Refinance break-even calculator and formula

Put in the balance, the rate and the years left on the loan you have, then the rate and the term of the loan replacing it, then what the new loan costs to arrange. The calculator prices both loans, subtracts one payment from the other, and divides the closing costs by that saving.

The headline answer is a number of months. Before that month the closing costs are still bigger than everything the lower payment has saved. From that month on, the saving is yours.

Under it sit the two interest totals, one for each loan. They are there because the two answers can point in opposite directions, and only one of them is the payment. Refinancing swaps one debt for another, so neither figure is a forecast: both payments come out of the same amortisation formula the loan payment calculator uses.

Two payments, one subtraction, one division.

$$\text{months} = \frac{C}{M_{\text{old}} - M_{\text{new}}}$$

$C$ is the closing costs. Each payment is the level amount that clears its own balance over its own term:

$$M = P \times \frac{i}{1 - (1 + i)^{-n}}$$

Here $n$ is the number of monthly payments and $i$ is the nominal annual rate divided by 12, which makes the rate that belongs in it the note rate the loan actually charges. It is not the APR. An APR folds the fees into the rate to express the two as one number, so feeding an APR into this formula and then putting the fees in $C$ as well charges you for them twice: once inside the payment and once in the numerator. Price the old loan on the balance you still owe and the years you have left, not on what you originally borrowed, because the balance is what the new loan has to pay off.

On the numbers in the worked examples, $300,000 at 7.25 percent with 25 years left is $2,168.42 a month, and the same balance at 6.25 percent over a fresh 30 years is $1,847.15. The saving is $321.27, and $5,000 divided by $321.27 is 15.56 months.

That division is the whole of the method, which is why the break-even month is the figure usually quoted. It is also why it answers one question rather than two.

A refinance does not resume the old schedule at a better rate. It starts a new one.

A level payment splits into interest and principal, and the split moves with the balance. Interest is charged on what you still owe, so the first payments of any loan are mostly interest and the last are mostly principal. A loan 5 years in has already made 60 payments at the interest-heavy end of its schedule and will never make them again. Replacing it starts a fresh schedule at that same end, and adds however many payments the new term is longer by. The amortisation guide walks through the same split payment by payment.

Read the last two rows against each other, because they disagree. The column that breaks even first is the column that costs the most, and the column that costs least breaks even last.

In the middle column the rate fell by a full percentage point and the interest went up. The extra sixty payments did that, not the rate: holding the term at 25 years and changing only the rate would have taken interest down, and holding the rate at 7.25 percent and changing only the term would have taken it up by more than the rate cut took it down.

Priced over the 25 years actually left, the same 6.25 percent loan pays $1,979.01 a month and charges $293,702.44 of interest, so it beats the loan it replaces on the payment and on the lifetime cost at once. It also breaks even more slowly: the monthly saving is smaller, so $5,000 of costs takes 27 months to come back rather than 16. That is the awkward part of using break-even as the deciding number. On these figures it ranks the 30 year version first while the 25 year version is the one that costs less.

It measures one thing precisely: how long the lower payment takes to give back the cash you spent at closing. Three things sit outside that measurement and change what you do with it.

How long you hold the loan. The month only arrives if you are still holding the loan when it does. Sell in month 10 of a 16 month break-even and the costs were never recovered, which is why the break-even month is worth comparing against how long you expect to stay put rather than against zero.

When the money moves. A dollar saved next month and a dollar of interest avoided in year 28 are counted as equal by a simple division. They are not equal, and discounting both sides is what the net present value calculator does. The time value of money guide explains why the two methods disagree and by roughly how much.

What is in the closing costs. Lender fees, an appraisal, title work and recording, and any points paid to buy the rate down. On most consumer mortgage refinances in the United States the lender has to issue an itemised loan estimate on a standard form, and that document prices this sum better than any rule of thumb does. Rules elsewhere differ, and some products are carved out even there, so the itemised quote is the thing to ask for rather than a figure quoted as typical. A no-closing-cost refinance is not free either: the lender covers the fees and charges a higher rate, so the cost moves out of the break-even sum and into a smaller monthly saving, which is why the two versions only compare properly once both are priced. Tax treatment is a separate question and it moves: in the United States, points paid on a refinance are generally spread over the life of the loan rather than deducted in the year they are paid, and the wider rules on mortgage interest change from year to year. That is a question for the current rules and a tax adviser rather than for this page.