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If you trade in your car and they pay off the balance of your old note, does that help your score? Will that show a paid off car loan?
Yes, it will show as a closed auto loan account with a $0 balance. The account will remain on your report for up to 10 years, helping your AAoA. Other than that, you won't see much of a bump. Installment loan utilization has extremely little effect on your FICO score.
Just as a side note, make sure that you are aware of the timing of how your loan will be paid off, you don't want to incur any lates due to the dealership dragging their feet.