The short answer to the question is: "It's all in the numbers."
How do you get the numbers?
First, you need to obtain an ACCURATE Good Faith Estimate of Settlement Costs from your Mortgage Broker (a Mortgage Broker will have access to more programs and options than your "Bank" or "National Lender" will).
Then you calculate your monthly savings based on your Current Mortgage Payment minus your New Mortgage Payment. Your Mortgage Broker can help you with the calculations. If you can recapture the cost of refinancing (through the lower payments) in 24 to 36 months then I would consider it worthwhile. (This assumes that you will be keeping the loan on this property long enough to recapture the cost of refinancing.)
When you refinance your mortgage the loan amount will be based, in part, on the current appraised value of your home. If the value is high enough you may be able to eliminate the PMI that you may be currently paying or pay off that "piggyback" loan that you took out when you originally purchased your home. The potential savings from either of these items may be more valuable to you than the benefit received from a lower interest rate. Again, your Mortgage Broker can help you figure it out.
If you are "shopping rates" always ask for a Good Faith Estimate from the Loan Officer you are talking to - if they can't or will not provide you with one, hang up - they are probably one of the "Bait and Switch" outfits that unfortunately still exist in out industry.
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Additional Benefits to consider:
You might also be able to "cash out" some of the built-up equity in your home, which you can use to consolidate debt, improve your home, take a vacation -- whatever! With lower rates and balances, you might also be able to build up home equity faster with a shorter-term new mortgage.