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Many cars on the road still owe outstanding finance. This isn't a problem in and of itself, and it happens all the time. The name on the contract is yours when you buy a car on finance, but you won't own the vehicle until all of the costs are paid in full. You won't be able to sell the car as well while you're making payments since the lender legally owns it. You will be stuck in a bind if you are not careful enough.
Check Outstanding Finance on car to learn how to tell if a car has a loan owed to a finance firm and what to do if you are buying a car with outstanding finance without realizing it.