But you could just as easily lose your job in the 13th year of a 15 year note and have a higher payment to come up with than if you have a bad spot. I may lose my job, or I may not. But one thing is for certain...if I don't refinance, I still have $90k of interest to pay. A refi will lower my rate 2 pts and increase my monthly payment by $66.00 and cuts my interest down to $40k. Yeah, I lose my interest deduction sooner, but so what? That means that $50k won't be going to service my debt. That's money in my pocket. My lost tax benefit is no where near that amount.
But this isn't about tax deduction though.
Your payments relative to your income and via inflation will be significantly cheaper the farther you go.
The more money is spent immediate to the time of borrowing, the closer to its real value. Which is high value cash that could be put elsewhere rather than the bank.