Should you pay points on a mortgage? The break-even math
A lender offers two versions of the same mortgage: a lower rate if you pay points upfront, or the standard "par" rate with no points. The points offer has the smaller monthly payment, so it looks like the obvious pick — but you paid cash today for a saving that arrives a little at a time. Whether that trade is worth it comes down to one question: how long will you keep the loan?
The method
The monthly payment on an amortizing loan is M = P × r / (1 − (1 + r)^−n), where P is the amount borrowed, r is the monthly interest rate (annual rate ÷ 12 ÷ 100), and n is the number of monthly payments. Compute M for both offers. The monthly saving from the lower rate is M(par) − M(points). Divide the upfront points cost by that monthly saving and you get the break-even month — the point at which the accumulated monthly savings finally cover what you paid upfront. Keep the loan past that month and the points offer wins; sell or refinance before it and the par offer would have cost less.
A worked example
A $300,000 mortgage, 360-month (30-year) term. Offer A: 3.5% with $8,000 in points. Offer B: 4.25% at par, no points.
- Offer A's monthly rate:
3.5 ÷ 12 ÷ 100 ≈ 0.0029167. Payment:300,000 × 0.0029167 / (1 − 1.0029167^−360) ≈ $1,347.13. - Offer B's monthly rate:
4.25 ÷ 12 ÷ 100 ≈ 0.0035417. Payment:300,000 × 0.0035417 / (1 − 1.0035417^−360) ≈ $1,475.82. - Monthly saving:
$1,475.82 − $1,347.13 = $128.69. - Break-even:
$8,000 ÷ $128.69 ≈ 62.16months — so the 63rd payment is the first one where the points offer is ahead.
Keep the loan the full 30 years and the points offer saves ($1,475.82 − $1,347.13) × 360 − $8,000 = $38,328.40 over the par offer. That is the number lenders like to show. It assumes you keep the loan for 360 months, which is rarely true — the average homeowner refinances or sells well before then.
What happens if you sell in 7 years
Say you actually expect to sell or refinance at 84 months (7 years), well past the 63-month break-even. Total cost at that point, upfront fees plus every payment made so far:
- Offer A:
$1,347.13 × 84 + $8,000 = $121,158.92. - Offer B:
$1,475.82 × 84 = $123,968.88.
Offer A still costs $2,809.96 less at 7 years — past break-even, so it wins, just by a much smaller margin than the 30-year headline number suggests. Sell at month 40, before break-even, and the comparison flips: the points paid would not yet have been recovered, and the par offer would have been cheaper.
Why total cost, not APR
APR tries to fold points and fees into one rate, but it assumes you hold the loan to the end of its term — the one assumption most buyers don't actually meet. Comparing the two payments directly and computing your own break-even month answers the real question: given how long you actually expect to keep this loan, which offer costs less? That number depends entirely on your own timeline, which no rate disclosure knows.
What this doesn't include
This is payment and break-even arithmetic only. It doesn't include property tax, insurance, PMI, or opportunity cost on the $8,000 paid upfront (money that could otherwise sit invested), and it doesn't predict how long you'll actually keep the loan — that estimate is yours, and the honest move is to check the answer at a few different horizons rather than trust one guess.
Run your own numbers
The free Loan Side-by-Side tool compares up to four offers at once, computes the break-even month between every pair automatically, and ranks them both over the full term and over a horizon you choose — entirely on your device.