The month the points pay for themselves, and what they earn if you stay.

The facts, in one place.

Six quotable sentences on when buying down the rate pays.

1. A discount point is cash paid at closing to lower the rate on a mortgage. The convention is that one point costs 1% of the loan, and the rate cut it buys is the lender's to quote: about 0.25% a point is common, and the cut often shrinks after the first point.
2. The rule of thumb divides what the points cost by the drop in the monthly payment. The truer count follows the interest each loan charges month by month, and it is a little shorter, because the lower rate also pays the balance down faster, so the bought-down loan is ahead by more than the payment saving alone.
3. Example: $400,000 for 30 years at 6.75%, one point for a 0.25% cut. The point costs $4,000 and the payment falls from $2,594.39 to $2,528.27. The rule of thumb says 61 months and the interest count says 48 months. Kept 7 years, the point leaves you ahead by about $3,039.
4. When every point buys the same cut, every count pays for itself in the same month, so more points buy a larger saving, not a sooner one. When the cut shrinks, the break-even stretches: at 0.125% a point instead of 0.25%, the same point takes 96 months to pay for itself and leaves you behind at 7 years.
5. Points are an investment, and the return is the payment saving plus the lower balance owed when you leave. Kept 7 years, the example point earns about 14.6% a year, well above the 6.75% the same cash would have earned paying down the loan. Kept 3 years it earns a loss of about 14.7% a year, because the points were paid and most of the saving never arrived.
6. A seller credit toward points costs you nothing, so it has paid for itself on day one. The fair question is whether the same dollars would do more as a price cut. In the example the credit lowers the payment by $40.18 a month more than the price cut does, the price cut leaves $2,147 more equity at 7 years, and the credit is ahead overall from month 65.

By how many points you buy.

How the cost, the saving, and the break-even move with the count.

How the count works.

A discount point is prepaid interest: cash at closing in exchange for a lower rate for the life of the loan. The rule of thumb every rate sheet carries divides the cost of the points by the drop in the monthly payment. It is close, and it is slightly pessimistic, because a lower rate does two things at once. It lowers the payment, and it shifts more of each payment from interest to principal, so the bought-down loan's balance falls faster than the plain loan's. The payment saving is the part the borrower sees. The faster amortization is the part the rule of thumb misses.

The truer count treats each loan as what it costs over time: the payments made plus the balance still owed at any month. Both loans here have the same principal and the same term, so for either one that sum is the loan amount plus the interest paid so far, and the comparison reduces to the interest each has charged, month by month, against the cost of the points. The points are ahead once the interest they have saved exceeds what they cost. The verdict is read at the year you expect to sell or refinance, since a break-even reached after you have left is no break-even, and the return figure prices the same cash flows the way an investment would be priced, with the payment savings to the horizon and the lower balance at it discounted back to the cost. When every point buys the same cut, cost and saving scale together and every count breaks even in the same month, which is why the question is usually how much to buy, not whether one point pays while two do not. A lender whose cut shrinks after the first point changes that, and the slider lets you price the later points on their own terms.

A seller concession toward points is a different question, because the points cost you nothing and the fair comparison is the same dollars off the price. The price cut shrinks the loan from the first day, so it leaves more equity at any horizon if the home is worth the same either way. The credit lowers the rate on the whole loan, so it lowers the payment more, and month by month the interest it saves catches the head start the price cut had. The tool reports the month it does and the position at your horizon.

Methodology.

