Let’s start with what average annual rate of return (or annualized return) is NOT:
The above is an arithmetic average, and can work out to be very different than annualized return. If you make an investment, the annualized return at the end is what you will use to pay bills or buy groceries. Annualized return is what you eat.
Now, you know that the return you make on an investment is Value at the End vs. the Value at the Beginning. Or, to state it mathematically:
Return = End / Beginning - 1
You invest $1,000. And 3 years later you sell that investment for $1,100. You made:
1100 / 1000 - 1 = 0.10 or 10% cumulative return
But that 10% is the return for the whole 3 years. You want to know what equivalent rate you compounded at annually, in order to end up making 10% total.
Annualized Return = (End / Beginning)(1 / Num Years) - 1
Or, continuing our example above:
(1100 / 1000)(1 / 3) - 1 = 0.032 or 3.2% annualized return
Dirt simple. And note that it works for fractional years too.