Paying off your car loan can affect your credit scores. Assuming you paid your car loan on time, every time, it will almost certainly reflect positively on your credit report.
Once the loan is paid in full, your credit report will be updated to show "paid in full". Allow a full billing cycle or two for the account to be updated to show a "paid" status. Lenders update the status at the end of each billing cycle, so it could take as much as a month or a bit more before your credit report is updated.
Anytime you make a significant change to your credit history, such as paying off a loan, you may at first notice a slight drop in scores. However, the drop is usually small and short term. If there are no other negative issues in your credit history, your scores will likely come back up after a month or two, after your credit history stabilizes.
If you have made your car payments as agreed and the auto loan does not show any late payments, that loan will stay on your credit report as positive history for 10 years from the date it was paid. Positive history stays on longer than negative history so it will help you maintain a strong credit history.
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Scoped on: 5/30/2017