Mortgage Refinance Calculator

Background.

Picture a homeowner who owes $120,000 at 7% with ten years left to pay. A lender offers 5% on a new 30-year loan, with $5,000 of closing costs added to the balance. The monthly payment falls from $1,393.30 to $671.03, a saving of $722.27, and the closing costs are earned back in under seven months. By the measure most people use, that is an easy yes. Yet the new loan takes $241,569.73 in payments against $167,196.21 left on the old one: $74,373.52 more, because ten years of payments have become thirty.

Both readings are correct, and they answer different questions. The monthly figures tell you what you keep each month and how quickly the up-front costs come back. The lifetime figures tell you whether you will hand the lender more or less money before the house is free and clear. A refinance that wins on both counts is a clear improvement. One that wins only on the monthly count is buying breathing room now with payments later, which can still be the right call for a household squeezed by today's payment, as long as it is a deliberate choice.

The calculator sets the loan you have against the one you are being offered. From your balance, rate and years remaining, and the new rate, term, closing costs and any cash you plan to take out, it works out both monthly payments and four comparisons: the monthly saving, the break-even month, the interest saved over the life of the two loans and a net cost that compares total payments, with any cash you take out netted off.

It deals in fixed-rate loans and in principal and interest only. Property tax, homeowners insurance and mortgage insurance sit outside the comparison, as do prepayment penalties, adjustable rates, the tax value of mortgage interest and whatever the monthly savings might earn if you invested them.

What is mortgage refinance calculator?

Refinancing replaces your mortgage with a new loan secured by the same house. The new lender pays off the old balance, and from then on you pay the new loan on its own rate and schedule. A rate-and-term refinance changes the rate, the length of the loan or both, and the new balance is roughly the old payoff plus any closing costs you finance. A cash-out refinance borrows more than the payoff and hands you the difference at closing; conventional cash-out loans are generally limited to 80% of the home's appraised value, and they are usually priced a little above a rate-and-term loan. Either way it is a full new mortgage: a new application, usually a new appraisal, a new title policy and a new set of closing costs, even though nothing about the house has changed. A so-called no-cost refinance still has those costs; the lender covers them with a credit in exchange for a higher rate.

How to use this calculator.

1. 01Enter the current loan balance from your latest statement, where it usually appears as the unpaid or outstanding principal. The amount you originally borrowed is the wrong number, and so is a payoff quote padded with interest to a future date.
2. 02Enter the note rate on your existing loan, not the APR, and the whole years left on it. A 30-year loan that began five years ago has 25 left; if you have been paying extra, count the years until the balance on your statement would actually reach zero.
3. 03Enter the rate on the lender's Loan Estimate and pick the new term from 10, 15, 20, 25 or 30 years. Freddie Mac's weekly survey of average rates is a useful check that the quote is in the market's range.
4. 04For closing costs, take the total from page 2 of the Loan Estimate, subtract any lender credit, and leave out prepaid interest, homeowners insurance and the initial escrow deposit, which you would pay anyway or get back from the old servicer's escrow refund. If your current loan carries a prepayment penalty, add it here.
5. 05Leave cash out at $0 for a rate-and-term refinance. For a cash-out refinance, enter the amount you will receive at closing.
6. 06Read the monthly saving and break-even month against how long you expect to keep the loan, then check lifetime interest saved and the net refinance cost before deciding. If interest saved is negative, or the net cost is positive, look at what a shorter new term would do to the payment.

The formula.

Both payments come from the standard amortising-loan formula, PMT = P × r(1 + r)ⁿ ÷ ((1 + r)ⁿ − 1). P is the amount borrowed, r is the monthly rate (the annual rate ÷ 100 ÷ 12) and n is the number of monthly payments. It is the present value of an annuity solved for the payment: the level monthly amount whose discounted value at the loan's own rate equals the balance, so the last payment leaves exactly zero owing.

For your current loan P is the balance, r comes from your current rate and n is the years remaining × 12. For the new loan P is the balance plus closing costs plus cash out, because the calculator assumes the costs are financed rather than paid at the table. The monthly saving is the current payment minus the new one; it turns negative when the new payment is higher, as it usually is with a shorter term or a large cash-out.

The break-even month is closing costs ÷ monthly saving. It is 0 when you enter no closing costs, and it shows 9,999 when the saving is zero or negative, the marker for a refinance that never recovers its costs through a lower payment. This simple division ignores two things: interest charged on the financed costs, and the slower principal repayment of a loan that has gone back to month one. Both push the real recovery point a little later, and for a short remaining term much later.

Lifetime interest saved is the interest left to pay on the current loan minus the interest on the new one. Interest on the current loan is its payment × months remaining minus the balance; interest on the new loan is its payment × months in the new term minus the new principal. Financed closing costs and cash out are part of the new principal, so they are repaid but are not counted as interest. Net refinance cost is a different measure: the new loan's total payments minus the current loan's remaining payments minus any cash out you receive. The closing costs are already inside the new principal, so they are counted once, and the figure is the saving in total payments after the fees (negative is a saving). With no cash out, interest saved equals the saving in net cost plus the closing costs. Neither total discounts future dollars, and that tilts both against a longer term: a payment made 28 years from now is worth less in today's money than one made next month, so a stretched loan looks somewhat worse here than it would on a present-value basis.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Consumer Financial Protection Bureau — Refinancing Your Mortgage
2. [2]Freddie Mac — Primary Mortgage Market Survey (PMMS, weekly mortgage rate series)
3. [3]Federal Reserve — Consumer Credit and Mortgage Statistics (G.19 / Mortgage Debt Outstanding)
4. [4]IRS Publication 936 — Home Mortgage Interest Deduction (cash-out limits, TCJA rules, points amortization)
5. [5]Brealey, Myers & Allen — Principles of Corporate Finance, 13th ed., Chapter 2 (Present Value of an Annuity; PMT formula derivation)
6. [6]Consumer Financial Protection Bureau — Loan Estimate and Closing Disclosure under TILA-RESPA