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If you plan on keeping the car for the full term I don't see why you shouldn't carry it for the full 60 months, definitely since you have 0% interest accumualting on the car.
From what I read around here despite being paid off or not the loan will still appear on your CR as an installment loan long after its paid off.
If it's 0% and you don't need to purchase something major like another car or a mortgage, etc.
The reason to pay off early would only be because you need to remove the debt / monthly payment that brings your uti to high to be approved at best rates.