numbers, such as a company’s earnings per share or a stock’s price. The average annual growth rate formula considers compounding, which is the effect of a number repeatedly growing upon itself each year. A higher average annual growth rate means a particular number is growing faster each year.

1. Determine the number of years for which you want to calculate the average annual growth rate of a particular value, and determine that value at the beginning and end of that period. For example, assume you want to calculate the average annual growth rate of a stock’s price over five years. Assume the stock’s price was \$20 and \$35 at the beginning and end of this period, respectively.

2. Substitute the values into the average annual growth rate formula: [((V/B)^(1/N)) - 1] x 100. In the formula, N represents the number of years of the stock’s growth, V represents the ending price and B represents the beginning price. In this example, substitute the values to get [((\$35/\$20)^(1/5)) - 1] x 100.

3. Calculate the numbers inside the parentheses. In this example, divide \$35 by \$20 to get 1.75, and divide 1 by 5 to get 0.2. This leaves [(1.75^0.2) - 1] x 100.

4. Raise the number in parentheses to the power of the exponent. In this example, raise 1.75 by 0.2 to get 1.12, which leaves (1.12 - 1) x 100.

5. Calculate the numbers in parentheses. Multiply your result by 100 to calculate the average annual growth rate. Continuing with the example, subtract 1 from 1.12 to get 0.12. Multiply 0.12 by 100 to get a 12 percent average annual growth rate.

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