What a discount point buys
A discount point is prepaid interest. You hand the lender 1% of the loan amount at closing and the lender writes the note at a lower rate. On a $300,000 loan, one point is $3,000 and typically buys somewhere between an eighth and three eighths of a percentage point off the rate — 0.25 is the common quote, but it moves daily with the secondary market and it is never a fixed law.
Two things follow immediately. First, the cost is certain and paid today; the benefit is a stream of smaller payments spread over years. That is a classic present-value problem, not a subtraction. Second, the benefit stops the moment the loan does. Sell the house, refinance, or pay the loan off, and every future payment saving you were counting on disappears. Points are a bet on how long you will keep this specific note — not on how long you will own the house.
Because Regulation Z treats bona fide discount points as a prepaid finance charge, they are folded into the disclosed APR on your Loan Estimate. That is why a loan with points shows an APR meaningfully above its note rate, and why comparing two offers on note rate alone is misleading. The loan APR calculator shows how large that gap gets.
The three numbers that answer the question
The simple break-even. Divide what you paid by what you save each month:
break-even months = points% × loan ÷ (M(base) − M(bought down))
Both payments come from the standard amortised loan formula M = P·r/(1 − (1+r)−n), with r the annual rate divided by twelve and n the number of payments. Notice that the loan amount appears in the numerator and, through M, in the denominator too. It cancels. The break-even month for one point at a given rate, reduction and term is the same on a $150,000 loan as on a $1.5 million one.
Interest saved to maturity. If you never sell and never refinance, the total saving is simply the monthly saving multiplied by the number of payments, because both loans start at the same principal and both finish at zero: (M(base) − M(new)) × n. This is the largest and least likely of the three figures — most mortgages are retired long before maturity.
Net present value. The simple break-even leaves out two real effects. The savings arrive over time, so they are worth less than face value — that is what the discount rate corrects. And the lower-rate loan pays down principal faster, so at any moment before maturity you owe less on it. That balance advantage is real money you collect when you sell. The calculator adds it:
NPV = PV(monthly savings over h months) + PV(balance advantage at month h) − point cost
Set the discount rate to what your cash would otherwise earn after tax. A cautious saver might use a Treasury yield; someone who would instead pay down a card balance should use that card's rate, which is usually far higher and makes points look much worse.
Worked example: one point on a $300,000 loan at 7%
A lender quotes 7.00% with no points, or 6.75% for one point, on a 30-year fixed loan of $300,000. You expect to keep the loan seven years and you value cash at 4%.
- Cost. One point on $300,000 is 0.01 × 300,000 = $3,000, due at closing.
- Payment at 7%. The published factor is 6.65302 per $1,000, so M = 6.65302 × 300 = $1,995.91.
- Payment at 6.75%. The factor is 6.48594 per $1,000, so M = 6.48594 × 300 = $1,945.78.
- Monthly saving. 1,995.91 − 1,945.78 = $50.12.
- Simple break-even. 3,000 ÷ 50.12 = 59.9 months, just under five years.
- If held to maturity. 50.12 × 360 = $18,043 of interest avoided.
- Balance advantage at seven years. After 84 payments the 7% loan stands at $273,443 and the 6.75% loan at $272,366 — a difference of $1,077 of extra principal you have already retired.
- Net present value. The 84 monthly savings discounted at 4% ÷ 12 are worth 50.12 × 73.162 = $3,667. The balance advantage discounted 84 months is 1,077 × 0.75613 = $814. Together, 3,667 + 814 − 3,000 = +$1,481.
So the answer at a seven-year horizon is yes — but only just. Move the horizon to four years and the sign flips, because you never reach the break-even month. That sensitivity is the whole point of the exercise.
How to read the break-even month
Compare the break-even month against a realistic holding period, not an aspirational one. People consistently overestimate how long they keep a mortgage: rate moves trigger refinances, jobs move households, and adjustable loans get replaced. If your honest answer is anything under about five years, a break-even near 60 months is a coin flip, and a break-even beyond 100 months is a clear no.
