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Right- car is a 2014 with 125,000 miles so it's definitely possible they won't refi at all. My income is about $63,000/yr, and I have about $35,000 of my own student debt from grad school to pay back but that has been put on hold until at least Sept.
You have quite a lot piling onto your plate, so I think at this time you should forgo the car refi. Simply because it's another HP you can do without at the moment. And it wouldn't really do much good unless you have the cash to makeup the difference. Which would also take away cash from your down payment on a second vehicle, one that you don't want to be in the same situation with later.
The best way to ride out being upside down is to just finish out the loan and use it as a secondary car, or just sell it outright.
@Anonymous i will echo this definitely ride out the car loan.
@Anonymous @Now to get to the student loan. My opinion is to utilize either citizens or discover (discover definitely does 2 years for removal) and have your son check for pre qualifications for credit cards and get one to use responsibly. The reason this is so important is because there are loans out there that require as little as $10k income 2 years credit history (revolving) and a 660 score or higher and if you hit all of those things they will allow your son to sign on his own loan.
this is kind of my thought process.... co-sign for your son have him get a credit card and make minimum payments ($50-$60 bucks a month) on his student loan balance whether that is made by him getting a job or by you this will start the clock on the release of co-signer requirements. I would recommend using some of the work study money to make 60 dollar a month payments for two years and then request to release you as a co-signer. Now at this point his credit should meet requirements for quite a few lenders because of 2 years of positive payments on student loans and 2 years of responsible credit card use and in two years you are off Scott free of all of the loans and future loans while still putting your son in a position to succeed.