Refinance Break Even Calculator

Purpose and model boundary

Use this calculator when you hold a fixed-rate mortgage and have been quoted a replacement for it. It answers one question directly: how many months of the lower monthly payment it takes to repay the cash you hand over at closing. Around that answer it reports the payment on each loan, the total still to pay under each, how many years the new loan adds to the term, and, when you say how long you expect to keep the loan, whether you will still be there once the costs have been repaid.

The comparison is made against the term you have left, not against a fresh full term. A loan with 25 years remaining and a new 30-year loan are two different products, and a payment that falls because the schedule was stretched over five more years is not the same thing as a payment that falls because the rate fell. This calculator reports the years added to the term as an output of its own and raises a status message whenever that number is positive, so the re-extension is named rather than absorbed into the saving.

Closing costs are handled two ways, and the two answer different questions. Paid at closing, they are cash out of your pocket, and the break-even month is how long the monthly saving takes to give it back. Added to the loan, nothing leaves your pocket, so there is nothing to repay and no break-even month exists at all. The cost instead moves into the balance you borrow, raises the new payment, and shows up in the lifetime comparison. A break-even figure quoted in that second case would be a break-even on money that was never spent.

What this calculator does not model, stated plainly because each omission can move the answer more than the rate does. Any rate that changes after closing: both loans are treated as fixed for their whole term, so an adjustable-rate offer is outside the model. Mortgage insurance, which a refinance can add or remove and which on some loans dominates everything else here. Cash taken out, so a cash-out refinance is not what is being priced. The tax treatment of points paid on a refinance, which differs from the treatment of points paid on a purchase. The opportunity cost of the closing cash, which for a large cost and a small monthly saving is not negligible. Prepayment penalties on the loan you already have. The two payments are principal and interest only, so property tax, homeowners insurance, association dues and any other escrow item are outside both sides of the comparison.

Inputs and units

All ten inputs are required. Years Before Moving must be at least one year and may not be left blank on the published calculator.

Rate Uncertainty and Cost Uncertainty are required sensitivity controls. They do not alter the headline result at the New Rate and Closing Costs entered above them. They define an 11 × 11 comparison surface of plausible offers around those two figures.

Governing relationships

Both payments come from the same level-payment relationship. For a principal P, a monthly rate r and a count of monthly payments n, the payment is

payment = P x r / (1 - (1 + r)^-n)

where r is the annual rate divided by 12, and n is the number of years multiplied by 12 and rounded to a whole month. When the monthly rate is effectively zero that expression cannot be evaluated, so a separate branch divides the principal evenly across the months: payment = P / n. When the month count rounds to zero or less, the payment is reported as zero rather than as an error.

The two payments differ only in what they are given.

• The payment on the loan you have uses P equal to Current Balance, r from Current Rate, and n from Years Remaining. It is the payment over the term that is actually left, which is the point of the whole exercise.
• The payment on the loan offered uses P equal to the new loan amount, r from New Rate, and n from New Term Years.

The new loan amount is Current Balance, plus Closing Costs when you chose to add them to the loan. The cash at closing is Closing Costs when you chose to pay at closing, and zero when you chose to add them. Exactly one of those two carries the cost, which is why the two choices never double-count it.

From there:

• monthly saving is the payment on the loan you have less the payment on the loan offered;
• break-even months is the cash at closing divided by the monthly saving, and zero when either the monthly saving is not positive or there is no cash at closing;
• total still to pay on the loan you have is its payment multiplied by its whole-month count;
• total still to pay on the new loan is its payment multiplied by its whole-month count, plus the cash at closing;
• lifetime difference is the old total less the new total, so a positive figure means the refinance costs less in the end;
• years added to the term is New Term Years less Years Remaining, reported as it falls out, which means a shortening refinance reports a negative number;
• saving by the move date is the monthly saving multiplied by the whole months until you move, less the cash at closing.

The four charts read off the same figures. The first plots the running total saved, month by month from month zero to month 120, against a flat line at the cash paid at closing. The second puts the two monthly payments side by side. The third shows the probability distribution of the net position across the offer grid, with dollar amounts on the horizontal axis and chance on the vertical axis. The fourth compares the rate and closing-cost sensitivity slices through the table centre.

The sensitivity table reruns Saving By Move Date 121 times. Its rows move Closing Costs from 2.5 Cost Uncertainty standard deviations below the entered estimate to 2.5 above it. Its columns move New Rate from 2.5 Rate Uncertainty standard deviations below the quoted rate to 2.5 above it. Every cell is where you stand on the entered moving date for that exact offer.

