CardTrak.com - Credit Card Questions and Answers at CardTrak.com: My credit card charges a monthly fee with or ...
 

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Q: My credit card charges a monthly fee with or without a balance. Why is it bad to completely close a credit card once you've paid off the balance?
A: This is an exception as most prime issuers do not charge fees. In your case it makes perfect sense to close the account. Just make sure the credit bureaus show that you closed the account and not the creditor.

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