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Goal 2) You have to go through a HAFA certified agent to get a loan modification through HAMP. It gives a process and is federally backed. This process is suppose to be faster yet you need to have a financial hardship. Or do a normal loan modification to lower the interest rate. The amount of interest you will save will help you will your retirement. You are thinking long term so you have an advantage. The market should bounce back. I don't know if the IRA would work but you can ask a lender. Renting sounds like a great idea, but know there is work involved.
thanks for the additional details. Is your current payment based on a loan amount close to the $108,000?
Some things to consider, if you re-fi with the intent to rent out the home and no longer use it as your primary residence you will most likely be at a higher interest rate than if a re-fi for your primary residence, also you will most likely be required to have 20% equity for an investment property. You need to talk to a mortgage broker for the details.