# How to Compute Average Annual Rate of Return

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.

## 16 thoughts on “How to Compute Average Annual Rate of Return”

1. Great article. I’m just getting into understanding my IRA/401K portfolio and this is one of the clearest explanations of how to calculate average annual returns I’ve read. Talking to our financial people only gave me a headache!

2. Anonymous says:

yes I think luminous is correct

3. This is good… now what if you are regularly adding to your position? For example, re-investing dividends, employee stock purchase plan, or regular contributions to your portfolio? Is it still easy to computer the average ROR?

4. r2j says:

Really nice. Thankyou

a very useful example for my students

6. elvina says:

excellent!!!

7. kate says:

But in table 2, how did you calculate the annual ROR?

8. kate, annual ROR is price this year divided by price a year ago. for example, for 2001:

97.80/111.19 -1 = -.1204 or -12.04%

9. Ian mcpherson says:

Thank you, clear and simple.

.

10. George says:

The way the formula is written, the expression “1 / num years” is shown as an exponent. How do I calculate 1.1 to the 1/ 3 power?

11. George says:

Never mind, I just remembered computers

12. Jack Robertson says:

GG bra thanks mate its alright. explanantion is clearish