 # Compound annual growth rate (CAGR)

Compound annual growth rate (CAGR) is an investment’s mean annual growth rate (AGR) over a specific period. It is used to accurately determine the return on investment for anything that can lose or gain value over time from investment portfolios to art.

### How to calculate CAGR?

CAGR smooths out the fluctuations in annual growth rates. It doesn’t take into account that some years are worse than others. Investors can use the value of CAGR to calculate the amount they should have at the end of a longer investment period. The formula for CAGR is the following:

CAGR = (Ending value / beginning value)^[1/(number of years)] – 1

For example, you invested 1000 euros. By the end of the first year, your investment grew to 5000 euros (AGR of 400%). But by the end of the second year, the investment’s value had lowered to 4000 (AGR of -20%). The third year was better again and the value grew to 7000 euros (AGR of 75%). In this case, the CAGR would be:

GAGR = (7000/1000)^(1/3) – 1 = 0.91 = 91%

This means that if the annual growth rate in this example would have been 91% every year, the outcome (7000 euros) would still have been the same.

The compound annual growth rate is the best measure to compare the performance of different investments over time. But it doesn’t take into account investment risk and it doesn’t show the volatility of investments. Therefore, it may give a false sense of steady growth. In addition to CAGR, it is important to also consider these factors when making investments.