Mortgage Points Calculator

The worked trade

On a $300,000 30-year loan, one point ($3,000) buys the rate from 6.5% down to 6.25%: the payment drops from $1,896.20 to $1,847.15 — $49.05 a month. The break-even — the cost divided by that saving, shown to the nearest month — is 5 yr 1 mo; hold the loan its full term and the point nets $14,659. Sell or refinance well before the break-even and the trade loses. Every figure is computed by the same tested engine as the calculator above when the page is built. The loan, the two rates and the point are illustrative inputs chosen for the arithmetic, not quotes: what one point costs — 1% of the loan amount — is the engine's pricing convention, matching the form label, while the 0.25-percentage-point reduction it buys here is one fictional quote, and the rate reduction per point differs by lender and day.

What the engine computes, step by step

The form hands five inputs to one engine function — the loan amount, the quoted rate, the bought-down rate, the term, and the number of points, which defaults to one when the field is blank. The function validates them, runs the steps below in order, and returns a typed result or an explicit, human-readable error. The interface only formats what comes back; it never does arithmetic of its own.

1. Validation. The bought-down rate must be below the quoted rate, and the points figure must be more than zero and no more than 10; anything else is refused before any arithmetic runs. Enter the same rate in both fields and the engine answers "The bought-down rate must be below the quoted rate." Enter zero points and it answers "Enter between 0 and 10 points."
2. Payment at the quoted rate. The standard amortized-loan (PMT) formula with monthly compounding, the convention behind US mortgages and most consumer loans: the annual rate ÷ 12 is the monthly rate, years × 12 is the number of payments (360 here), and the result is the one fixed payment that retires the balance at the last month — $1,896.20 on $300,000 at 6.5%.
3. Payment at the bought-down rate. The same formula on the same loan amount and the same term, at the lower rate: $1,847.15 at 6.25%. Only the rate changes between the two payments — the engine does not add the points to the loan or shorten the term.
4. Monthly savings = quoted payment − bought-down payment = $49.05.
5. Cost of the points = loan amount × 1% × points. The engine prices one point at 1% of the loan — its convention, matching the form label — so $300,000 × 1% × 1 = $3,000. Fractional points scale the same way.
6. Break-even = cost ÷ monthly savings = $3,000 ÷ $49.05 = 61.2 months. The engine returns the exact quotient; the result box rounds it to the nearest whole month and shows 5 yr 1 mo.
7. Savings if held to full term = monthly savings × number of payments − cost: $49.0525 × 360 − $3,000 = $14,659. The multiplication uses the saving as the engine holds it internally, beyond the cent the result box displays, which is why the rounded $49.05 does not reproduce the total exactly by hand.

The break-even is a quotient, shown to the nearest month

Break-even is the cost of the points divided by the monthly saving and nothing more. It counts payments from the first one on the loan, not from a calendar date; it treats the saving as the same amount every month, which holds because both payments are fixed; and it does not ask what else the $3,000 could have earned in the meantime. The quotient is usually fractional, and this page's result box rounds it to the nearest whole month — a different convention from the refinance calculators, which round up. In Example A the quotient is 61.2, displayed as 5 yr 1 mo. By the end of month 61 the accumulated saving is 61 × $49.0525 = $2,992.20 (using the unrounded saving), still $7.80 short of the $3,000; by the end of month 62 it is $3,041.25, and the cost is covered. When the fraction is below one half, as here, the displayed month is the last one before the cost is covered. Example B below rounds the other way: its quotient of 61.5 rounds up to 62, the first month by whose end the saving ($6,048.25) covers the $6,000 cost. Either way the display is within a month of the exact quotient.

Changing one input at a time

Example B keeps the fictional $300,000 loan, the 6.5% quote and the 30-year term, but pays 2 points ($6,000) for a fictional 6% rate. The payment falls to $1,798.65, a saving of $97.55 a month, and the full-term line is $29,119. The second quarter-point saves $48.50 a month, slightly less than the first's $49.05 — the payment formula is not a straight line in the rate — so two points break even in 61.5 months (5 yr 2 mo), a little later than one.

Example C is Example A's trade on a 15-year term. The payments are larger — $2,613.32 at 6.5% and $2,572.27 at 6.25% — but the saving between them is smaller, $41.05 a month, because less of a shorter loan's payment is interest, and interest is the part the rate acts on. The cost is unchanged at $3,000, so the break-even stretches to 73.1 months (6 yr 1 mo), and with only 180 payments to accumulate over, the full-term line falls to $4,390.

