# What is the Compound Annual Growth Rate (CAGR)?

by on February 15, 2012

The Compound Annual Growth Rate (CAGR) is defined as the year-over-year growth rate of an investment over a specific period of time.  The formula for calculating this number is rather complex, but the principle isn’t all that difficult to grasp, although it is good to know that the CAGR isn’t the actual return.  Rather, it is an imaginary number which represents how the investment would have grown if it grew at a steady rate.

For many people this concept of a number which isn’t actually real can be a bit confusing.  While not an actual accounting term it defines an annualized gain which has been smoothed out over the period of investment.  It ignores the typical ups and downs that occur as an investment is held.

The formula, found at Investopedia.com, is as follows:

The best way to understand it is to apply it.

For example, if you invested \$5,000 in 2007, and it had grown to \$8000 in 2010 and was worth \$9,500 in 2012 you would see these results.  (\$9,500 / \$5,000 = 1.9) raised to the power of 1/6 and then subtract 1.  The final percentage is 1.1129 – 1 = .1129 or a return of 11.20%.

Over the 6 year period which you held that investment your Compound Annual Growth Rate (CAGR) would be over 11%, which is quite respectable.  As you can see the highs and lows that occurred during this period are smoothed over, and you just see the “final results”.  This generalized view is useful for assessing the overall value of a particular investment.