Compound annual growth rate

Equation

For annual values, CAGR is defined as:

${\displaystyle \mathrm{C}\mathrm{A}\mathrm{G}\mathrm{R}(t_0,t_n)={\left(\frac{V(t_n)}{V(t_0)}\right)}^{\frac{1}{t_n-t_0}}-1}$

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.

In practice, CAGR calculations are often performed in Microsoft Excel. A convenient built-in function is ${\displaystyle =RRI(nper,pv,fv)}$, where ${\displaystyle nper}$ represents the number of periods, ${\displaystyle pv}$ denotes the present value (initial investment), and ${\displaystyle fv}$ represents the future value (final value of the investment). The RRI function (Return Rate on Investment) returns the equivalent constant interest rate per period, effectively matching the CAGR when applied over a specified period. It is also possible to use the IRR function on a range of cells where the first cell is set to the present value as a negative number, the last cell is set to the future value, and all other cells are set to zero.

CAGR is a good method to compare returns of 2 investment instruments (Bonds/stocks/Gsecs etc) over a multi-year period.