refinance calculator

Refinance calculator to compare your current mortgage vs. a new loan. See new payment, monthly savings, break-even date, and total interest savings including closing costs and points.

# Date Payment Interest Principal Balance

Full original guide (expanded)

Authoritative Data Source & Methodology

Primary references:

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The Formula Explained

Standard amortized monthly payment:
\\[ PMT = P \\, \\cdot \\, \\frac{i(1+i)^{n}}{(1+i)^{n}-1} \\] where \\(P\\) is principal, \\(i = \\tfrac{APR}{12}\\) is the monthly rate, and \\(n\\) the number of months.

Remaining total interest for a loan is: \\[ I_{total} = PMT \\cdot n - P \\] Break-even months approximate when cumulative savings exceed upfront costs \\(C\\): \\[ m_{BE} \\approx \\min\\{m : \\sum_{k=1}^{m} (PMT_{old}-PMT_{new}) \\ge C\\} \\] (In this tool we compute break-even via a monthly cumulative comparison; if costs are rolled into the new principal, interest on those costs is reflected in \\(PMT_{new}\\).)

Glossary of Inputs & Outputs

  • Remaining Balance: Current principal owed on your existing mortgage.
  • Remaining Term: Time left until payoff of your existing loan.
  • Current APR / New APR: Annual Percentage Rate used for interest calculation.
  • Closing Costs: Upfront refinance costs (lender/title/fees; add prepayment penalty if any).
  • Discount Points: Upfront % of loan to lower the interest rate.
  • Roll Costs: Option to add costs/points into new principal (increasing interest over time).
  • Monthly Savings: Old payment minus new payment.
  • Break-Even: Month/date when cumulative savings exceed costs.
  • Total Interest + Costs (New): New loan interest plus all refinance costs (including rolled-in amounts).

How It Works: A Step-by-Step Example

Example: Remaining balance $300,000; 25 years left at 6.75% APR. New 30-year loan at 5.75% APR; $4,500 costs; 0 points; costs rolled in. The tool:

  1. Computes your old payment via the amortization formula with \\(P=300{,}000\\), \\(i=0.0675/12\\), \\(n=300\\).
  2. Builds the new principal (adds rolled-in costs if selected), then computes the new payment with \\(i=0.0575/12\\) and \\(n=360\\).
  3. Calculates monthly savings and simulates cumulative savings vs. upfront costs to find the break-even month/date.
  4. Compares remaining interest on old loan to interest+costs on the new loan to show total savings.

Frequently Asked Questions

Is a longer new term always better if the rate drops?

No. A longer term can lower the monthly payment but often increases total interest paid. Use the totals displayed to gauge true savings.

What if I’m far into my existing mortgage?

Late-stage loans are mostly principal; the interest you can avoid may be smaller. The break-even calculator helps you judge if costs are recovered.

How do prepayment penalties affect results?

Add the penalty to Closing Costs to correctly reflect break-even and total savings.

Can I simulate paying points to buy down the rate?

Yes. Enter points % and adjust New APR to the quoted buy-down rate; the tool includes the points cost (rolled or upfront).

Does the tool include taxes/insurance/HOA?

No. It focuses on principal & interest. Add escrow items separately for your full housing payment.

Last accuracy review:

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[PMT = P \\, \\cdot \\, \\frac{i(1+i)^{n}}{(1+i)^{n}-1} \\]
PMT = P \\, \\cdot \\, \\frac{i(1+i)^{n}}{(1+i)^{n}-1} \
Formula (extracted LaTeX)
\[I_{total} = PMT \\cdot n - P \\]
I_{total} = PMT \\cdot n - P \
Formula (extracted LaTeX)
\[m_{BE} \\approx \\min\\{m : \\sum_{k=1}^{m} (PMT_{old}-PMT_{new}) \\ge C\\} \\]
m_{BE} \\approx \\min\\{m : \\sum_{k=1}^{m} (PMT_{old}-PMT_{new}) \\ge C\\} \
Formula (extracted text)
Standard amortized monthly payment: \\[ PMT = P \\, \\cdot \\, \\frac{i(1+i)^{n}}{(1+i)^{n}-1} \\] where \\(P\\) is principal, \\(i = \\tfrac{APR}{12}\\) is the monthly rate, and \\(n\\) the number of months. Remaining total interest for a loan is: \\[ I_{total} = PMT \\cdot n - P \\] Break-even months approximate when cumulative savings exceed upfront costs \\(C\\): \\[ m_{BE} \\approx \\min\\{m : \\sum_{k=1}^{m} (PMT_{old}-PMT_{new}) \\ge C\\} \\] (In this tool we compute break-even via a monthly cumulative comparison; if costs are rolled into the new principal, interest on those costs is reflected in \\(PMT_{new}\\).)
Variables and units
  • P = principal (loan amount) (currency)
  • r = periodic interest rate (annual rate ÷ payments per year) (1)
  • n = total number of payments (years × payments per year) (count)
  • M = periodic payment for principal + interest (currency)
  • T = property tax (annual or monthly depending on input) (currency)
  • I = homeowners insurance (annual or monthly depending on input) (currency)
  • HOA = homeowners association dues (monthly) (currency)
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
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Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).