Both axes are probability-weighted. Probability Refinance Pays is the weighted share of those rate-and-cost combinations where Saving By Move Date is above $0. Position P10, Position P50, and Position P90 report the unfavorable tenth, midpoint, and favorable tenth of the same offer distribution. This probability is about the offer you finally receive, not about how long you keep the loan.

Calculation sequence

1. Check the entries against the published input rules. A value outside its stated range is rejected before anything is calculated.
2. Decide where the closing costs sit. If they are added to the loan, the cash at closing is zero and the costs join the amount borrowed. If they are paid at closing, the cash at closing is the full cost and the amount borrowed is the balance alone.
3. Calculate the payment on the loan you have, over the whole months implied by Years Remaining, using the zero-rate branch if the rate is effectively zero.
4. Calculate the payment on the new loan, over the whole months implied by New Term Years, on the amount borrowed from step 2.
5. Subtract the new payment from the old one to get the monthly saving.
6. Divide the cash at closing by the monthly saving to get the break-even months, returning zero instead whenever the saving is not positive or there is no cash to repay.
7. Multiply each payment by its own whole-month count, add the cash at closing to the new side, and subtract to get the lifetime difference.
8. Subtract Years Remaining from New Term Years to get the years added to the term.
9. Multiply the monthly saving by the whole months in the required Years Before Moving horizon and subtract the cash at closing.
10. Build the 11 × 11 sensitivity table by rerunning Saving By Move Date for every rate-and-cost pair.
11. Weight both axes to return Probability Refinance Pays and the 10th, 50th, and 90th percentile positions for the offer distribution.
12. Evaluate the status conditions below in order and return the first one that is true.

Outputs and interpretation

Three outputs carry the answer. Break Even Months says how many months of the saving it takes to repay the cash you paid at closing. Past that point the saving is yours, before it you are behind, and zero means there was nothing to repay. Monthly Saving is the difference between the two payments, and a negative figure means the new loan costs more each month, which can still be the better deal when it shortens the term. Lifetime Difference compares the total still to pay under each loan, and it is the figure to read when the term changed, because a lower payment over more years can cost more in total.

Read the lifetime difference next to the years added to the term, not on its own. That pairing is the point of the calculator. A quote that drops the payment while adding five years can show a real monthly saving and a much smaller, or negative, lifetime difference at the same time, and both numbers are true. Compare the two total-remaining figures rather than the two monthly payments whenever the terms are not equal.

The conditional table appears after all four charts. Read down to see the effect of closing-cost uncertainty and across to see the effect of rate uncertainty. The table body and its four supporting figures come from the calculation service. The page verifies the table centre against the scalar Saving By Move Date and displays the returned values; it does not calculate probability or percentiles in the browser.

Validation and status logic

The workbook evaluates these conditions in the order shown and returns the status of the first one that is true. Later conditions are never reached once an earlier one has matched, so the order is the precedence, and the final row is the fallthrough that applies when nothing above it did.

One status message is not fixed text. Where the table shows <term extended years>, this calculator substitutes the actual number of years the new loan adds, written to one decimal place, so the message names the size of the re-extension rather than only its existence. The delivered test cases record these three concrete forms:

• CHECK: the new loan runs 5.0 years longer than the one you have, so part of the lower payment is re-extension rather than saving
• CHECK: the new loan runs 15.0 years longer than the one you have, so part of the lower payment is re-extension rather than saving
• CHECK: the new loan runs 24.0 years longer than the one you have, so part of the lower payment is re-extension rather than saving

Two features of the order are worth reading twice. The four rows that follow the balance check test states the published input rules already refuse, so on this page they are the model checking a second time rather than messages you will normally meet. And the term-extension check sits above the moving-date check, so a quote that both stretches the term and outlasts your stay reports the re-extension, because that is the finding that changes the decision.

Assumptions and limitations

• Both loans are fixed-rate and fully amortizing, and each is assumed to run to the end of its stated term. Nothing here models a rate that moves after closing, an interest-only period, or a balloon.
• The payments are principal and interest only. Property tax, homeowners insurance, association dues and other escrow items are excluded from both sides, so neither figure is the amount that leaves your bank account each month.
• Mortgage insurance is not modeled. A refinance can add it or remove it, and where it does, the effect can be larger than the rate difference this calculator is measuring.
• Terms are converted to whole months by rounding years times twelve, so a fractional year is rounded to the nearest month before any payment is calculated.
• The lifetime totals assume both loans are held to term. They do not discount future payments, so a dollar paid in year 28 counts the same as a dollar paid today, and they take no account of what the closing cash would have earned had it not been spent.
• Break-even is measured in cash only: the closing cash divided by the monthly saving. It gives no credit for the difference in how fast each loan repays principal, so it is deliberately the more conservative of the two common definitions and it is the one a reader can check by hand.
• Cash taken out is not modeled, and neither is any prepayment penalty on the loan you have.
• Points are treated as part of the closing cost. Their tax treatment is not modeled, and on a refinance that treatment differs from a purchase.
• The result is only as good as the quote behind it. The rate has to be one actually available to you, and the closing cost has to be the complete figure from the loan estimate rather than a partial one.
• The sensitivity distribution covers uncertainty in the final rate and closing costs only. Years Before Moving is held at the value entered and is not assigned a probability.

