In most cases the answer is yes, the credit card company can charge interest and fees after an account has been closed. What, if any, interest and fees could be added to your balance would be dictated be the specifics of your credit card agreement.
Your best bet would to be to pay off the balance of your debt as quickly as possible. When paying it off, be sure that you don’t get hit with “residual interest” for the days in the billing cycle before you paid the balance in full. “Residual interest” is interest that accrues on some accounts from the first day of the billing cycle in which you paid the balance in full until the date that the bank credits your payment.
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