Closing old credit accounts, even if they have 0 balance will likely negatively effect your credit score in two ways:
First, if closing the accounts shortens the length of your average credit history, your score will be negatively impacted. If you are worried about your credit score, keep older accounts open to keep credit history.
Second, if closing these accounts will significantly reduce your outstanding credit and cause you to use a larger percentage of your outstanding credit, your score will be negatively impacted.
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