How long will my oldest credit account appear and influence my credit report?

A positive account will continue to appear for 10 years after the tradeline is closed. Closing will drop your score a bit since you are decreasing your available credit ratio. If there is no fee, I would just leave it open, making a small charge quarterly.

If you have to close your oldest credit account, try to pay off the outstanding balances on all your cards. This way, your credit utilization ratio won't get affected much. However, it also depends on how much credit limit you have on this card which you want to close. Even if it continues to appear in your credit report for 10 years, it's effect reduces with time.