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If I can drop from 4.375% APR to 3.7% (or slightly lower) by going from a 30- to a 20-year note, I can save over $100,000 in interest over the life of my loan. However, like most folks, I have no idea if I will still be in this house 20 years from now. Is this a bad idea? My payments will go up slightly ($150/month), and allegedly I can deduct the points from my taxes (in the US), but how long would I need to stay in this house before selling would represent a financial mistake, on, say, $4000 closing costs?

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For a refinance, you deduct the points over the terms of the loan, here 1/20 per year.

Since you don't mention the mortgage balance, I'll offer a back of envelope answer. You will save .675%/yr on the declining balance. If your loan is $200K, it will take about 3 years to break even, saving the $4000 cost. After that, it's all gravy. You can use your own balance and get a precise calculation.

  • Loan value would be $340K. When I punch the numbers into the BankRate mortgage refinance break even calculator, it says that my break even on "total savings after taxes" would be 30 months, but then says that "total savings vs prepayment" is 43 months. Does that basically say that if I just prepaid on the current note to the tune of the additional amount I'm going to be paying for the shorter note, it would take 43 months of doing that before the shorter note would surpass, in terms of producing greater long-term interest savings? – defurr Nov 23 '16 at 2:15
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This is a fairly straightforward math problem, but you haven't given us all of the variables. You can build a spreadsheet showing monthly payment, balance, interest, and PMI, etc. and calculate this yourself.

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