Mortgage extra payment calculator

A scheduled amortising payment is sized to clear the loan on a fixed date. Part of it is that month's interest, and the rest reduces principal. An extra amount paid against principal does not change the scheduled figure. It just makes that month's principal reduction larger, so next month's interest is calculated on a smaller balance.

On $300,000 at 6.5 percent over 30 years the scheduled payment is $1,896.20. The first month's interest is $300000 \times 0.065 / 12 = 1625$, so $1,625, and the rest of that scheduled payment is principal. Add $200 extra and that month's principal reduction is larger by exactly that extra. The extra does not sit in a side account. It comes off the balance before the next interest charge is computed.

That is the same mechanism the loan payment calculator already shows, run with a higher payment. The reason this page exists is the comparison: the original schedule against the faster one, in months and in interest, so the extra has a price in time rather than only a price in cash.

The closed-form month count is a logarithm. Each extra dollar raises $p$ and shortens $n$, but the shortening is not linear. On the default loan, $200 extra cuts 83 months off 360. Another $200, taking the extra to $400, cuts 132 months off the original term, which is 49 months more, not another 83. The second $200 still helps. It helps less than the first $200, because the easy months to remove are the last ones, where the scheduled payment is almost all principal already.

That flattening is the picture on the extra-payment explorer. It is also why 'pay an extra $200' and 'pay an extra $400' are not twice the decision. The first increment takes the longest, highest-interest tail off the loan. The next increment is working on a shorter remaining tail.

Interest saved is the other reading of the same fact. The original schedule on this loan pays $382,633.47 of interest. With $200 extra that falls to $279,184.67, a cut of $103,448.79. With $400 extra it falls to $222,801.45, a cut of $159,832.02. Again the second increment is real and smaller.

The logarithm is only defined when $p$ is larger than that month's interest. If the combined payment does not cover $iB$, the balance grows, and there is no payoff date to compute. The calculator returns that case as a statement rather than as an infinite number of months, because 'infinity months' is not an answer a reader can use.

On a 6.5 percent loan the first month's interest on $300,000 is $1,625. A payment that does not cover that interest, extra or not, never catches up. This is the same trap the credit card payoff calculator names for revolving balances, and it is rarer on a mortgage only because the scheduled payment is already set above that floor. It becomes relevant if someone cuts the payment below the schedule, or if a teaser rate ends and the new interest exceeds what they had been paying.

Prepayment penalties, the lost return on the extra dollars if they would otherwise have been invested, and the value of a cash buffer all sit outside this page. The arithmetic answers one question: if this extra is paid against this loan every month until it clears, how many months and how much interest come off. Whether those dollars should be the extra is a different question, and paying down debt versus investing is the place that comparison starts.

The extra is also assumed constant. A rising extra, a one-off lump, or a refinance into a new rate is a different schedule. A lump at the start is a smaller principal; put it in as a lower amount borrowed. A refinance is the refinance break-even calculator.