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Even with the money down, seems like a lot of new auto credit in a short period of time. They might want your wife on the loan with you, to show a need for a second new vehicle auto loan. You didn't mention your income, so of course verifiable income can make a difference. I am sure there's a bank that will do it, but at what interest rate and cost to you.
The Mazda 3 is an excellent car, just bought a 2014 touring model for my daughter. My suggestion is buy the car you think is your best long term solution knowing that you will likely get a crappy APR but buy smart and keep the loan to value ratio as close to 100-110% as possible so you can refinance in a few months when your scores recover a bit and you have aged your accounts. Mazda uses Chase as their captive lender so you may not get much love from them, I would suggest building a relationship with a good credit union and see if you can get a decent APR from them. If not take what you can get and refinance later. I was able to keep my LTV reasonable and built enough on my scores that after 5 months I was able to refi a Santander loan at 12.5 to NFCU at 4.29. I am sure you can do the same.
The difference in your current car loans versus getting another new car loan: 1) significant difference in amount owed on the impala versus proposed new vehicle 2) you just added a brand new traverse, $30-40k I assume. So now you're trying to go from owing lets just say $42k to over 50k on vehicles, just out of bankruptcy and you just opened a new auto loan.
Im not saying it's impossible, but I don't think it will be easy to get a "good" rate. As you well know, there's more to a lending decision than just a number - there's data that shows why the score is what it is. Personally, I think you'd have better luck with Ford, Nissan, or Chrysler.
@Anonymous wrote:Your situation here is so complicated and I guess, it would be better if you can discuss it with the dealers or agents. As a great tips here, you can find your options just in case for the Toyota Corolla, https://dsrleasing.com/car-listings?make=toyota&model=corolla. You can also contact them through the trade in issues. Hope this might help you.
Surprise, surprise.