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I've been reading articles that refer to an average yearly return of about 7%, and I'm not sure how they're calculated. I started my Roth IRA in April '05 with $3000. If I sold all my stocks today, I'd have (after fees) $3700. To find whether I've beaten the stock market, do I simply divide $3,000 into $3,700 for an 8.11% return?

No, here's the formula for a simple total return:

(final value - initial value) / (initial value)

So that your gain of $700 is an increase of 23% on the $3000. If you have a 100% return this means you've doubled your money.

Now, if you want to annualize this, we notice that this is 5 months later and so we take that 23% gain and perform the following function on it:
(1.23)^(12/5) = 1.6435096841883352708412102299812 or approximately 64%.

What the annualizing does is to take the return you have and see what it is per year. So if you have a 6 month return of 10%, the annualized form is 21% since this is (1.1)^2.

Was I blindly lucky(even with my poor timing), am I doing the math wrong, or is there something I don't understand?

You were lucky and there are likely lots of things you don't understand. There are lots of things I don't understand either but that doesn't mean they don't work well in spite of everything else, e.g. my immune system, digestive system, etc.

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