Accelerated amortization
Extra principal lowers the outstanding balance faster than scheduled amortization, reducing the interest accrued in subsequent periods. The effect compounds, which is why even modest extra payments can remove years from the payoff horizon.
Opportunity cost
Paying extra on a mortgage delivers a guaranteed return equal to the loan’s interest rate. Compare this to alternative investments—if you can reliably earn more elsewhere after taxes, it may be worth investing the surplus instead.