Read the sign of the net present value rather than the break-even alone when the two disagree. The break-even ignores the balance advantage, so it is the harsher test; NPV can be positive slightly before the simple break-even is reached, because you also collect the extra principal at sale. The gap between them is small at low rates and widens as rates rise, since a higher rate means a larger share of each payment is interest and a bigger difference in amortisation speed.
Be careful about the reduction per point. Lenders rarely offer a constant exchange rate: the first point often buys 0.25, the second 0.20, the third less again. If you enter one figure and apply it to three points, you will overstate the saving. Get the actual rate sheet and price each step separately.
Finally, remember what the alternative use of the cash is. Three thousand dollars applied as extra principal instead of as points also reduces interest — check that path with the extra payment payoff calculator before deciding. And if the same $3,000 would otherwise clear a revolving balance at 22%, the mortgage buydown is not the best use of it; the debt consolidation calculator frames that comparison.
Break-even months for one point, 30-year fixed
| Base rate | Buys 0.125% | Buys 0.25% | Buys 0.375% |
|---|---|---|---|
| 5.00% | 131 mo | 66 mo | 44 mo |
| 7.00% | 119 mo | 60 mo | 40 mo |
| 9.00% | 111 mo | 56 mo | 37 mo |
Each cell is 0.01 divided by the difference between the two per-dollar payment factors r/(1−(1+r)⁻³⁶⁰). A larger reduction per point shortens the break-even roughly in proportion; the base rate matters much less than the size of the reduction you are offered.
Mistakes that distort a points decision
- Assuming a constant reduction per point. Rate sheets price the second and third point worse than the first. Apply the sheet's actual steps rather than multiplying the first one.
- Confusing discount points with origination points. An origination point is the lender's fee and buys you no rate reduction at all. Only bona fide discount points belong in this calculator.
- Using the length of home ownership instead of the life of the loan. A refinance ends the buydown just as surely as a sale does.
- Ignoring who pays. Seller-paid or lender-credit points change the cash flow completely. If the seller funds the buydown, your outlay is zero and the break-even question disappears.
- Forgetting the tax treatment. Points on a purchase of a principal residence may be deductible in the year paid, while points on a refinance are generally amortised over the loan term. That shifts the after-tax cost and it depends on your circumstances — check IRS Publication 936.
- Comparing a points loan to a no-points loan on note rate alone. That is exactly the comparison APR exists to fix.
A temporary buydown is not the same thing
A 2-1 or 3-2-1 buydown reduces the rate only for the first two or three years, after which the note rate applies. The upfront cost is funded into an escrow account that subsidises the early payments. That is a cash-flow product, not a rate reduction, and the arithmetic here does not describe it: the payment saving stops on a fixed date regardless of how long you keep the loan. Permanent discount points change the rate for the entire term.
Where points sit among the levers
Points, term and down payment are three different ways of spending money to reduce interest, and they are not interchangeable.
Points lower the rate and leave the payment schedule shape intact. The benefit is proportional to the balance outstanding, so it is largest early and shrinks as you amortise — which is precisely why a short holding period kills it.
A shorter term usually carries a lower rate as well, and cuts total interest far more aggressively, but it raises the required payment and removes flexibility. Compare a 15-year note against a 30-year one with the mortgage payment calculator before assuming points are the cheaper route.
A larger down payment reduces the balance the rate applies to, and below 80% loan-to-value it also removes mortgage insurance. Dollar for dollar, escaping PMI often beats buying points; the PMI calculator quantifies that threshold.
Accelerating payments costs nothing to arrange and can be stopped at any time, which points cannot. The biweekly payment calculator shows what a thirteenth annual payment is worth on the same loan.
The calculation here uses the ordinary fixed-rate amortised loan formula and assumes a fixed rate for the full term, no prepayment penalty, and points paid in cash at closing rather than financed. If you roll the points into the loan balance, the comparison changes: you are then paying interest on the points themselves, and the break-even lengthens. And if you plan to refinance the moment rates fall, price that scenario with the refinance break-even calculator and use the shorter of the two horizons.