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If that's your score after the shortsale you should be fine. Do you have any other auto loans other than the current one? One certainly helps but the more the marrier. With a solid auto history your auto enhanced FICO will be higher than you regular score. Financing won't be an issue but leasing is different ball of wax that needs higher scores. You'll likely have north of a 680 auto score and shouldn't have any issues getting a lease, granted won't be the best terms but you should be able to get approved.
Just out of curiosity what's going you wanting to lease? My experience with my kids is they have a way to killing the interior of a car. No matter the precations taken they will stain everything. This could be a costly issue come turn in time. With the really nice warranties of certified used cars you may want to take a look at that option as well.
Good luck.
I think you should talk with the dealer before the private party sale.
You may be pleasantly surprised at how much they can give you. It will just take some negotiating.
IMO, Do not lease a vehicle. It is the worst thing you can do in your situation. With a lease the only good thing about it is the monthly payments are lower but that one fact doesn't offset all the negative factors associated with leasing a vehicle. At the end of the lease you don't own anything AND you will have a big amount due at the end of the lease term for damage done to the vehicle and for excess mileage. All you have when you lease anything is a payment there is no equity build up whatsoever. You have thrown away the entire payment each and every month for the entire term of the lease and gotten nothing for it other than the privilege to spend more money at the end of the lease! On top of that, you are charged the absolute maximum for the vehicle plus if you decide to do a buy out you have to pay out the lease then do the purchase and it runs much, much more than if you financed right from the beginning.
Don't get me wrong, car dealerships and their salesmen love leases because they make the absolute most money on the vehicle and you pay the most over the lifetime of the vehicle. Plus, after you have paid the most, they get the vehicle back in their possession! What a deal for them, but not for you.
Given your situation, why don't you sell your vehicle privately and take the funds and buy a used SUV. You can negotiate a reasonable price for the vehicle and get your financing from a CU so you don't end up with the dealership gamesmanship that is played there. Get your pre-approval first. Put down as much as you can, getting a zero down payment type financing is a sure way to increase your negative equity position right off the bat.
You are here on this board to learn sound financial decision making as well as work on your credit. This is your chance to put what you have learned to work.
If you are a member of a local CU, they tend to offer pre-approvals good for 60 days which would allow you time to sell the car privately if you don;t do it through a dealer. Also if you take a copy of your CR to them, they may give you an idea if they would approve you without applying. Worth a shot. Why are you interested in a lease? If it is a payment issue, then If you knew that your credit and money situation would be much better in say 2 or 3 years and you can keep withing the mileage bounds for the lease, then a lease could be an option for you. Also extending the payments out might help as well and you could always pay extra later if you can.
Thank you all for the advice. I really appreciate it and will update once eveyrthing is done.