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True, but if you pay a normal 30-year mortgage, you end up paying much more in interest (twice as much, no?) than what the house is actually worth. Even if you pay it off quicker, you still pay much more. I haven't done the math, but wouldn't it be faster to live in a *very* cheap room and save up the money for the house, and then, in about 10 years, pay cash? That way, compound interest works with you instead of against you.
But the interest payments are tax-deductible, so you're really only paying a portion of that interest. In the early years of your loan, your equal monthly payments consist of predominantly interest, so the effect is especially powerful. And the higher your marginal income tax rate is (federal plus state plus sometimes even local), the more compelling the deductions are.
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