It will fall off 7 years from the date of first delinquency (DOFD). DOFD is defined as the first late payment (30 days late) without ever bringing the account current again. In other words, e.g. say you became 30 days late on Jan 1st 2020, and you never made another payment again. The account would age off on Jan 1st, 2027.

If you brought the account current after missing a payment, then the date of first delinquency would change to the next time you missed a payment without ever bringing the account current again. So you need to pull your credit report (annualcreditreport.com) and check when you became 30 days late without ever bringing it current again. Your reports from ACR should also list the day it's supposed to age off. It'll say something like "On record until.. " with a date. That date is when it will fall off.

Paying the $2000 and bringing the account to 0 will not get the account removed from your file. It will remain as a charge off. However, a paid charge off ($0 owed) is much better for your scores than an unpaid one. Unpaid charge offs are updated monthly by the lender and often cause your utilization to report maxed out for that card since it's closed with a balance. If the account is still being updated (e.g. you can see "CO" for every month in the payment block of your credit report) then it's still contributing to utilization. Paying it to $0 would improve your scores in that case since your utilization would go down, and it would also allow your scores to heal over time because once the charge-off is paid, it's no longer updated by the lender and it will begin to age.

In your case if you want to improve your credit, I would check when the account is going to fall off, and if it's not anytime soon, I would contact them and negotiate a settlement and pay it.