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OP,
Are you referring to use your trade as a down payment? If you have negative equity of 5k in it, then it is not considered a down payment. What is your gross income? I think you will be hardpress to borrow 50k with such short credit history because you have limited comparable credit to the new loan you would be seeking. In your situation I would keep paying on the installment loan (I am assuming it an auto loan?) to build your AAOA and show around 18-24mo's worth of payments.. just my opinion, but I think I would look for a cheaper vehicle if I was in your situation.
As most will also say, a Credit Union would be your best bet in this situation, you could also give the Cap One Auto Navigator a shot to see if your pre-approved?
From a Loan Underwriter's standpoint they will see quite a few new accounts with no payment history, and a fairly short installment loan account that isn't necessarily comparable to the type of loan ($50k+ with negative equity) to compare this new loan with.
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I really think waiting would be your best bet to get your AAOA higher and show more payment time on your CC's/Installment loan.