Compound Annual Growth Rate

The compound annual growth rate, also known as CAGR, is a formula that is applied to an investment to help determine the investment's annual smoothed return. The final percentage that you get upon calculating the compound annual growth rate is a smoothed rate of return that shows the positive or negative growth of your investment over a specified period of time.

The CAGR is used by investors to understand what an investment has historically yielded on a yearly basis. Obviously, this formula can’t predict what the future yields of a particular investment will be, but it can be used as a barometer to gauge the investment's future viability within the market. This number can also be used to calculate an investment's average growth-rate over several years.

Compound Annual Growth Rate Formula

The formula for calculating the compound annual growth rate of an investment uses the number of years in an investment period and the nth root of a growth rate’s total percentage. The formula is fairly straight-forward.

CAGR = ((ending value / beginning value) ˆ 1/compound period) – 1

Using this formula, we can create an example of a compound annual growth rate based on an amazing fictitious stock offering. As we research the stock, we see that it has solid annual growth and is probably worth purchasing. In the year 2006 our amazing stock had a beginning value of $1000. In 2007 the stock jumped to $1200. Then in 2008 the stock ended at $1500 and by 2009 was a hefty $2500 per share. If we place these numbers into our formula, it will look something like this:

((2500 / 1000) ˆ 1/3) – 1 = 0.3572

The amazing stock that we purchased back in 2006 had an annual return rate of 35.72%. Not bad!

Using the CAGR formula allows us to take an investment's measure by eliminating the volatility, or the up and down changes that occur during the fiscal year. Overall, this gives us a much better impression of how the investment is actually performing than if we looked at it month-by-month or even week-by-week. CAGR is especially helpful when you are making decisions on long-term investments.

One very common use of the compound annual growth rate of investments is to compare two investments side-by-side. This allows you to get a feel for how they are performing over a long period of time. This formula can also be used to determine the growth of your own personal portfolio.

The CAGR is a handy formula for calculating the value of investments and there are actually calculators available on the Internet that can compute your CAGR if you’re uncomfortable using the given formula.


Tim Ord
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