It is always better to get agreements with regard to payment arrangements in writing. If you are struggling to pay your debts, you might consider bankruptcy as a possible solution. I recommend you consult with a bankruptcy attorney in your area. You can find a good one by clicking the Find A Lawyer tab on this website.
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This is a lot of money. Will you ever be able to pay it off with monthly payments? If you are looking to settle, you can often get a better deal by offering a lump sum of cash instead of going the payment route - maybe $20K instead of $52? See an article published by my esteemed colleague in Ohio for more information on this topic. Hope this perspective helps!
Impossible to say. This sort of arrangement is not uncommon. It might still impact your credit, depending on how the lender will report the loan during repayment.
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Your entire financial picture (not just your credit) as well as your future goals should be considered here. Will you need credit anytime soon? Did the bank handle everything in a commercially reasonable manner (as per the Uniform Commercial Code), or did some cowboy banker flip the boat to his buddy for next to nothing? How accessible would your assets be if the bank got a judgment, and are there legitimate things you can do to put those assets out of reach? How litigious is the bank (or, if you know who the bank sells bad debt to, how litigious is their habitual Junk Debt Buyer)?
Without going into all of it, it's difficult to advise you. However, there is an old saying among bankers: "Your earliest loss is your best loss." Having already repossessed and sold the collateral, the bank may be quite amenable to taking a lump-sum settlement. You might consider offering ten cents on the dollar for a full and final settlement and release (keeping in mind that you will have about $46,800 of cancellation of indebtedness income to grapple with come tax time next year--they will send you a 1099c form).