## May 4, 2008

### How to calculate annual percentage growth.

There are a number of financial topics where it is useful to know the annual growth rate of an asset or cost. Lets say for example that I invested \$1000 in a stock in 2003 and today in 2008 that the stock is worth \$1300. How do I know the annual % growth of my investment?

This is what is called the Compound Annual Growth Rate (CAGR). The Investopedia article on CAGR tells us that the formula for CAGR is:

CAGR = ( Ending value / Starting value ) ^ (1 / # of years ) - 1

Note the ^ symbol there means that the first figure from (ending value / start value) is taken to the power of the second figure ( 1 / # years). If you are in Windows for example the built in calculator has a x^y button in the scientific view mode. Or you can also use the ^ symbol in a formula in Excel.

So lets figure the CAGR for my example. The figures are :
Ending value = \$1300
Starting Value = \$1000
# of years = 5 (2008 - 2003)

So the calculation would be:

CAGR = (1300/ 1000) ^ (1/5) -1
= 1.3 ^ 0.2 - 1
= 1.0538 - 1
= 0.0538
CAGR = 5.38%

OK lets apply this to another example. Lets say that in 1998 I bought a house for \$160,000 and today in 2007 the house is worth \$225,000. How much has my house appreciated in value per year?

CAGR = (225000/160000) ^ (1/9) - 1
= 1.40625  ^ 0.11111 -1
= 1.0386 -1
= 3.86%

You can also use the formula to find out how much % an asset has lost value. Lets say that my house peaked at a value of \$240,000 in 2005 and then dropped to \$225,000 in 2007. What is my annual rate?

CAGR = (225000/240000) ^ (1/2) -1
= - 0.03175
= -3.175% 