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Compound annual growth rate
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<h2 id="equation">Equation</h2> <p>For annual values, CAGR is defined as: </p> C A G R ( t 0 , t n ) = ( V ( t n ) V ( t 0 ) ) 1 t n − t 0 − 1 {\displaystyle \mathrm {CAGR} (t_{0},t_{n})=\left({\frac {V(t_{n})}{V(t_{0})}}\right)^{\frac {1}{t_{n}-t_{0}}}-1} <p>where V ( t 0 ) {\displaystyle V(t_{0})} is the initial value, V ( t n ) {\displaystyle V(t_{n})} is the end value, and t n − t 0 {\displaystyle t_{n}-t_{0}} is the number of years. </p><p>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.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> </p> <h2 id="applications">Applications</h2> <p>These are some of the common CAGR applications: </p> <ul><li>Calculating and communicating the mean returns of <a href="/facts/Investment_fund/IVmtjrVd">investment funds</a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a></li> <li>Demonstrating and comparing the performance of investment advisors<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a></li> <li>Comparing the historical returns of stocks with bonds or with a savings account<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a></li> <li>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.</li> <li>Analyzing and communicating the behavior, over a series of years, of different business measures such as sales, <a href="/facts/Market_share/kvXSlhlB">market share</a>, costs, <a href="/facts/Customer_satisfaction/upP4jHb9">customer satisfaction</a>, and performance.</li> <li>Calculating mean annualized growth rates of economic data, such as <a href="/facts/Gross_domestic_product/zQRgyFKc">gross domestic product</a>, over annual, quarterly or monthly time intervals.<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a></li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Annual_growth_%25/WnD5syC7">Annual growth %</a></li> <li><a href="/facts/Arithmetic_mean/L3Pv333o">Arithmetic mean</a></li> <li><a href="/facts/Rate_of_return/CldGgD1f">Average annual return</a></li> <li><a href="/facts/Continuous_compounding/e0DKKjBs">Continuous compounding</a></li> <li><a href="/facts/Geometric_mean/6Nf6uk1A">Geometric mean</a></li> <li><a href="/facts/Exponential_growth/m4yEqKJ7">Exponential growth</a></li> <li><a href="/facts/Internal_Rate_of_Return/DLTUfSMI">Internal Rate of Return</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Mark J. P. Anson; bdgdgdhd J. Fabozzi; Frank J. Jones (3 December 2010). The Handbook of Traditional and Alternative Investment Vehicles: Investment Characteristics and Strategies. John Wiley & Sons. pp. 489–. ISBN 978-1-118-00869-0. <a href="978-1-118-00869-0" target="_blank">978-1-118-00869-0</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>root. "Compound Annual Growth Rate (CAGR) Definition | Investopedia". Investopedia. Retrieved 2016-03-04. <a href="http://www.investopedia.com/terms/c/cagr.asp" target="_blank">http://www.investopedia.com/terms/c/cagr.asp</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Emily Chan (27 November 2012). Harvard Business School Confidential: Secrets of Success. John Wiley & Sons. pp. 185–. ISBN 978-1-118-58344-9. <a href="978-1-118-58344-9" target="_blank">978-1-118-58344-9</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>"How is average annual growth calculated?". Bureau of Economic Analysis. January 11, 2008. <a href="https://www.bea.gov/help/faq/463" target="_blank">https://www.bea.gov/help/faq/463</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>"Compound Annual Growth Rate CAGR: Summary and Forum". www.12manage.com. Retrieved 2019-05-02. <a href="https://www.12manage.com/methods_cagr.html" target="_blank">https://www.12manage.com/methods_cagr.html</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>"Compound Annual Growth Rate CAGR: Summary and Forum". www.12manage.com. Retrieved 2019-05-02. <a href="https://www.12manage.com/methods_cagr.html" target="_blank">https://www.12manage.com/methods_cagr.html</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>"Compound Annual Growth Rate CAGR: Summary and Forum". www.12manage.com. Retrieved 2019-05-02. <a href="https://www.12manage.com/methods_cagr.html" target="_blank">https://www.12manage.com/methods_cagr.html</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>"How is average annual growth calculated?". Bureau of Economic Analysis. January 11, 2008. <a href="https://www.bea.gov/help/faq/463" target="_blank">https://www.bea.gov/help/faq/463</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> </ol>