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You can cancel your account at any time, but the longer you don't make a payment...the more it hurts your credit and the more late charges and finance charges occur.
What you should do is call the credit card company and let them know you want to cancel your credit and set up an automatic payment plan. I know you said they weren't that great to talk with, but you've got to make the call. They will want you to pay your regular monthly payment, AT LEAST...but you may want to ask them what's the minimum amount they will allow you to pay.
The only thing about setting up an AUTOMATIC plan, is that they will take the money out of your bank account no matter what....So let's say that one month you have something come up and you can't pay that $50 (or whatever), too bad. They will take it out anyways.
As long as you pay it off over time, you'll be okay. If you close it and never pay on it, the credit card company will send your account to a collection agency who will persue the money from you. Sometimes, they will offer a deducted amount just to get you to pay the bill in whole. I had an Old Navy card that had over a $500 balance, and they were willing to settle for around $300.
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