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Welcome grapelady!
If your payment history is unblemished, you should go to SoFi.com and see if you qualify for a personal loan. They like high income (check), unblemished payment history (???) and don't shy away from high utilization. You can see if they will give you a pre-approval (only a SP (soft pull)) of your credit. The benefit of a personal loan is that you will pay down the higher interest debt and your scores will climb. FICO scores treat a personal loan better than having credit card balances.
If you qualify, I highly recommend you go that first. The big WARNING is to not run up the credit card balances again and get on a budget.
However, I would recommend that you apply to PenFed Credit Union. It will be one Equifax Hard Pull and that will get you into the credit union, apply for a car loan, a credit card and line of credit if you so desire. They use your one credit pull for 90 days and don't pull for each product. It will only take a small (tax deductible) donation to join, think I donated $25.
As far as your tade in, if you live near a car max take your current car in for a FREE buy offer. They are one of the largest buyers of cars and this will give you a starting number of what your car is really worth. In most states when you trade in your car you only pay the difference between what the new car costs minus the trade in value. In my state with 9% + interest, your trade in of $10,000 would save around $900 in interest.
Good luck and if you have any questions fire away....
Apply for the most you plan to spend. Doesn't mean you have to spend that amount. Once approved , you can find the car and haggle the price until your comfortable with it. From there call Penfed and give them the exact amount and vehicle information. They'll cut a check to the dealership and you, it will then be sent to you to sign and give to finance manager.
Penfed may asked what vehicle you intend to buy before hand along with the VIN number. Either way, the process is fairly simple.
I was denied the Penfed loan! It said too many accounts open. I don't have that many, so I called to ask. I made the mistake of being a co-signer which they are counting against me. The loans I co-signed for are all in a good state and always have been.
Oh sorry to hear that. Those loans must be affecting your DTI?
Sorry to hear about not being approved, and yes co-signed loan will count against your DTI.
Did you try SoFi.com with the soft pull pre-approval?