Can you do anything with XNA without being 18? They shouldn't let you sign up if no.
You could try to call Microsoft to get a refund, but I doubt you'll get one (they're not Valve). You could dispute the charges with your CC company if you're OK with never using the account on Live again.
A lot of people seem to be having this problem. It seems reasonable to put somewhere on the site an obvious notice or an age verifier.
i would try calling 1800-4-my-xbox. a week or 2 ago i purchased xna and then realized you could get it for free with microsoft dreamspark. i called them up and they refunded my money. only later did i learn that i needed to re-buy it anyway in order to peer review songs which didnt work with the dreamspark free trial. but anyways they did refund my money for xna, but keep in mind that i called to cancel like 2 hours after i originally purchased it. give it a try though.
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Don't you have to be at least 18 to get a credit card?
Mom and dad ought to be paying more attention to what junior is doing with their money.