I have a car that I still owe $5k on. I want to trade it with another person, no dealership involved. Can I just trade straight up and keep my loan, even though I don't own the car that the loan was originally for anymore?
Your agreement with your lender is that your loan is to be secured by a lien on your car, the specific car described in the loan agreement. Transferring that car to anyone else without the permission of your lender (always get this sort of permission in writing) would be a violation of the loan agreement, and your lender would be within its rights in most states to require repayment of the loan in full.
If the car you want to have after the trade is at least as valuable as the one you want to be rid of, you can ask your bank to consider a substitution of one vehicle for the other. It's not a thing that most lenders do routinely, so don't be surprised if you get puzzled looks and even an outright refusal.
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