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Term: Compound Annual Growth Rate – CAGR

24 Jul 2014


The year-over-year growth rate of an investment over a specified period of time.

The compound annual growth rate is calculated by taking the nth root of the total percentage growth rate, where n is the number of years in the period being considered.

This can be written as follows:

Compound Annual Growth Rate (CAGR)


CAGR isn’t the actual return in reality. It’s an imaginary number that describes the rate at which an investment would have grown if it grew at a steady rate. You can think of CAGR as a way to smooth out the returns.

Don’t worry if this concept is still fuzzy to you – CAGR is one of those terms best defined by example. Suppose you invested $10,000 in a portfolio on Jan 1, 2005. Let’s say by Jan 1, 2006, your portfolio had grown to $13,000, then $14,000 by 2007, and finally ended up at $19,500 by 2008.

Your CAGR would be the ratio of your ending value to beginning value ($19,500 / $10,000 = 1.95) raised to the power of 1/3 (since 1/# of years = 1/3), then subtracting 1 from the resulting number:

1.95 raised to 1/3 power = 1.2493. (This could be written as 1.95^0.3333).1.2493 – 1 = 0.2493Another way of writing 0.2493 is 24.93%.

Thus, your CAGR for your three-year investment is equal to 24.93%, representing the smoothed annualized gain you earned over your investment time horizon.

Covid-19 – Johns Hopkins University

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