Refinance and break-even arithmetic

A refinance comparison on this site is two loans priced with the same formula, then subtracted. The engine prices the payment that clears the balance you enter over the months you have left at the current rate, prices a second payment that clears the same balance over the new term at the new rate, and reports the difference. The closing costs you enter are divided by that difference to give the break-even month. Nothing else goes in. This guide walks through each step on fictional inputs and lists what the comparison leaves out. Every figure below is computed, when this page is built, by the engine that powers the Refinance Calculator and the Refinance Break-Even Calculator.

What the engine computes

Both refinance calculators run the same seven steps. The only formula is the standard amortized-loan (PMT) formula with monthly compounding — the convention behind US mortgages and most consumer loans, derived in How the monthly payment formula works — followed by multiplication, subtraction and one division.

1. Current payment. PMT on the current balance, the current rate ÷ 12, and the remaining months.
2. New payment. PMT on the same balance, the new rate ÷ 12, and the new term.
3. Monthly saving. Current payment − new payment. It can be zero or negative.
4. Break-even. Closing costs ÷ monthly saving. When the saving is not positive the engine returns no break-even, because there are no savings to recoup with.
5. Interest left on the current path. Current payment × remaining months − balance.
6. Interest over the new loan. New payment × new term in months − the amount refinanced.
7. The lifetime line. The Refinance Calculator reports a lifetime saving: interest left − new interest − closing costs. The Break-Even Calculator reports extra lifetime interest: new interest − interest left, before costs — unless the costs are rolled into the loan, in which case they enter through the larger amount refinanced (see below). Same inputs, opposite sign, and only the first subtracts the costs as a separate term.

The interface layer only formats and displays what the engine returns — it never does its own arithmetic. The same holds for this page: if the copy and the code ever disagreed, the site would fail to build rather than publish inconsistent numbers.

A same-term example, step by step

Take a fictional $240,000 balance at 7.25% with 24 years left, and an offer of 6% over 24 years with $4,800 of closing costs, not financed. Because the new term equals the remaining term, the comparison isolates the rate.

The monthly saving is the current payment minus the new payment, computed at full precision: $186.31. The two payments in the table are rounded to the cent for display, so subtracting the displayed figures can land a cent away from the engine's result. Dividing the $4,800 of costs by the saving gives 25.8 months, which the tool pages round up and display as 2 yr 2 mo. The interest left on the current path is the current payment × 288 − $240,000, which at full precision comes to $267,068; the new loan accrues $213,412 over its 288 months. Subtracting the second from the first and then the costs leaves a lifetime saving of $48,856. Every line points the same way here: a lower payment, a finite break-even, and less interest overall.

Why payment × months − balance is the schedule total

The refinance engines do not walk a month-by-month schedule. For a fixed-rate, fully amortizing loan they do not need to: every payment is the same, so the sum of payments is payment × months, and the part of that sum that is not the balance repaid is interest. The amortization engine — which does compute the schedule one month at a time so that extra payments and payoff dates are exact, as How amortization works describes — agrees on the fictional loans to the cent: $267,067.92 from the schedule against $267,067.92 from the closed form for the current loan, and $213,412.04 against $213,412.04 for the new one. The build checks that agreement.

The break-even month is a quotient

Break-even is closing costs ÷ monthly saving and nothing more. It counts from the first payment on the new loan, not from a calendar date. It treats the saving as the same amount every month, which holds because both payments are fixed. And it says nothing about the balance: the two loans reduce principal at different speeds, and the quotient ignores that — the lifetime line is where the balance comes back in. The engine returns the exact quotient; the calculator pages round it up to the first whole month by the end of which the accumulated saving equals or exceeds the costs. In the example above that is the difference between 25.8 and 2 yr 2 mo.

A term reset, month by month

The Refinance Break-Even Calculator takes terms in months, so the remaining term can be entered as years plus months. Take a fictional $210,000 balance at 6.75% with 14 yr 6 mo left, and an offer of 5.5% over a fresh 30 yr with $5,400 of costs, not financed.

