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You can just think of your interest rate plus your MIP as one rate. If you have a 3.375% rate and you are paying 1.25% annual MIP (not sure what your rate is, it would depend on when in 2012 you got your case number and what loan product you have), you effectively have a 4.625% rate. Can you get better than that with a refi?
Even if you can get better than 4.6%, how much better? How long are you going to stay in the house to recoup the costs for the refi? You said you think your house may have depreciated? Are you going to have to bring cash to close? Will you be at greater than 80%LTV and need PMI? If so, you're going to have to factor that in as well.
Walt makes excellent points and brings up questions that need to be considered.
agree with walt and shane.....
remember.... that pmi is why you got that awesome rate and didnt pay much more