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I think it is a myth that closing a card lowers your score. I was told it stays on your report for another ten years as a positive TL. Hopefully by the time it falls off you have other cards that have a long history.
Now, say this was your oldest card, and you close it, and don't open a new tradeline (CC) for ten years, then yes, the average age could suffer.
It is not a myth. Closing a credit card:
1) Will eventually effect your average age of accounts (AAoA), and
2) May eventually effect your oldest account, and, most importantly,
3) Will remove the CL for the TL from your UTIL calculation as soon as any balance reporting on the TL is paid off.
Always better to measure twice and cut once when considering closing an account. Of course other economic factors may weigh in favor of taking a FICO hit in order to save money.