Mortgage Refinance Break-Even Calculator

Enter what you still owe on your mortgage, its rate and the years left on it, then the rate, term and closing costs of the loan that would replace it. The calculator finds the month the refinance has paid for itself: the first month in which the cash its payments have saved covers the extra you still owe on the new loan. It also shows the usual estimate, closing costs divided by the drop in the monthly payment, and a table of where you would stand if you sold or refinanced again after one year, two, three and so on. The defaults describe a 300,000 balance at 7.5% with 27 years left, refinanced at 6.5% over a new 30-year term with 6,000 of closing costs paid at closing.

Why the payment drop overstates the saving

The usual rule divides the cost of refinancing by the monthly saving:

months = closing costs ÷ monthly saving

Chase's guide to the break-even point puts it in exactly that form, dividing 5,000 of costs by 200 of monthly savings to get 25 months. The trouble is that a new loan restarts the clock. Part of a lower payment is a lower rate, which is a real saving, and part of it is a longer schedule, which only spreads the same debt over more years. The rule counts both as savings, so it treats owing more later as money in hand now.

Take a 200,000 balance at 6% with ten years left, refinanced at 5.75% over thirty years with 17,000 of costs added to the loan. The payment falls from 2,220.41 to 1,266.35, so the rule says 18 months. After those 18 months, though, the new balance is 35,678 higher than the old one would have been, and the refinance never catches up: once both loans are repaid it has cost 189,438 more.

How the break-even is worked out

Both payments come from the standard amortization formula, the same one the mortgage calculator uses:

M = L × i ÷ (1 − (1 + i)⁻ⁿ)

Here L is the amount borrowed, i the annual rate ÷ 12 and n the number of monthly payments. Years left can be fractional and are rounded to whole payments. The calculator then runs both loans forward a month at a time. Cash saved starts at minus the closing costs if you pay them at closing, or at zero if they are added to the loan, and each month it grows by the return you enter and gains the difference between the two monthly outgoings, mortgage insurance included. The figure that decides the answer is

net gain = cash saved − (new balance − old balance)

The break-even point is the first month in which the net gain is zero or more. The table shows the same three figures at each horizon in whole units, and every judgement on the page is made on figures rounded that way, so the months called ahead are exactly the ones in which the table's net gain would be at least zero. The usual estimate is worked in cents and rounded up to a whole month. With no return and no mortgage insurance, the net gain in any month is simply the interest the new loan has saved less the closing costs, whichever way they are paid.

The default example

At 7.5% a 300,000 balance with 324 payments left costs 2,162.20 a month, and at 6.5% over 360 payments it costs 1,896.20, a saving of 266.00. The usual rule gives 6,000 ÷ 266.00 = 22.56, or 23 months. After 24 payments the saved payments have repaid the costs and left 384 in hand, but the new loan's balance is 481 higher than the old one's, so the net gain is −97. A month later it is 650 against 506, and the refinance is ahead from month 25 on. If both loans run to the end the refinance saves 11,920. Added to the loan instead, the 6,000 raises the new payment to 1,934.13 and moves the break-even to 29 months.

The two estimates are two months apart here. They drift apart as the rate cut shrinks. At 7% the usual rule says 37 months, but the refinance is ahead only from month 53 to month 260 and ends 23,973 behind, because the longer loan's balance falls more slowly and from then on it charges more interest each month than the old loan would have. At 7.25% the rule says 52 months and the refinance is never ahead at all.

Mortgage insurance

A refinance can end private mortgage insurance, or start it, so each loan can carry it. Under the Homeowners Protection Act of 1998, which covers loans on a single-family principal residence made from July 29, 1999, a lender must end PMI automatically once the balance is scheduled to reach 78% of the home's original value, and in any case at the midpoint of the loan's term, as long as the payments are current. For a refinance the original value is the appraisal the lender relied on. The calculator charges the premium up to and including the payment that crosses either line, working from each loan's schedule, so it assumes the current loan has not been paid ahead. You can also ask for cancellation once the balance reaches 80%, which the calculator does not assume, and the Act sets other dates for loans classed as high-risk. Insurance made available under the National Housing Act, which includes FHA's, or under the laws behind VA and rural housing loans is not PMI under the Act: choose For the life of the loan when a premium will last until the loan is repaid. Premiums stay at the amount you enter.

With the defaults, 125 a month of PMI on a home worth 350,000 when the loan was made would run for 75 more payments. Refinancing away from it brings the break-even forward from 25 months to 17.

Where the measure comes from

Refinancing has been national policy before: between 1933 and 1936 the Home Owners' Loan Corporation bought more than a million delinquent mortgages from lenders and refinanced them for the borrowers.

Regulators have since put a longer view in front of borrowers. Since October 3, 2015 the Loan Estimate that US lenders give most mortgage applicants has shown, under In 5 Years, the principal, interest, mortgage insurance and loan costs scheduled to be paid over the first five years, next to the principal paid off in that time. The gap between the two is what five years of the loan cost, and setting it against the same figure for your current loan is the comparison this calculator makes month by month.

Getting the decision right is worth money. Benjamin Keys, Devin Pope and Jaren Pope estimated that in December 2010 about 20% of US households who would have gained from refinancing, and appeared able to, had not done so, at a median cost of about 11,500 dollars in present value. Waiting has a value too, because refinancing now gives up the chance to refinance later at a lower rate. Sumit Agarwal, John Driscoll and David Laibson published the first closed-form rule for when to refinance in 2013, and their threshold depends on the discount rate, the chance of moving or repaying early, how volatile mortgage rates are, the cost of refinancing and the tax rate.

What the calculator leaves out

Property tax and homeowners insurance belong to the house rather than the loan, so a refinance leaves them unchanged and they are left out. So are cash-out refinances, adjustable rates and the tax deduction for mortgage interest, which shrinks along with the interest for anyone who itemizes. Both loans are assumed to be paid exactly on schedule, since paying extra on either changes the comparison. And a return above zero makes every figure a future value: the table then shows the cash you would have at that point, not what it is worth today.

These figures are estimates for comparing a refinance with keeping your loan; an actual offer depends on your credit, the appraisal and the lender's fees and rules. See the site disclaimer.