Compound annual growth rate

For annual values, CAGR is defined as:

${\displaystyle \mathrm {CAGR} (t_{0},t_{n})=\left({\frac {V(t_{n})}{V(t_{0})}}\right)^{\frac {1}{t_{n}-t_{0}}}-1}$ 

where ${\displaystyle V(t_{0})}$  is the initial value, ${\displaystyle V(t_{n})}$  is the end value, and ${\displaystyle t_{n}-t_{0}}$  is the number of years.

CAGR can also be used to calculate mean annualized growth rates on quarterly or monthly values. The numerator of the exponent would be the value of 4 in the case of quarterly, and 12 in the case of monthly, with the denominator being the number of corresponding periods involved.^[4]

These are some of the common CAGR applications:

• Calculating and communicating the mean returns of investment funds^[5]
• Demonstrating and comparing the performance of investment advisors^[5]
• Comparing the historical returns of stocks with bonds or with a savings account^[5]
• Forecasting future values based on the CAGR of a data series (you find future values by multiplying the last datum of the series by (1 + CAGR) as many times as years required). As with every forecasting method, this method has a calculation error associated.
• Analyzing and communicating the behavior, over a series of years, of different business measures such as sales, market share, costs, customer satisfaction, and performance.
• Calculating mean annualized growth rates of economic data, such as gross domestic product, over annual, quarterly or monthly time intervals.^[6]

• Annual growth %
• Arithmetic mean
• Average annual return
• Continuous compounding
• Geometric mean
• Exponential growth
• Internal Rate of Return