The payment falls from $1,895.50 to $1,192.36, a saving of $703.14 a month, and the break-even quotient is 7.7 months — 8 mo once rounded up. Taken alone, those two lines point one way. The lifetime line points the other: the current path has $119,816 of interest left over its 174 months, while the new loan accrues $219,248 over 360 months — $99,432 more lifetime interest, before counting the costs. The engine's own note on this result calls it the term-reset trap, where a lower payment stretched over a restarted clock costs more overall. Both figures are correct. The payment is lower because the debt is spread over more months; the interest is higher for the same reason.

Setting the new term equal to the remaining term shows the rate effect on its own. The same offer over 14 yr 6 mo gives a payment of $1,754.07, a saving of $141.43 a month, a break-even of 3 yr 3 mo, and $24,609 less lifetime interest — the lifetime line changes sign.

What rolling the costs into the loan changes

With the roll-in option on, the amount refinanced becomes the balance plus the closing costs — $210,000 + $5,400 = $215,400 in the reset example — and the new payment is priced on that larger amount: $1,223.02 instead of $1,192.36. The monthly saving shrinks to $672.48, and because the engine still divides the entered closing costs by the saving, the break-even stretches to 9 mo. The new loan's interest is computed on the financed amount, so the extra lifetime interest rises to $105,070.

When the new payment is not lower

A fictional $180,000 balance at 5.5% with 12 years left, offered 6.25% over 12 years with $3,000 of costs, gives a current payment of $1,710.31 and a new payment of $1,779.91. The monthly saving is −$69.60: the new payment is $69.60 higher, so the engine returns no break-even, and the Refinance Calculator reports the break-even as never (new payment is higher). The lifetime line still computes: $66,285 left on the current path against $76,306 on the new loan, a lifetime saving of −$13,022 after costs — that is, $13,022 more cost after costs, which is how the calculator displays it. A negative lifetime saving is a valid output: the new loan costs more on both lines.

What the comparison does not include

• Only principal and interest. The refinance engines take a balance, two rates, two terms and a closing-cost figure. Property tax, insurance, PMI and HOA are not in the comparison; on the Mortgage Calculator they are estimates from the rates and amounts you enter.
• Fixed-rate, fully amortizing loans only. As the methodology page states, the calculators do not model adjustable-rate mortgages, interest-only periods, balloon payments, or negative amortization.
• Rates and costs are your inputs, not quotes. The calculator pages say it directly: rate quotes are lender-specific, and closing costs are lender- and deal-specific. The engine computes from the figures entered and has no other source for them.
• No calendar, no discounting, no holding period. Break-even counts payments from the first one on the new loan; money is not discounted; interest already paid never enters the engine, which starts from the balance you type; and how long the loan will be kept is not an input — the break-even is a month count to set against it.
• Rounding. Internally every calculation keeps the full precision of IEEE-754 double-precision arithmetic; on screen money is rounded to the cent, or to whole dollars for large totals like lifetime interest. Your lender's figure may differ by a few cents depending on their rounding and day-count conventions — the difference is presentational, not an error.

Common misreadings

• A lower payment is read as a lower cost. The reset example has a payment $703.14 a month lower and $99,432 more lifetime interest. The payment line and the lifetime line answer different questions.
• A short break-even is read as a verdict. It marks the month by which the costs have been recovered from monthly savings, on a cash basis. The lifetime line is separate and can carry the opposite sign at the same time.
• "Interest left" is read as interest over the whole original loan. It is counted forward from the balance entered. Interest already paid never enters the engine.

Frequently asked questions

Not financial advice: this guide explains the arithmetic the refinance calculators perform on the figures you enter. The calculator models the arithmetic; it does not know your lender's terms. Your lender's figure may differ by a few cents depending on their rounding and day-count conventions — the difference is presentational, not an error. Values are processed locally in your browser and never transmitted. See the methodology page and the guides index.