Compound annual growth rate (CAGR) is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element of the business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry or sector. CAGR is equivalent to the more generic exponential growth rate when the exponential growth interval is one year. Formula CAGR is defined as: where is the initial value, is the end value, and is the number of years. Actual or normalized values may be used for calculation as long as they retain the same mathematical proportion. Example In this example, we will compute the CAGR over a three-year period. Assume that the year-end revenues of a business over a three-year period, , have been: {| class="wikitable" border="1" |- ! Year-End ! 2004-12-31 ! 2007-12-31 |- | Year-End Revenue | 9,000 | 13,000 |} Therefore, to calculate the CAGR of the revenues over the three-year period spanning the "end" of 2004 to the "end" of 2007 is: Note that this is a smoothed growth rate per year. This rate of growth would take you to the ending value, from the starting value, in the number of years given, if growth had been at the same rate every year. Verification: Multiply the initial value (2004 year-end revenue) by (1 + CAGR) three times (because we calculated for 3 years). The product will equal the year-end revenue for 2007. This shows the compound growth rate: For n = 3: For comparison: the Arithmetic Mean Return (AMR) would be the sum of annual revenue changes (compared with the previous year) divided by number of years, or: In contrast to CAGR, you cannot obtain by multiplying the initial value, , three times by (1 + AMR) (unless all annual growth rates are the same). the arithmetic return (AR) or simple return would be the ending value minus beginning value divided by the beginning value: Applications These are some of the common CAGR applications: Calculating and communicating the average returns of investment funds Demonstrating and comparing the performance of investment