Ignoring unusual complications, the amount saved on taxes should always be some fraction of the interest savings. So interest savings should definitely be higher than tax savings. Example, if you pay 1,000 per month on interest and your marginal tax rate is 30%, then you pay 12,000 in interest for the year and you save .30 * 12,000 in taxes. The tax savings isn’t going to be more than the interest itself. Possible complications, like not itemizing, hitting the alternate minimum tax, hitting limits on deductibility are only going to reduce the tax savings but not change the interest cost. The tax deduction reduces the sting of paying interest each month but it should never more than offset it.
That said, there are other valid reasons to hold off paying down a mortgage. The money you take out of savings to pay off the mortgage is now no longer earning interest or investment gains. If you have a low interest rate mortgage, it’s possible the lump sum you take out of savings for paying off the mortgage, could have earned more than the interest you saved. Say your mortgage rate is 3%. By taking 300,000 out of savings and paying off the mortgage, you will save approximately 9,000 in interest next year but lose a tax benefit of .30 * 9,000 so your net savings is $6,300. If that same 300,000 was left in the stock market for the year and the market rose 10% then you would have gained 30,000 but then had to pay taxes of .3 * 30,000 on that gain for a net gain of 21,000. But of course the rate of return on the stock market is not guaranteed. So this consideration really comes down to where the money would otherwise sit if you didn’t pay off your mortgage and your risk tolerance, ie the peace of mind PPs have referred to.
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