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In short YES. With a 20% down payment and a strong cosigner then a dealer should have no problem working out a deal for you. In most cases we advise securing financing before you go to the dealership. With your challenges (new job / past history) I think just letting the dealer handle it is best. Most large dealers have a special financing manager that deals with credit challenges. Call a few in your area and speak with them before showing up. I'm sure you'll get a good feeling from at least one.