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No, having a auto installment loan is not helpful for mortgages. You already have an installment loan with your student loan so it won't add to the mix of credit. You would be in much better shape working on your unsecured revolving credit lines.
What are your current FICO scores?
First grats on almost getting that BK monkey off of your back! GJ. He is probably right about adding an autoloan will not help if you're trying to get the mortgage right away. However I would hate to see anyone buy a car in cash & not get credit for spending all that money. If it were me, I would finance the car and then pay it off. It may hurt your credit in the long run b/c of HP, new inquiry, new account, etc. but I think in the long run it would help b/c it shows you were successful in manging that new account (especially after the BK) I think a good closed new account especially for such a high dollar amount as a new car, would look great. Shows responsibility & finance stability post-BK. But I'm not an expert & I have no experience with mortgages, etc. so that's just me.
I would think that with just one secured credit card, thats probably where you are deficient. 2-3 revolving accounts are usually better for your score than just one secured account. You may take a temporary hit for the inquiries, and AAoA, but in the long run you'll be better off.