Assuming the car you are purchasing has book value near the 40K you are willing to pay, you should not have much problem getting financed for such a small percentage.
"Should" being key word.
You are still very close to the discharge date.
Your interest rate will be extreme.
FYI:
In industry lingo, the banks that your obligations were discharged with you "took down."
You are essentially black listed for life from those institutions. Even if you are simply asked to co sign 25 years from now on a car for your daughter, your name/SSN will kill the deal..
