Ryan, it all depends on what your house appraises for now, and what your loan balance is. So long as the balance is under 80% of the appraised value you won't need the insurance. Also, most 30 yr fixed mortgages do not have a penalty if you pay them off early (past the first couple of years), so I recommend staying with a 30 yr mortgage and making extra principal payments. That will pay it off in 15 or 20 years (depending on how much extra you pay), saving you all the interest just like you had a 15 or 20 yr mortgage, but if times get tough you can just drop back to the regular payment which will be a lot lower with a 30 yr mortgage than a 15 yr mortgage. Sort of a free insurance thing

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All true + great advice, but,If you have good credit you should be able to refinance to a much better rate then the 6.25 + still do the 30 yr.
You can also set it up so that you pay bi-weekly,instead of monthly,which makes 1 extra payment a yr.+ takes something like 7 yrs off of the mortgage + you barely even notice that you made an extra payment,I think you set up an account + they take it out automatically,+ i believe they give you a slightly better rate too if you do it that way,+ it makes life easy because you don't have to send a check every month + you get the other benefits i mentioned also.It's been a while since i've done a mortgage but i always did it that way + it works out great,+ you can also do the extra principal payments on top of that as ijames stated,+ cut even more time off the mortgage.Your bank can give you more info on all this.
Also,there is almost always closing costs on a refinance, but they can usually roll them into the new mortgage,so there is "no money out of pocket", which is what may have been the case of the lady on the Clark Howard show,+ not actually "no cost".
In a way it is no cost,because you didn't actually lay out any extra cash,but closing costs are added to the mortgage balance,but it is offset by a lower interest rate +lower payment ,so it is like "No Cost" in the long run.
It will all hinge on how good your credit score is + how much equity you have in your house, if it will work or not. Good Luck