Refinance Payment-Cost Recovery Methodology

The numbers the page asks for

The formula

Step 1 — Monthly payment

We use the standard amortizing mortgage payment formula for both the current loan and the new loan:

P = principal (remaining balance for the refi case)
r = monthly interest rate = (annual rate %) / 100 / 12
n = total number of months in the term

Monthly payment = P × (r × (1 + r)^n) / ((1 + r)^n − 1)

We compute the formula twice — once with the current rate and remaining term, and once with the proposed rate and term. The difference is the monthly principal-and-interest payment reduction. It excludes property tax, homeowners insurance, mortgage insurance, association dues, and escrow changes.

Step 2 — payment-cost recovery months

scheduled payment reduction through month k =
  current payment × min(k, current term months)
  − proposed payment × min(k, proposed term months)

payment reduction after costs at month k =
  scheduled payment reduction through month k − stated closing costs

Each payment stream stops at that loan's scheduled payoff. The recovery month is the earliest whole month when payment reduction after costs is zero or positive and does not fall below zero again before the planned move. This prevents the model from crediting a current-loan payment after that loan would already be paid off. The recovery status does not determine whether refinancing is financially beneficial.

Step 3 — estimated remaining loan balance at the move date

For each loan, the calculator estimates principal remaining after the number of monthly payments entered. The payment count is capped at the loan's full scheduled term.

B(k) = P × (1 + r)^k − M × [((1 + r)^k − 1) / r]

B(k) = remaining principal after k payments
P = starting principal
M = scheduled monthly principal-and-interest payment
r = monthly interest rate
k = payments made before the planned move

For a zero-interest loan, the balance is principal minus scheduled payments made. Comparing the two remaining balances exposes a common term-reset problem: a lower payment can leave substantially more principal due when the home is sold.

Step 4 — estimated cash-and-balance difference at the move date

payment reduction after costs =
  [current payment × min(months until move, current term months)]
  − [proposed payment × min(months until move, proposed term months)]
  − stated closing costs

additional refinance balance at move =
  proposed-loan remaining balance − current-loan remaining balance

estimated cash-and-balance difference at move =
  payment reduction after costs − additional refinance balance at move

A positive result means the scheduled payment reduction after stated closing costs exceeds any additional remaining balance at that date. A negative result means it does not. This is still a limited estimate: it excludes taxes, insurance, PMI changes, financed costs, opportunity cost, and transactions after the selected date.

Step 5 — factual status line

• No monthly payment reduction — the proposed scheduled principal-and-interest payment is not lower.
• Not recovered within planned stay — payment reduction does not equal stated closing costs before the move date.
• Recovered within planned stay — payment reduction equals stated closing costs before the move date.

The status is not a refinance recommendation. The result also displays the move-date cash-and-balance difference and flags when the proposed term exceeds the current remaining term.

What this calculator does NOT account for

Honesty about limits is part of the math. The calculator includes scheduled principal-and-interest payments and estimated remaining loan balances at the planned move date, but it still omits several real factors:

1. Payments after the planned move date. The model estimates each balance at the selected date, but it does not total interest or payments after that date. If the home will be kept longer than entered, compare complete amortization schedules.
2. Opportunity cost on the closing cash. $5,000 paid at closing is $5,000 not invested elsewhere. Strict net-present-value comparisons would discount future savings. This calculator does not.
3. Discount points. Include any points in stated closing costs, but separately compare the price of the points with the rate reduction and loan horizon before deciding.
4. Tax effects. The model does not estimate mortgage-interest deductions or other tax consequences. Tax treatment depends on the borrower and current law; obtain a tax-adjusted comparison when relevant.
5. PMI, taxes, insurance, and escrow. The payment inputs model principal and interest only. Changes to mortgage insurance, property tax, homeowners insurance, or escrow are not included.
6. Cash-out refinance. Cash-out refis are a fundamentally different decision: you're borrowing more, often at a higher rate than a rate-only refi, in exchange for liquidity. This calculator is built for rate-and-term refis only.
7. ARM vs. fixed. Rates and payments shown assume a fixed-rate loan. Adjustable-rate mortgages have a teaser period followed by rate changes; you can't honestly break-even-analyze them with a single static rate.

Reference cases (sanity-check the math)

The calculator runs eight inline reference and edge cases on load and logs assertion failures to the browser console. The repository acceptance suite executes the same calculation function in Node.

Why the result summary is at the top

The first result states only whether and when monthly principal-and-interest reduction recovers stated closing costs relative to the planned move date. The same summary also shows the estimated cash-and-loan-balance difference and any longer-term warning. It deliberately does not tell a user to refinance.

Sources and references

The formulas and concepts used here are standard mortgage mathematics. For external verification:

• Consumer Financial Protection Bureau — Understanding refinance closing costs
• IRS Publication 936 — Home Mortgage Interest Deduction (for tax-effect context)
• Standard mortgage payment formula — taught in any introductory finance course; matches outputs of Bankrate, NerdWallet, and Calculator.net within rounding tolerances.

No proprietary data, lender feeds, or paid API is used. The calculator is fully self-contained client-side JavaScript with no network calls after page load.