Applying for an auto loan?

I'm looking to apply for an auto loan with Well Fargo for about 16000. I'm trading in my car as a down payment. The thing that worries me is would I need a co-signer. My credit score is 714, but I applied for a personal loan for about 3000 but was turned down because of my short length of history. Would I be denied again because of that or if I do get approved would I have a higher interest rate?