Is it true that if you close a credit card account, it hurts your credit history? That it's actually better to simply stop using the card? I am wondering because I am considering getting a JetBlue American Express credit card so I can get points towards free flights. The card costs $40 per year, however. So I am wondering if I get to a point where I do not use JetBlue flights anymore, and want to cease using the card, would it hurt my credit history if I close my account (and thusly stop the $40 per year payments)?