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Why does paying the same amount at a lower rate accelerate payoff?

A lower rate means less interest is charged each month, so more of every payment reaches your principal balance.

Interest is charged on the balance you still owe. When your rate drops, less of each monthly payment is needed to cover interest — which means more of it reduces your principal. If you also keep paying your old, higher payment amount, even more extra money goes to principal every month. A smaller balance then generates smaller interest charges the next month, and the effect compounds over the life of the loan.

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