What this calculator does
Find out whether a new mortgage would save you money, and how long it takes to pay off. You compare the rest of your current loan with a new offer. The calculator shows how much your monthly payment changes. It also shows the month your closing costs are paid back, called the break-even month. You'll see the difference in total interest and your savings so far at the end of each year. And you'll see whether the new loan ends sooner or later than the old one.
Refinancing means swapping your current loan for a new one, usually for a lower rate, a different length, or both. It comes with closing costs, the fees you pay to set up the new loan. So a lower payment doesn't settle the question on its own. You also want to know how long the savings take to cover those costs. And you want to know whether starting a fresh loan means paying more interest overall.
Where it's used
Why this math matters outside the classroom:
- Break-even point. Closing costs of $4,000 divided by $150 a month in payment savings take 27 months to recover.
- New payment. Homeowners find the payment on the remaining balance at a new rate and term and compare it with today's payment.
- Term changes. Moving from 30 years to 15 years can raise the payment while lowering total interest, and the comparison shows both.
- Planning to move. Owners who expect to sell within a few years compare that time with the break-even month.
Grade level and standards: Grades 11–12; Common Core State Standards for Mathematics HSA.SSE.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter what you still owe, your current interest rate and how long is left on the loan.
- Enter the new rate, the length of the new loan and the closing costs.
- Choose whether you'll pay the closing costs in cash or add them to the new loan.
- Read your monthly savings and break-even month. Then compare the interest and lifetime numbers. The yearly table shows where you'd stand if you sold or refinanced again at a given point.
What the inputs mean
- Time left on current loan
- Enter the time left, not the loan's original length. The calculator works out your current payment from what you owe, the rate and the time left. So it covers principal and interest only: the loan itself plus the interest on it.
- Closing costs
- Lender fees, the appraisal, title costs and anything else you pay to get the new loan. Points, which are fees you pay upfront to lower the rate, belong here too.
- How closing costs are paid
- Adding the costs to the loan means you don't pay cash now. But it makes the new loan bigger, so the payment and the interest go up.
Formula and method
payment = P × i ÷ (1 − (1 + i)^(−n)), with i = rate ÷ 100 ÷ 12 monthly savings = current payment − new payment interest on a loan = payment × n − principal interest difference = current-loan interest − new-loan interest break-even month = closing costs ÷ monthly savings, rounded up lifetime savings = current payments × n − (new payments × n + cash closing costs) savings to date after m months = current payment × min(m, n_current) − new payment × min(m, n_new) − cash closing costs
In the formulas, P is the amount borrowed (the principal), i is the monthly interest rate and n is the number of monthly payments. The monthly rate is the yearly rate divided by 12, because interest is charged every month. For the savings so far, m is the number of months that have passed. n_current and n_new are the payments left on the current loan and the payments on the new one.
Both payments come from the same standard formula. It finds the one monthly amount that pays off a loan, with interest, in exactly n months. For your current loan, the calculator runs it on what you owe today over the time left. That matches your real payment as long as you've never paid extra.
The break-even month is the simple payback point. It's how many months of lower payments it takes to add up to the closing costs. It doesn't count how fast each loan builds equity, the share of the home you own outright. That can matter when the new loan is longer.
Worked example
You owe $280,000 at 7.25% with 27 years left. A new 30-year loan at 6% has $5,000 of closing costs, paid in cash.
- Current payment: $280,000 at 7.25% over 324 months ≈ $1,971.74.
- New payment: $280,000 at 6% over 360 months ≈ $1,678.74.
- Monthly savings: $1,971.74 − $1,678.74 = $293.00.
- Break-even: $5,000 ÷ $293.00 ≈ 17.1, so month 18.
- Interest: $358,844.79 left on the current loan versus $324,346.93 on the new one, a difference of $34,497.86.
Result: The refinance saves $293.00 a month and pays back its costs in month 18 (1 year 6 months). After the $5,000 in costs, you'd save about $29,497.86 over the life of the loans. That's true even though the new loan ends 3 years later than the current one. At the end of year 1 you're still $1,483.98 behind. By the end of year 2 you're $2,032.04 ahead.
Understanding the result
If you expect to keep the loan well past the break-even month, the lower payments will likely more than cover the costs. If you might sell or refinance again before then, you may not get the closing costs back.
Look at the interest difference, not just the payment. A longer loan can lower your payment but raise your total interest. When that happens, the interest difference shows as a negative number.
The yearly table also shows what you'd still owe on each loan. When the new loan is longer, its balance falls more slowly. So if you sell early, you might owe more than on the old loan, even though you paid less each month.
Assumptions and limitations
- Both loans have fixed rates and monthly payments, paid at the end of each month. Interest is charged each month at the yearly rate ÷ 12.
- Your current payment is principal and interest only, worked out from what you owe over the time left.
- Taxes, insurance and PMI (mortgage insurance) are left out, because they usually don't change when you refinance.
- A dollar saved years from now counts the same as a dollar saved today. Future savings aren't adjusted for inflation or what the money could earn.
- It doesn't handle cash-out refinances (borrowing extra to take cash out), adjustable rates or fees for paying a loan off early.
- The break-even month doesn't count the difference in how fast each loan builds equity.
- It doesn't include any tax effects of mortgage interest.
Frequently asked questions
What is a good break-even period?
There's no single rule. Compare the break-even month with how long you expect to keep the home and the loan. A break-even that comes well before then is more comfortable than one near the end.
Should I add closing costs to the loan?
It saves you cash today, but you pay interest on those costs for as long as you have the loan. Switch the option back and forth to compare the payment, break-even month and interest both ways.
Why does the new loan cost more interest even with a lower rate?
Starting a new long loan spreads what you owe over more payments, and you pay interest on each one. To keep the savings without the longer timeline, try a shorter new loan. Or keep paying your old payment amount on the new loan.
How much does the rate need to drop to make refinancing worth it?
There's no fixed rule. It depends on what you owe, the closing costs and how long you'll keep the loan. With the default numbers, a drop from 7.25% to 6% saves $293 a month and pays back $5,000 of costs in 18 months. A smaller drop on a smaller loan can take many years to break even, so try your own numbers.
Is it worth refinancing to a 15-year loan?
A shorter loan usually raises the payment, but it cuts total interest sharply and pays off the house sooner. With the default numbers, a 15-year loan at 6% raises the payment from $1,971.74 to $2,362.80. So there's no monthly break-even. But it cuts the interest still to be paid by about $213,540.95 and ends the loan 12 years sooner. The 'interest saved' and 'paid off' results show that trade-off.
Why doesn't my current payment match my statement?
Your statement often includes escrow, money your lender collects for taxes and insurance. This calculator compares principal and interest only, which is the part a refinance changes.
How this calculator is checked
Method: Standard level-payment formula for both loans; break-even as closing costs ÷ monthly payment savings, rounded up to a whole month. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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