Hi there
No, it wouldn't be duplicate content as it's the same page, but it's not necessary as a user looking at cars probably isn't interested in financing until they find a car they like and see a price.
What I would do instead there is make sure that you have finance content on the listing pages. I wouldn't go too in-depth, but make sure that you let them know you have financing options available or experts they can talk to at the dealership if they have questions or concerns.
Now, don't link off of the listing because you want the users to stay there, but make sure you have a form that they can contact you with if they have interest in the car. You can even have a checkbox that says "I would like to know about financing options" or something along those lines, so when your client receives the form, they know this person wants to talk about financing.
Keep financing links under financing in the top navigation and give users/potential customers a little content and the option to chat more if interested on your listing pages.
Hope this helps! Good luck!