Mortgage Refinance Calculator

The refinance maths, explained

A refinance is a simple trade: you pay a one-off cost today to lower your payments or shorten your term. Whether that trade is worth it comes down to three calculations, all of which this tool performs exactly.

Step 1 — what you still owe today

B_k = P(1 + i)^k − M × [ ((1 + i)^k − 1) ÷ i ]

P = original loan amount
i = monthly rate (annual rate ÷ 12)
k = payments already made
M = original monthly payment

This is the Freddie Mac Form 91 closed-form balance identity. It gives the outstanding principal after k payments without rebuilding the whole schedule, which is what the calculator uses to find the balance you would refinance.

Step 2 — the new payment

M = P × [ i(1 + i)^n ] ÷ [ (1 + i)^n − 1 ]

P = balance + cash out + (rolled closing costs)
n = new term in months

This is the standard amortising payment formula from Regulation Z Appendix J. The new principal is your outstanding balance plus any cash you take out plus any closing costs you choose to finance.

Step 3 — the break-even month

Break-even month = ceil( closing costs ÷ monthly saving )

monthly saving = current payment − new payment

This is the number most refinance calculators hide. If you sell the home or refinance again before the break-even month, the refinance has cost you money. The CFPB recommends treating the break-even as a hard floor: only refinance if you are confident you will stay in the home longer than that.

Step 4 — the lifetime interest difference

Remaining interest (stay) = current payment × months left − balance
Total interest (refi)     = new payment × new term − new principal
Lifetime saving           = remaining interest − total interest

This is the figure that exposes the term-reset trap. A lower rate on a longer term can easily increase your lifetime interest even though the monthly payment falls. In the default scenario here the borrower saves $66,930 by refinancing to 6.00% over 25 years — but the same balance at 6.25% over a fresh 30 years would cost about $20,000 more in interest than staying put.

Worked examples

United States — $320,000 at 7.25%, 5 years paid, refinancing to 6.00%

After 60 payments the balance is $302,012.38 and the current payment is $2,182.96. Refinancing to 6.00% over 25 years with $4,500 of closing costs gives a payment of $1,974.86 — a saving of $208.10 a month. The break-even is 22 months and the lifetime interest saving is $66,930.

United States — the term-reset trap

The same $302,012.38 balance refinanced to 6.25% over a fresh 30 years gives a payment of $1,887.25, saving $295.71 a month with a break-even of just 16 months. But the lifetime interest rises by about $20,022 versus staying put. The monthly saving is real; the overall cost is higher.

United Kingdom — remortgaging a £250,000 balance

A UK borrower with £250,000 outstanding on a 5.75% deal, remortgaging to 4.50% over 20 years with £1,500 of arrangement and valuation fees, sees the payment fall from roughly £1,568 to £1,581 — broadly flat — but saves over £40,000 in interest across the term. UK fixes are short, so the break-even on fees is usually recovered within the fixed period.

How to use this calculator

1. Enter your original loan amount, the current rate and the original term — not today's balance.
2. Set how many payments you have already made. The calculator derives your outstanding balance from this.
3. Enter the new rate and choose the new term from the offer.
4. Add the closing costs you were quoted.
5. Open Advanced options to add a cash-out amount or to roll the closing costs into the new loan.
6. Read the break-even and lifetime interest saved figures before deciding.