How to Compute Compound Annual Growth Rate – CAGR

June 8, 2006

Ricemutt over at Experiments in Finance has written some wonderful posts (here, here, and here) on financial math. It was through her (I think Ricemutt is a “her,” but I’m not positive on that) posts that I discovered the meaning of Compound Annual Growth Rate or CAGR as it is commonly known. Yes, I was aware of CAGR but I never really thought about it much. I didn’t know it at the time that I put my Average vs. Geometric Average post together using an Excel spreadsheet, but CAGR and Geometric Average are the same thing. And, to top it off, I found a formula for calculating them that is MUCH easier than I previously understood. That’s good for all of us!

If you remember from the Average vs. Geometric Average post, the beginning value of the example was $10,000 and at the end of 20 years, the ending value was $95,421.19. To compute the CAGR for this example you use this formula:

CAGR = [(Ending Value ÷ Beginning Value)1/n] – 1

where “n” is the number of time periods (20 years for this example)

Substituting the numbers from the example, the equation looks like this:

CAGR = [($95,421.19 ÷ $10,000)1/20] – 1

CAGR = [9.542119.05] – 1

CAGR = 1.119392 – 1

CAGR = .119392 or 11.94%

That’s the exact same answer we got in the previous post:

Actual Returns

Interesting stuff. Isn’t math fascinating?

10 responses to How to Compute Compound Annual Growth Rate – CAGR

  1. I am trying to compute the 10-year compound rate for the following: 33.17%, 28.44%, 20.95%, (-9.14%), (-11.94%), (-22.05), 28.54%, 10.82%, 4.96%, 15.79%. I tried using the formula but was unable to compute. Can you help me?

  2. I have been searching the formula to compute my compounded return of my investment. Your example solve half of my problem.

    On top of the annual growth rate (which may be negative), I have re-investment each year which complicate the computation of my real compounded return rate.

    For example:

    Year 1 (initial capital: 100, yearly return: 10%)
    Year 2 (reinvest 50, yearly return: -2%)
    Year 3 (reinvest 100, yearly return: 15%)

    What is my compounded return at end of year 3???

    Please help.

  3. how can we find out compond growth annual rate with the help of microsoft excel or satistical softwares like SPSS and SX etc., And also I need explanation how it can be computed.

  4. i have year wise sales like:
    2001- $15000
    2002- $10000
    2003- $25000
    2004- $30000
    2005- $18000
    2006- $21000
    2007- $75000
    2008- $22000

    What will be CAGR….?

    kindly let me know the formula

    Braja Kishore

  5. 15000


  6. (22000/15000)^(1/7)-1

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