Mortgage Discount Points and the Break-Even Math
Educational explainer, not financial or lending advice — every dollar figure below is computed at build time by the same tested engine that powers this site's calculators. The rate quotes in the example are illustrative, current as of September 2026, and change over time; actual point pricing varies by lender and by day. Principal and interest only — taxes, insurance, and escrow are out of scope.
A discount point is one of the few line items in a mortgage offer whose entire logic fits on an index card: pay some interest up front, owe less interest every month after. Whether a given point trade recovers its cost is not a matter of opinion or prediction — it is a division problem, and this page works one example of it end to end: what a point is, what one point does to a $300,000 loan, where the 61-month break-even comes from, and why the break-even only means something next to a second number the arithmetic cannot supply — how long the loan actually survives.
One point is 1% of the loan — by definition
A discount point is prepaid interest. One point costs 1% of the loan amount — that part is a definition, not a quote — and buys a permanently lower note rate for the life of the loan. On a $300,000 loan, one point is $3,000, and fractional points scale the same way. What the point buys is the negotiable half: the rate reduction per point differs by lender, loan program, and day, so the same 1% of loan can purchase different amounts of rate at different desks. Points are also distinct from origination fees, which are often quoted in "points" too but are charges for making the loan rather than a rate buydown — a loan estimate lists the two separately.
The worked trade, computed in full
Start at the quoted rate. A $300,000 thirty-year fixed loan at 6.50% carries a principal-and-interest payment of $1,896.20 a month, from the standard amortization formula. The very first payment splits into $1,625.00 of interest (the full balance times one month of the 6.50% rate) and only $271.20 of principal; held for all 360 payments, the loan accrues about $382,633 of total interest. That split and its drift over the term are the subject of the How Amortization Works guide.
Now the trade. Suppose one point — $3,000 — buys the rate down to 6.25%. The engine recomputes:
| Scenario | Rate | Monthly P&I | Upfront cost |
|---|---|---|---|
| Quoted, no points | 6.50% | $1,896.20 | $0 |
| One point paid | 6.25% | $1,847.15 | $3,000 |
| Difference | 0.25 pp | $49.05 saved/mo | $3,000 |
The point converts $3,000 today into $49.05 of payment relief every month the loan exists at that rate. The Mortgage Points Calculator runs this exact computation for any loan amount, rate pair, and number of points, and the Mortgage Calculator rebuilds the full payment at either rate.
The break-even is a division problem
When does the monthly relief repay the upfront cost? Divide one by the other:
$3,000 ÷ $49.05 ≈ 61 months (5 yr 1 mo)
The savings accumulate $49.05 at a time; around month 61 — roughly five years in — the accumulated total passes $3,000. Every month before that, the trade is net-negative: money has been paid that the savings have not yet returned. Every month after, it is net-positive, and the surplus grows by $49.05 a month for as long as the loan survives at that rate. Nothing about the borrower's intentions appears anywhere in that fraction — which is exactly why the fraction alone cannot settle the question.
The horizon is the other half of the comparison
The break-even is one number; the decision structure needs a second one: the number of months this loan is actually expected to exist at this rate. A sale ends the loan. A refinance ends the loan. Either event stops the $49.05-a-month accumulation instantly, and the unrecouped remainder of the $3,000 is not refunded — the bought-down rate dies with the note. So the entire mechanical content of a points decision is a comparison between two durations: expected months in the loan versus break-even months. Longer than 61 months, the arithmetic favors the point; shorter, it does not. How anyone estimates their own horizon — job, family, neighborhood, the chance that rates fall far enough to make refinancing attractive — is outside what a calculator can supply. The same duration-versus-duration comparison governs refinancing closing costs, where the Refinance Break-Even Calculator performs the identical division with different inputs.
Points and a larger down payment move different variables
The same $3,000 could instead be added to the down payment. The two uses of the cash pull different levers in the payment formula. A point changes the rate: the loan amount stays $300,000, and every month's interest accrues more slowly. A larger down payment changes the principal: the rate stays 6.50%, but the balance that interest accrues on is smaller from day one, and so is every payment. The shapes of the two benefits differ, too. The point's value arrives $49.05 at a time and is contingent on keeping the loan past the break-even; the smaller balance from a bigger down payment is real from the first day regardless of when the loan ends, because less was borrowed at all. Which lever moves a particular loan's numbers more is not a question with a general answer — it depends on the amounts, the rate trade offered, and the horizon — and the Mortgage Calculator recomputes the payment under either change so the two can be read side by side.
Frequently asked questions
Is one point always 1% of the loan amount?
Yes — that part is a definition, not a market quote. One discount point costs 1% of the loan amount, so on a $300,000 loan one point is $3,000. What varies by lender and by day is the other side of the trade: how much rate reduction that 1% buys. The 0.25-percentage-point reduction in this page's example is one illustrative quote, not a constant.
How is the break-even month computed?
Divide the upfront cost by the monthly payment saving. In the worked example, $3,000 ÷ $49.05 ≈ 61 months (about five years). Before that month, cumulative savings are smaller than what was paid; after it, they are larger. The Mortgage Points Calculator on this site runs the same division for any loan, rates, and points.
What happens to the points if the loan ends before the break-even?
The bought-down rate lives and dies with the loan. Selling the home or refinancing stops the monthly savings from accumulating, and the unrecouped remainder of the upfront cost is not returned. Mechanically, points paid on a loan that ends before the 61-month break-even recovered only that many months of savings — the rest is simply spent.
Are discount points the same thing as origination fees?
No. Both are often quoted in "points" (percent of the loan), which causes the confusion, but they buy different things: discount points are prepaid interest that lowers the note rate, while origination fees are charges for making the loan and lower nothing. A loan estimate lists them separately.
Does buying a point change how the payment splits between interest and principal?
Yes, as a consequence of the lower rate. Each month's interest is the remaining balance times the monthly rate, and the rest of the payment retires principal — so a lower rate shrinks the interest slice and grows the principal slice from the first payment onward. The How Amortization Works guide walks through that split in full.
Not financial advice: an educational walkthrough of the arithmetic only. Actual point pricing, rate reductions, and tax treatment vary by lender, program, and year — the figures above are illustrative, current as of September 2026, and change over time. Every dollar amount is computed at build time by the same tested engine as the calculators, so this page cannot drift from the tools. Confirm any consequential figure with a licensed mortgage professional. See the methodology page.