You are missing one important thing: inflation.
Every dollar you pay on the mortgage principle today will be worth less tomorrow. You can pay off a 300.000 dollar mortgage over 30 years, but by the end of it that 300.000 dollars might be the price of a midsize family van instead of a house.
Obviously, not paying down the principle has a cost too since the interest stays high, but it could be worth calculating which approach is best financially.
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