1. Inputs. The loan amount, the term (30 or 15 years), the rate with no points, the points bought (in eighths, from 0 to 4), the rate cut each point buys and the cost of each point as a share of the loan (both defaults from the assumption record, both the lender's to replace), the years you expect to keep the loan, and who pays the points.
2. The two loans. The rate with points is the plain rate less the points times the cut. The level monthly payment on each loan from the same principal, its rate, and the term. The cost of the points is the points times the cost per point times the loan, and the cost to you is that figure or zero when the seller pays.
3. The simple rule. The cost to you divided by the drop in the monthly payment.
4. The month-by-month count. Both loans are run to the end of the term, accruing interest and applying the payment. The bought-down loan's position at any month is the plain loan's interest so far, less its own interest so far, less the cost to you. The true break-even is the first month the position is at or above zero, and month zero when the points cost you nothing.
5. The horizon and the lifetime. At the chosen year, payments made plus balance owed plus the cost to you on each loan, and the difference. Over the full term, the interest on each loan and the lifetime saving after the cost.
6. The return. The yearly rate, compounded monthly, at which the cost to you equals the present value of the monthly saving over the horizon plus the present value of the lower balance owed at it, found by bisection. It is compared in words with the plain rate on the loan, which is what the same cash would have earned paying down principal. No return is reported when the points cost you nothing.
7. The points that pay off. The largest points count in the slider's range whose true break-even falls within the horizon, searched from the top in eighths.
8. The seller credit against a price cut. The same dollars off the price with the down payment unchanged, so the loan is smaller by the concession and carries the plain rate. Both payments, both balances at the horizon, the equity edge of the price cut (the difference in balances), the position of the credit against the price cut (payments made plus balance owed on each), and the first month the credit is ahead.
9. The chart. Interest paid so far on the plain loan and the cost to you plus interest paid so far on the bought-down loan, as two lines that cross at the true break-even.
10. Validation. The scheduled payment on a 30-year $300,000 mortgage at 6 percent ($1,798.65); zero points changes nothing; the default case ($400,000 for 30 years at 6.75 percent, one point at one percent for a quarter-point cut, kept seven years) pinned at $2,594.39 and $2,528.27, a simple rule of 61 months, a true break-even of 48 (the first month's interest saving is $83.33, and the saving grows as the bought-down balance falls faster), and a return of 14.6 percent, which a second method recovers by summing the discounted savings month by month; kept to the end of the term the balances are both zero and the return prices a level annuity of the saving; the position identity (payments plus balance less the loan equals the interest so far) on both loans; the seller-paid case with a cost of zero, a break-even at month zero, the price cut leaving more equity, and the credit overtaking it within the horizon by exactly the payments saved less the extra balance; two points costing and cutting twice as much; and a two-year stay that never pays off with a return below the mortgage rate. A transcription error fails the build.
11. Not modeled. Discounting outside the return figure, the tax treatment of points, a cut per point that changes with the count, adjustable rates, mortgage insurance, and what the cash could earn elsewhere other than the loan's own rate. Hypothetical throughout. Educational, not advice.

Revision history.

The assumption tools' history.

September 7, 2026

Added should you buy points (the bought-down loan against the plain one on the same principal and term, so the position is the interest saved less the cost of the points; true break-even as the first month at or above zero beside the simple rule; the horizon verdict; the return the points earn to the horizon as the monthly-compounded rate at which their cost equals the present value of the saving plus the lower balance owed, by bisection; the largest points count that pays off within the horizon; and the seller-paid case set against the same dollars off the price).

September 7, 2026

Added two mortgage assumption tools: refinance break-even (the simple rule, closing costs over the monthly saving, beside the month-by-month count of interest paid on each loan, where total cost is the balance plus the closing costs plus the interest so far, so the new loan's position is the interest saved less the costs; the reset-the-clock effect flagged when a longer term catches up), and 15-year or 30-year mortgage (the same cash on both paths, the 15-year payment invested after the loan is gone against the difference invested for thirty years, compared at year 15, year 30, and a chosen horizon, with the break-even return by bisection).

September 7, 2026

Added three assumption tools: Roth or traditional 401(k) (the same take-home cost grown at one return and taxed at each end, so the answer turns on the two rates; the plan limit from the annual record), pay off the mortgage or invest (two month-by-month paths, the extra to the mortgage and then the freed payment invested, against the extra invested throughout, with the optional interest deduction), and how much life insurance (the present value of the income to replace as a growing annuity, plus debts, final expenses, and education, less existing coverage and savings, beside the ten-times-income rule).

September 6, 2026

Added two assumption tools: sell or keep the house (carrying costs and appreciation against rent and the return on freed equity, with the home-sale exclusion), and the long-term care cost projection (today's rate at care inflation to the start year, summed over the years of care, with the set-aside today).

September 4, 2026

First release of the longevity projection (year-by-year, spending and outside income indexed to inflation, a fixed return on the remainder, with the sustainable-spending solver) and the pension-versus-lump-sum comparison (the lump sum invested and paying the pension, with the break-even return solver).

Canonical address: https://consideratecapital.com/tools/mortgage-points-calculator