Does a beneficiary have to pay finances charges on property?
If your father passes away and leaves you his vehicle, on which he still owes payments, will you still have to pay the finance charges if you pay off the balance?
In two words: quite possibly.
A finance charge, while annoying, is quite simply the amount the car seller will impose for the privilege of buying the car on credit. Terms vary wildly -- and are negotiable, with few legal restraints on the final agreement. What is ironclad law is that the buyer must be given a written agreement spelling out the exact terms of the finance charge. So if this is a particular concern for you now, you might want to take a gander at that agreement.
The hopeful news may be that shorter payment terms almost always translate to lower finance charge amounts. So if you took title to your father's car and were able to pay it off in full sooner than he intended to pay, you would be in an excellent position to negotiate a lower finance charge.