A discount point is a fee paid to the lender at closing in exchange for a lower interest rate. It is not a discount on the loan — the loan is the same size. It is money now against a smaller payment later, and the only question that decides whether it is a good idea is how long you will keep the loan.
Someone has been offered a lower rate in exchange for paying a fee at closing and wants to know how long they would have to keep the loan for that fee to be worth paying.
One point costs one per cent of the loan amount. On $300,000 that is $3,000, paid at closing, and it does not reduce what you owe — the loan is still $300,000. What changes is the rate: at the conventional quarter-point-per-point, the rate falls from 6.5% to 6.25%.
That rate cut is worth $49.05 a month on a thirty-year term. The payment goes from $1,896.20 to $1,847.15. So $3,000 today buys a $49.05 reduction every month, and the break-even is $3,000 divided by $49.05 — 61.2 months, a little over five years.
The asymmetry is what makes this a real decision rather than a formality. If you keep the loan for thirty years, the $3,000 buys $14,658.89 of net saving after the fee is subtracted. If you sell or refinance in year three, you paid $3,000 and got about $1,766 of it back. Same fee, same rate, opposite conclusions — and nothing about the loan documents tells you which one you are.
The intuitive expectation is that each additional point takes longer to pay back, since you are spending more money. The arithmetic does not work that way. On the same $300,000 loan: one point costs $3,000 and saves $49.05 a month, breaking even at 61.2 months. Two points cost $6,000 and save $97.55, breaking even at 61.5 months. Three points cost $9,000 and save $145.49, breaking even at 61.9 months.
Both sides of the division scale together. The cost is exactly proportional to the number of points, and the monthly saving is very nearly proportional to it too, because the payment falls roughly linearly with the rate for changes this small. Divide one by the other and the points cancel out, leaving a number set by the loan, the term and the reduction per point — not by how many points you buy.
It is not perfectly constant. The break-even drifts out by about seven months across the range from one point to three, because the payment reduction is very slightly less than proportional as the rate falls. That drift is small enough to be a footnote rather than a decision factor, and the useful consequence is that the choice between one point and three is about how much cash you have at closing, not about whether the third point pays off.
The term is the first. The same rate reduction spread across fifteen years instead of thirty produces a smaller monthly saving, because there are half as many payments for it to be applied to. A smaller saving against the same cost pushes the break-even further out — which is why points are usually a weaker proposition on a short loan, even though a short loan is where the interest saving is largest.
The reduction per point is the second, and it is the one people assume rather than check. A quarter point per point is conventional but it is a quote, not a rule; some lenders offer less, and the offer changes with the market. A tenth of a point per point instead of a quarter nearly doubles the break-even. This calculator takes it as an input for exactly that reason — the number has to come from the offer, not from a default.
How long you will actually hold the loan is the third, and it is the only one the calculator cannot know. The break-even month is a fact about the loan; whether you pass it is a fact about your life. Selling, refinancing, or paying the loan off early all cut the calculation short at the point where the fee has not finished being repaid.
cost = loan × points ÷ 100 new rate = rate − points × reduction break-even = cost ÷ (old payment − new payment)
The break-even is a division of two quantities that both scale with the number of points, which is why it barely moves when you buy more of them. That is the least obvious thing on this page and it is arithmetic rather than opinion: doubling the points doubles the cost and very nearly doubles the monthly saving.
A $300,000 loan at 6.5% over thirty years. One point costs $3,000 and cuts the rate to 6.25%, taking the payment from $1,896.20 to $1,847.15 — a saving of $49.05 a month. The break-even is 61.2 months, or 5.1 years. Held for the full term, the net saving after the fee is $14,658.89. Sold in year three, the fee has returned about $1,766 of its $3,000.
Three points cost $9,000 and take the rate to 5.75%, for a payment of $1,750.72 — $145.49 a month less. The break-even is 61.9 months, which is seven months later than the single point despite costing three times as much. The net saving over the full term is $43,374.78. The lesson is that the extra two points do not extend the payback period meaningfully; they scale the whole position up.
With the points set to zero the calculator reports the quoted loan unchanged: the rate stays at 6.5%, the payment at $1,896.20, the cost of the points at $0 and the net saving at $0. The break-even is not a number here, and the calculator says so rather than printing zero months or an infinity. This is the baseline every other figure on the page is measured against, and it is the right comparison whenever the alternative to points is simply not buying them.
On a $300,000 loan at 6.5% over thirty years, with a conventional quarter-point reduction per point, about 61 months — a little over five years. That figure barely changes with the number of points: one point breaks even at 61.2 months, three points at 61.9 months. What moves it is the term, the reduction per point, and the rate.
Only if you keep the loan past the break-even month. If you expect to sell or refinance before then, the fee is a loss, because the benefit arrives entirely through the lower payment and you stop receiving it when the loan ends. The calculator cannot answer this part — the break-even is a fact, and your holding period is not.
In the United States, points paid on a mortgage used to buy or improve a principal residence are generally deductible in the year paid, while points on a refinance usually have to be spread across the life of the loan. The rules have conditions and this is not tax advice; a tax professional or the IRS publication on mortgage interest is the authority.
Because the payment is a nonlinear function of the rate. The relationship is close to linear for small changes, which is why the break-even barely moves, but the curvature is real and grows as the rate falls. That is the source of the seven-month drift between one point and three.
Yes, and the same break-even logic applies with a shorter clock. On a refinance the question is not how long you will keep the house but how long you will keep this particular loan before refinancing again — which is usually a shorter period, and makes the break-even harder to reach.