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?