Even if the account is closed with a zero balance it will continue to report for at least 10 years from closing date. It will be still be factored into your overall history as well as your AAoA for as long is it reports. It will stay on your reports as your other accounts also ago. The only thing closing the account will do will lower your available credit and that may skew your util. If you close it with a balance and both the balance and limit continue to report this card will still be included in your util. I don't see the need to pay the unnecessary interest on the balance to gain a few more years of age on the account. If you can pay it off, do so. One less bill. Other option is it just pay it off and sock drawer it if there's no AF. Keep it open until they close it for inactivity and gain a little more history on the account.
Also, my DH had a Citi/Shell card opened in 1997 that was closed in 1999. It is still reporting on 2/3 of his reports. I also have an old jewelry account opened in 1998 and closed in 2001 that says it will continue to report until 2021. So not all accounts just disappear after that 10 year mark.
