Unauthorized purchase

The description of your problem leads me to believe that the email you received is a Phishing email. Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support will help you to make that determination.

If you see 'apple.com/bill' or an unfamiliar charge on your statement - Apple Support describes how to investigate charges which may have appeared on your account statement.

Apple will always address you by your name or the name they have on file for you, not Dear Customer, Dear Client or by using your e-mail address.  The e-mail will be from @apple.com or @iTunes.com. E-mail addresses can be spoofed. You can go to Mail/View/Message/Show all Headers to see more. Apple emails won't have poor grammar/misspellings. Apple e-mails will never contain an attachment. Apple will never request personal information by email such as Social Security numbers, your Mother’s maiden name or full credit card numbers . 

The only exception to the above I have noticed is if you order something from the Apple Store (apple.com), your receipt will be addressed to Dear Apple Customer. That is a receipt for a purchase you initiated.

Identifying legitimate emails from the iTunes Store.     

Send the e-mail to Apple as an attachment to a new e-mail before deleting it. You can forward as an attachment by going to Mail/Message/Forward as attachment. Or control - click on the email and select Forward as attachment. Make sure you send it as an attachment to a new email. If you just forward it, it will probably be rejected. You won’t receive a response.

reportphishing@apple.com