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How to Compute Compound Annual Growth Rate – CAGR
By JLP | 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:
where “n” is the number of time periods (20 years for this example)
Substituting the numbers from the example, the equation looks like this:
That’s the exact same answer we got in the previous post:
Interesting stuff. Isn’t math fascinating?
Topics: Financial Math Basics | 6 Comments »
June 8th, 2006 at 8:51 am
Yup, I’m a her
June 9th, 2006 at 5:31 am
Star Money Articles for the Week of June 5
Here are interesting posts and news this week from the MoneyBlogNetwork members and beyond: AllFinancialMatters tells us how to compute compound annual growth rate. MightyBargainHunter asks whether you should pay it down or ING it. Five Cent Nickel dis…
June 9th, 2006 at 3:05 pm
[...] AllFinancialMatters looks at the Compoud Annual Growth Rate (CAGR) calculation, which is very helpful in financial analysis. [...]
December 11th, 2006 at 2:51 pm
[...] The formula for Compound Annual Growth Rate (CAGR) is: [...]
January 10th, 2007 at 12:23 pm
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?
September 28th, 2009 at 2:50 am
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.