Compound annual growth rate

{{short description|Geometric progression ratio that provides a constant rate of return over the time period}}

{| class="wikitable" align="right" |+ CAGR calculator | !Value !Year |- | Initial value | ${{calculator |id=initVal |default=100 |size=5 |type=number }} |{{calculator |id=initYear |default=1990 |size=4 |type=number }} |- | Final value |${{calculator |id=endVal |default=800 |size=5 |type=number }} |{{calculator |id=endYear |default=2005 |size=4 |type=number }} |- ! colspan="3" | CAGR of {{calculator|id=cagr|formula=round((pow((endVal/initVal),(1/(endYear-initYear)))-1)*100,1) |default=14.9 |type=plain }}% over {{calculator |id=period |formula=endYear-initYear |default=15 |type=plain }} years |} {{Macroeconomics sidebar}}

'''Compound annual growth rate''' ('''CAGR''') is a business, economics and investing term representing the mean annualized growth rate for compounding values over a given time period.<ref name="AnsonFabozzi2010">{{cite book|author1=Mark J. P. Anson|author2=bdgdgdhd J. Fabozzi|author3=Frank J. Jones|title=The Handbook of Traditional and Alternative Investment Vehicles: Investment Characteristics and Strategies|url=https://books.google.com/books?id=LKj39XK-ufsC&pg=PA489|date=3 December 2010|publisher=John Wiley & Sons|isbn=978-1-118-00869-0|pages=489–}}</ref><ref>{{Cite web|url=http://www.investopedia.com/terms/c/cagr.asp|title=Compound Annual Growth Rate (CAGR) Definition {{!}} Investopedia|last=root|website=Investopedia|language=en-US|access-date=2016-03-04}}</ref> CAGR smooths the effect of volatility of periodic values that can render arithmetic means less meaningful. It is particularly useful to compare growth rates of various data values, such as revenue growth of companies, or of economic values, over time.<ref name="Chan2012">{{cite book|author=Emily Chan|title=Harvard Business School Confidential: Secrets of Success|url=https://books.google.com/books?id=gLEqXqZyW00C&pg=PA185|date=27 November 2012|publisher=John Wiley & Sons|isbn=978-1-118-58344-9|pages=185–}}</ref>

== Equation == For annual values, CAGR is defined as:

:<math>\mathrm{CAGR}(t_0,t_n) = \left( \frac{V(t_n)}{V(t_0)} \right)^\frac{1}{t_n-t_0} - 1 </math>

where <math>V(t_0)</math> is the initial value, <math>V(t_n)</math> is the end value, and <math>t_n - t_0</math> 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.<ref>{{cite news |title=How is average annual growth calculated? |url=https://www.bea.gov/help/faq/463 |publisher=Bureau of Economic Analysis |date=January 11, 2008}}</ref>

In practice, CAGR calculations are often performed in Microsoft Excel. A convenient built-in function is <math>=RRI(nper, pv, fv)</math>, where <math>nper</math> represents the number of periods, <math>pv</math> denotes the present value (initial investment), and <math>fv</math> 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.<ref>{{cite web |title=How to Calculate CAGR in Excel |url=https://www.accelerate-excel.com/blog/cagr-excel |publisher=Accelerate Excel |date=May 24, 2025}}</ref> 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.

== Applications ==

These are some of the common CAGR applications:

* Calculating and communicating the mean returns of investment funds<ref name="www.12manage.com">{{Cite web|url=https://www.12manage.com/methods_cagr.html|title=Compound Annual Growth Rate CAGR: Summary and Forum|website=www.12manage.com|access-date=2019-05-02}}</ref> * Demonstrating and comparing the performance of investment advisors<ref name="www.12manage.com"/> * Comparing the historical returns of stocks with bonds or with a savings account<ref name="www.12manage.com"/> * 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.<ref>{{cite news |title=How is average annual growth calculated? |url=https://www.bea.gov/help/faq/463 |publisher=Bureau of Economic Analysis |date=January 11, 2008}}</ref>

== References == {{reflist}}

Category:Actuarial science Category:Mathematical finance