The division
The Federal Reserve's consumer guide to mortgage refinancings tells a reader to divide refinancing costs by the monthly savings. That quotient is the break-even period in the guide's worksheet. This page does that division with one change of bookkeeping: money is kept in cents, and the result is shown two ways. The first is the exact quotient. The second is the first whole month in which the monthly differences, added up, are at least the costs. If the new payment is not lower, there is no month to report.
The payments themselves are not typed. They come from the same function as themortgage payment calculator. The rate is nominal. The monthly rate is the annual percent divided by 12. The contractual payment is rounded half-up to the cent. Microsoft's PMT documentation describes those inputs and says the result is principal and interest, not taxes or fees. Theeditorial policy uses that same checked payment: $200,000.00 at 6% for 30 years is $1,199.10.
The form's opening example
The form opens on $200,000.00, a current rate of 6%, 30 years remaining, a new rate of 5%, a new term of 30 years, and $2,500.00 of closing costs. Those rates are round examples so the arithmetic can be checked. They are not a quote and not this week's average. Freddie Mac publishes the Primary Mortgage Market Survey for readers who want a weekly average. This page does not copy a survey number into the form, because a weekly average changes and an average is not an offer.
At those inputs the current payment is $1,199.10 and the new payment is$1,073.64. The difference is $125.46. Dividing $2,500.00 by that difference gives 19.93 months. The costs are covered in 20 months, because that is the first whole month whose accumulated differences reach the costs. The 5% payment is the cent-rounded PMT. The raw value is about $1,073.64 before you read it as currency, and the Federal Reserve guide's own illustration prints a 5% payment on this balance as $1,073 and a 6% payment as $1,199. Their dollar rounding and this site's cent rounding are why the two writeups do not show the same cents.
The guide's own worksheet
The Federal Reserve worksheet uses a current payment of $1,199, a new payment of $1,073, and savings of $126. It then multiplies by an after-tax factor. In the printed example the factor is 0.72, from one minus a 28% rate the guide chose for the illustration. One hundred twenty-six dollars times 0.72 is $90.72. The guide prints $91. It then divides $2,500 by $91 and prints 27 months.
Twenty-seven times $91 is $2,457, which is still short of $2,500. The first month that covers $2,500 at $91 a month is month 28. This page reports that whole month, and it also reports the unrounded quotient, 27.47 months, so the guide's printed 27 is not silently replaced. If you leave the tax field blank, the page does not apply a tax factor at all. The guide's 28% figure is their example, not a rate from the tax code and not a rate this site will fill in for you.
A lower payment is not the whole cost
Interest still owed on the current schedule in the opening example is$231,677.04. Interest on the new 30-year schedule is$186,513.24. The difference, current minus new, is$45,163.80. That comparison assumes you pay each loan exactly as scheduled and that you do not add the closing costs to the new balance. It ignores taxes, insurance, and mortgage insurance. It is not a statement that refinancing is a good or bad idea.
Stretch the new term and the payment can fall while total interest rises. Shorten it and the payment can rise even when the rate is lower. The 15-year versus 30-year page is the place to see that term effect on one rate. Break-even on the payment does not notice it unless you also read the interest line. The Federal Reserve guide makes the same point when it talks about people who expect to move: monthly savings that have not yet covered the costs are not a benefit if the loan ends first.
Costs, credits, and penalties
The costs field is cash you pay at closing. The CFPB's answer on no-cost refinances describes two other structures. One raises the interest rate and gives a lender credit. The other adds the costs to the loan amount. A higher rate shows up here as a higher new payment, which can erase the break-even or push it out. Costs added to the balance do not belong in the cash field. They belong in a larger balance, and they raise both the payment and the interest. This page will not guess a credit or a rolled-in amount you did not type.
A prepayment penalty on the current note is another cost. The CFPB says it is a fee some lenders charge for paying off all or part of a mortgage early, and that refinancing can be the event that triggers it. The Federal Reserve guide says a penalty lengthens the time to break even. Add it to the costs field if you know the figure from the note. This calculator does not know it. Paying extra principal on the loan you already have, with no new closing costs, is a different sum. That one is on thepayoff calculator.
What this page leaves out
- Cash-out amounts, discount points you did not include in costs, and lender credits you did not type.
- Mortgage insurance, escrow, and whether you will qualify.
- A tax deduction. The optional percent is only the guide's multiplication, not a return.
- Any advice about whether to refinance. The disclaimer covers that limit.
Giuseppe Ilarda, the site owner, writes and checks this calculator. The result is an educational estimate of principal, interest, and a division. It is not financial advice, not a Loan Estimate, and not a statement that a particular rate is available.