Example D halves the loan to $150,000 with everything else as in Example A. The cost halves to $1,500, the saving halves to $24.53, and the break-even is 61.2 months — identical to Example A's, because both the cost and the saving are the loan amount times something that depends only on the rates, the term and the points, so the loan amount cancels out of the quotient. The full-term line does scale with the loan: $7,329 here, half of Example A's.

Where the monthly saving comes from

Each month the schedule charges interest on the balance still outstanding — balance × (annual rate ÷ 12) — and the remainder of the fixed payment reduces the principal. In month one of Example A the balance is the whole $300,000, so interest is $1,625.00 at 6.5% and $1,562.50 at 6.25%; the principal reached in that first month is $271.20 and $284.65 respectively. The lower rate shrinks the interest slice and grows the principal slice from the first payment onward, and the gap persists down the whole schedule. Walked one month at a time by the amortization engine, the loan accrues $382,633 of interest over 360 payments at 6.5% and $364,975 at 6.25% — $17,659 less, which equals $49.0525 × 360 to the cent, using the unrounded saving. Subtract the $3,000 paid for the point and the result is the full-term line, $14,659. The Amortization Calculator shows the year-by-year rows at either rate, and How Amortization Works walks through the split.

Price it against your real horizon

The full-term line assumes every one of the 360 payments is made at the bought-down rate. The engine has no input for how long the loan will actually exist, and a sale or a refinance ends it: either event stops the $49.05-a-month accumulation, and the unrecouped remainder of the $3,000 is not returned — the bought-down rate lives and dies with the loan. So the mechanical content of the comparison is two durations set side by side: the months the loan is expected to survive at this rate against the 5 yr 1 mo break-even. Leave Example A after 24 months and the saving has accumulated to $1,177.26, $1,822.74 short of the cost; stay 120 months and it has reached $5,886.30, $2,886.30 past it; stay all 360 and the surplus is the $14,659 full-term line. How anyone estimates their own horizon is outside what a calculator can supply; the engine compares, and the reader decides.

The same $3,000 could instead be added to the down payment, which pulls a different lever 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 6.5%, but the balance that interest accrues on is smaller from day one, regardless of when the loan ends. Which lever moves a particular loan's numbers more depends on the amounts, the rate trade offered, and the horizon; the Down Payment Calculator recomputes the loan amount and loan-to-value under that change, and the Mortgage Calculator the payment, so the two can be read side by side.

How to read the result

• Break-even in … is the headline line: the cost ÷ monthly savings quotient, rounded to the nearest whole month and written in years and months — 5 yr 1 mo in Example A.
• Cost of N point(s) is loan × 1% × points, in whole dollars — $3,000 here. The label repeats the points figure the engine used, including the default of one.
• Payment at the quoted rate and Payment at the bought-down rate are the two PMT results, to the cent — principal and interest only.
• Monthly savings is their difference, to the cent.
• Savings if held to full term is monthly savings × number of payments − cost, in whole dollars. It is a net figure: the cost has already been subtracted.
• Copy result places a one-line summary on your clipboard: the break-even, the monthly saving, and the full-term line.

Money is shown to the cent, or to whole dollars for large totals; internally every calculation keeps the full precision of IEEE-754 double-precision arithmetic, and nothing is rounded between steps. Your lender's figure may differ by a few cents depending on their rounding and day-count conventions — the difference is presentational, not an error.

Where the calculator stops

The limits are the engine's, and the methodology page states them. The calculators model fixed-rate, fully amortizing loans. They do not model adjustable-rate mortgages, interest-only periods, balloon payments, or negative amortization: whichever rate you enter is held fixed for every month of the term, and the Fixed vs. Adjustable Rate guide describes the structure this engine does not price. Both payments are principal and interest only — property tax, insurance, PMI, and HOA are not in the comparison, and on the Mortgage Calculator they are estimates from the rates and amounts you enter: real figures vary by locality, reassessment, coverage, and lender, and PMI removal timing depends on your specific loan program. The only upfront cost the engine knows is the points, priced at 1% of the loan each; origination fees and other closing costs have no field here, and the Refinance Break-Even Calculator runs the closing-cost version of the same quotient. The rate reduction a point buys is your input, not a quote. There is no calendar, no discounting, and no holding period — the break-even is a month count to set against a horizon the engine does not know. And a correct calculation can still be the wrong calculation for your situation — choosing the right loan for a real-world decision is judgment we cannot automate.

Frequently asked questions

Not financial advice: a general educational estimate. Actual point pricing and rate reductions vary by lender and day; tax treatment has conditions. Values are processed locally in your browser and never transmitted. See the methodology page.