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I've seen a lot of advice saying that you shouldn't close accounts unless they are costing you money to increase account age. Let's say I have a credit card that costs $0p/a and I keep the account open. If I don't make any charges to the account will it fall off my credit report after a period of 7 years? If yes, what do I need to ensure that this doesn't happen?
If the account is open, it won't fall off your credit reports. Just use it every once in a while (every couple of months) as complete inactivity risks that the credit card company may eventually close your account for you. If you do close it (which if it costs you nothing don't) it will stay on your credit report for 10 years and then drop off.
Unless the creditor stops reporting, an open account should stay as long as the account is open. Once closed, it will continue to factor into AAoA. You just lose the CL factoring into your overall CL. A closed account, in good standing, can stay for up to 10 years from the date closed.
ETA: The up to 10 years is an estimate. It can come off before or stay for years longer. I have a closed account that has been reporting for over 15 years.
If you got rejected with a score of 756 you probably have a thin file. Your score is not the only thing that is looked at.