Closing a credit card can potentially hurt your credit score. This typically happens because closing an account reduces your total available credit limit, which can increase your 'credit utilization ratio' (the amount of credit used versus available). A higher utilization ratio is viewed negatively by credit bureaus. Additionally, closing an older card can shorten your average length of credit history, another factor that influences your score. It is generally advisable to keep older, well-managed accounts open, especially if they are free of annual fees.
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