FICO will score based on what is reporting at that moment. So, when your lender pulls a report or you pull a report from myFICO, you'll see that change reflected immediately...assuming that the action (e.g. dropped account, added TL, inquiry, etc.) would even result in a score change.
Without going into detail, paying a car loan down or off won't always result in a score increase. In some scenarios, paying it off could result in a decrease. For dropped baddies, most usually you will see an increase, but in some scenarios you can actually lose points. Depends on what is reporting, how it reports, your scoring bucket, overall credit, etc.
In your $840 on a $500 CL example, is $0 reporting right now? Paying it to $0 won't always result in a $0 balance reporting, especially if you use it and not PIF prior to the next statement cut. FICO will ding for being over the limit and utilization hurts too in that example. It also depends on your overall utilization and util with your other cards. If this is your only CC reporting, and assuming you have no CC COs reporting a balance, other LOCs, other HELOCs, or other items impacting util, then paying it to $0 would result in a small increase. If the balance you want reported is reporting now, then any score change that would have happened, did happen.
