How mortgage points work

A discount point is prepaid interest: 1 percent of the loan, paid in cash at closing, in exchange for a lower contract rate. On $400,000, one point is $4,000. Whether that $4,000 is a good trade depends on how long you keep the loan, because the saving arrives as a slightly smaller monthly payment stretched over years.

At 6.75 percent over 30 years the scheduled payment is $2,594.39. At 6.50 percent it is $2,528.27. The difference is $66.12 a month. Divide the $4,000 cost by that saving and the cash-flow break-even is 60.5 months, a little over five years. Leave before then and the points have not yet paid for themselves in lower payments. Stay to term and the interest bill falls by $23,803.31, which is many times the $4,000, because every remaining month is cheaper.

$$\text{cost} = B \times p \qquad n_{BE} = \frac{\text{cost}}{M_0 - M_1}$$

$B$ is the loan, $p$ points as a decimal, $M_0$ the payment at the higher rate and $M_1$ at the lower. That second figure, interest saved to term, is not a reason to buy points on its own. It assumes you keep this loan for 30 years, which most people do not. The break-even month is the figure that matches how long you actually expect to hold it.

The calculator above opens on those figures because they are the first worked example. How mortgages work is the surrounding machinery.

Dividing cost by monthly saving ignores that the $4,000 is paid today and the $66.12 arrives later. A present-value test would discount those savings at some rate, which lengthens the wait. This page uses the cash-flow test because that is the one a closing disclosure supports without picking a discount rate, and because naming a rate would pretend we know what else you would have done with the $4,000.

If those dollars would otherwise have paid down principal, the extra payment calculator is the comparison. If they would otherwise have stayed in cash, the cash-flow break-even is close to the right test. If they would otherwise have been invested, you need a return assumption this page will not supply.

A 15-year loan changes the arithmetic because there are fewer months of saving to recover the same points. On a $300,000 15-year loan, 1.50 points cost $4,500 and a cut from 6.25 percent to 5.875 percent saves $60.91 a month, so break-even is 73.88 months. Held to the 15-year term, interest falls by $10,964.36.

If the advertised lower rate does not actually cut the payment, there is no break-even. That sounds like a data-entry error, and it usually is: points paid for a rate that did not move, or a term that shortened enough to offset the rate cut. The calculator reports n/a rather than a negative month count, because a negative break-even is not an answer, it is a sign the two rates are in the wrong boxes.

Zero points on the same $400,000 30-year loan at 6.75 percent cost $0, save $0 a month, and save $0 of interest. The lower-rate box has to actually be lower, or there is nothing to recover.

Lender credits are the identity run backwards: you take a higher rate and the lender pays cash toward closing. The break-even then asks how long you must stay for the higher payment to cost more than the credit you took. Origination charges that do not buy a lower rate are just fees, in the same family as an origination fee, and they have no break-even of this kind.

Points are recovered only while this loan is the one you are paying. Refinancing in year three and the remaining un-recovered points are gone, along with the remaining payment saving, unless the new loan's rate is lower still. The refinance break-even calculator is the tool for that second decision. Do not add the two break-evens. They are sequential, and the first one is truncated by the second.

Tax treatment of points depends on the loan type and the jurisdiction, and it changes. This page counts the cash at closing and the payment saving, which is the arithmetic either way. Whether a deduction is available, and in which year, is a tax-year fact, not a formula one.

Comparing points using interest saved to term, then leaving the loan in year four, is the substitution that costs the most. On the default, interest to term falls by $23,803.31, which makes the $4,000 look cheap. The cash-flow break-even is 60.5 months. Leave at month 36 and you have recovered $36 \times 66.12 = 2380$ of the $4,000, so the points are still behind. The to-term figure is the prize for keeping this exact loan for 30 years. Most readers will not. Use the month count.

A larger down payment cuts the loan, which cuts both the payment and the interest, and it can also change whether PMI applies. Points keep the loan size and cut the rate. Run this page for points and the PMI calculator for the down-payment side, rather than folding them into one figure.

The figures throughout are teaching loans: one point on a $400,000 30-year, 1.50 points on a $300,000 15-year, and zero points as the identity check. They are there so every published number can be re-derived. This is educational material, not financial advice.