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}] – 1where “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:

Interesting stuff. Isn’t math fascinating?

Yup, I’m a her ðŸ™‚

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?

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.

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.

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

REgards

Braja Kishore

15000

22000

7

5.62%

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