Restrictions and non-computing states

The current balance must be above zero. A balance of zero or less is accepted by the entry rules and then refused by the model, which returns NOT VALID and no usable comparison, because there is no loan to replace.

Neither rate may be negative, closing costs may not be negative, and the years remaining, new term, and moving horizon must each be at least one year. The published input rules also cap each loan term at 40 years, so entries outside those ranges are turned away before any calculation runs. How the costs are handled has exactly two accepted values, Pay at closing and Add to the loan, and anything else is refused.

The moving horizon is required and must be one year or longer. It is always evaluated as the date at which the model tests whether the refinance has repaid its cash cost.

Adding the closing costs to the loan is a supported state, not an error, and it changes what can be reported. The cash at closing becomes zero, the break-even month becomes exactly zero because nothing was paid, and the cost appears instead in the new loan amount, in the new payment and in the lifetime difference. A break-even figure other than zero in that state would be a defect.

Shortening the term is also a supported state. It commonly produces a negative monthly saving, which sets the break-even to zero and raises a CHECK, while the lifetime difference stays strongly positive. The model is not rejecting the deal there. It is saying that break-even is the wrong measure for it.

Errors and warnings

Three different things can stop you seeing an answer, and they are not interchangeable.

A rejected entry happens before any calculation. A value outside its published range, or a choice that is not one of the two offered for how the costs are handled, is refused at the point of entry and nothing is calculated at all. The remedy is to correct the value. No result is produced, and none should be inferred from the blank fields.

A NOT VALID or CHECK status is the model's own finding about entries it accepted. NOT VALID means the entries do not describe a question this model can answer, and the figures beside it should not be read. CHECK means the calculation completed and the figures are real, but something about the case deserves attention: no payment saving to break even on, a term that runs longer than the one you have, or a move planned before the costs are repaid. A CHECK is a finding, not a failure, and the message says which one it is.

A connection or calculation-service failure is neither of those. It means the calculation service could not be reached or could not finish, so this page has no figures to show. That is a statement about availability and never a statement about your mortgage. A failure of this kind is never reported as a zero, never as a break-even of zero months, and never as a NOT VALID, because a service that did not run has found nothing. Retry, and if it persists the problem is on this side rather than in what you entered.

Both monthly payments use the standard level-payment relationship for a fixed-rate, fully amortizing loan. The Consumer Financial Protection Bureau describes that relationship and the way each payment splits between interest and principal in How do mortgage lenders calculate monthly payments? (Consumer Financial Protection Bureau, Ask CFPB, article 1965). The break-even relationship itself, the closing cash divided by the monthly saving, is elementary arithmetic rather than a cited method, and the figures behind it are reproduced independently in the validation blocks of the delivered workbook and its reviewer packet.

The closing-cost entry is meant to be taken from your own loan estimate rather than estimated. The Bureau's Loan estimate explainer walks through the form section by section, and What fees or charges are paid when closing on a mortgage and who pays them? (Consumer Financial Protection Bureau, Ask CFPB, article 1845) lists the charges that belong in that total, including origination, appraisal, title and recording.

Two of this calculator's stated exclusions are consequential enough to read about separately. Mortgage insurance, which a refinance can add or remove, is explained in What is private mortgage insurance? (Consumer Financial Protection Bureau, Ask CFPB, article 122). A charge for paying off the loan you already have is explained in What is a prepayment penalty? (Consumer Financial Protection Bureau, Ask CFPB, article 1957). Neither is modeled here, and either can be larger than the rate difference this calculator measures.

Points are entered as part of the closing cost, and their tax treatment is not modeled. The Internal Revenue Service states in Topic no. 504, Home mortgage points that points paid to refinance an existing mortgage are generally deducted ratably over the term of the loan, which is not how points on a home purchase are usually treated.

The lifetime totals are undiscounted, so they do not account for what the cash paid at closing might have earned elsewhere. For general background on how an initial amount compounds over time, see the U.S. Securities and Exchange Commission's Investor.gov compound interest calculator.

These sources provide consumer and tax context. They do not supply this calculator's assumptions and they do not certify its result. This calculator is informational and is not financial, tax, investment, mortgage or real-estate advice, and it is not a recommendation to refinance. Compare actual loan estimates, and take decisions about financing a home with a qualified professional who knows your circumstances.