Mortgage Calculator (USA) | Payment, PMI, Taxes

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Enter a home price, down payment, APR, and term. This calculator estimates your monthly payment and payoff month. Advanced options include property tax, insurance, HOA, PMI, and extra principal payments.

Down payment is what you pay upfront. The loan is the rest.
This is used to estimate the payoff month.
Property tax is usually paid monthly through escrow (escrow is a bill-paying account your lender can run).
PMI (private mortgage insurance) is often required with a small down payment. If you do not have PMI, leave this at 0.
This is a model assumption, not a promise. Your loan terms can be different.
Extra principal payments can reduce total interest and shorten the payoff date.

How to use this calculator

  1. Enter the home price in USD (the purchase price).
  2. Enter the down payment, then pick % or USD (down payment is the money you pay upfront).
  3. Enter the interest rate (APR) (APR is the yearly interest rate as a percent).
  4. Choose the loan term in years (how long you plan to take to pay it back).
  5. Set the first payment month (used to estimate your payoff month).
  6. If you want a more realistic monthly total, open Advanced options and add any costs you have: property tax, insurance, HOA, PMI, and extra payments.
  7. Press Calculate. Read: the monthly total, the principal-and-interest payment, the payoff month, and total interest.
  8. If you add extra principal payments, check the savings section (it estimates time saved and interest saved).

This is a planning estimate. Real loans can differ by fees, rate changes, escrow rules, and lender terms.

Definitions

  • Principal: the amount you borrowed (your loan balance).
  • Interest: the cost of borrowing money (paid to the lender).
  • APR: annual percentage rate (your yearly interest rate as a percent).
  • Escrow: an account your lender can use to pay bills like taxes and insurance for you.
  • Property tax: a tax charged by your local government, often paid monthly through escrow.
  • Homeowners insurance: insurance that covers damage to the home (sometimes required by the lender).
  • HOA: homeowners association dues (a monthly fee in some neighborhoods or buildings).
  • PMI: private mortgage insurance (often required when your down payment is small).
  • PMI cutoff: the loan balance level where PMI may end (this calculator models it as a percent of home price).
  • Extra payment to principal: extra money you choose to pay that reduces the balance faster.
  • Amortization: the loan schedule where the payment can stay the same, but the interest part usually starts high and shrinks over time.

Methodology and sources

What this calculator does

  • Calculates a fixed-rate monthly payment for principal and interest (P and I).
  • Adds optional monthly items (property tax, homeowners insurance, HOA, PMI) to show an estimated monthly total.
  • Builds a simple amortization model to estimate payoff month, total interest, and balances at a few checkpoints.
  • Models extra principal payments (monthly extra, plus an optional one-time extra in the first month) and compares them to a no-extra baseline.

Key definitions

  • Home price: purchase price of the home.
  • Down payment: entered as a percent of home price or a USD amount.
  • Loan amount (principal): home price minus down payment.
  • APR: annual percentage rate entered as a percent per year. This tool treats it as a nominal annual rate and converts it to a monthly rate by dividing by 12.

Monthly payment formula (principal and interest)

  • Let P be the loan amount, r be the monthly rate (APR/12), and n be the total number of monthly payments (years x 12).
  • If r = 0: payment = P / n.
  • If r > 0: payment = P x r x (1 + r)^n / ((1 + r)^n – 1).

Amortization model used

  • Each month, interest = current balance x r.
  • Scheduled principal = (monthly payment) – (interest). If this is negative (extreme APR edge case), principal is set to 0.
  • Extra principal is added (monthly extra every month, plus one-time extra in month 1).
  • If total principal would exceed the remaining balance, it is capped so the loan pays off exactly.
  • The payoff month is the month where the balance reaches 0 in the iteration.
  • Yearly chart points are recorded every 12 payments (plus the starting balance as point 0).

Monthly total shown (PITI-style add-ons)

  • Property tax: entered as USD per year or as a percent of home price per year, then divided by 12.
  • Homeowners insurance: entered as USD per year, then divided by 12.
  • HOA: entered as USD per month.
  • PMI: estimated as (PMI rate %) x (original loan) / 12, and only included when starting loan-to-value is above 80%.
  • These add-ons are included in the monthly total number shown, but they do not change the loan balance in the amortization math.

PMI cutoff shown (simplified)

  • The tool shows an estimated PMI end month when the loan balance falls to a chosen percent of home price (78% or 80%).
  • This is a model assumption. Actual PMI rules depend on loan type, payment history, appraisals, and your servicer’s process.

Scope and limits

  • Fixed-rate only. No adjustable-rate, interest-only, balloon, or negative amortization modeling.
  • Does not include closing costs, points, rate locks, or lender fees.
  • Taxes, insurance, HOA, and PMI can change over time. This tool treats them as constant monthly amounts.
  • Payoff month is an estimate based on monthly iteration. Real payoff timing can differ due to daily interest rules and how extra payments are applied.

Sources

This section describes the math used by this page’s calculator. It is not a quote of any lender’s terms.
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