MathBench

Mortgage Calculator

Enter the home price and down payment and see your whole monthly payment — principal & interest plus property tax, insurance, PMI, and HOA — with a breakdown chart, the date PMI ends, a year-by-year amortization schedule, and what the home really costs over the life of the loan.

Educational estimates only. This calculator is for planning and education. It is not financial, tax, or investment advice, and results may differ from what a lender, broker, or the IRS calculates for your situation. Confirm important decisions with a qualified professional.

Taxes, insurance & fees (estimates — fine to leave as-is or zero them out)

Monthly payment

— / month

    —loan amount
    —payoff date
    —total interest
    —total cost incl. down payment
    —PMI ends
    —total PMI paid
    Amortization schedule (year by year)
    YearPrincipal paidInterest paidRemaining balance

    Principal & interest only — taxes, insurance, PMI, and HOA are paid alongside and never reduce the balance.

    How this calculator works

    Start with the two numbers every listing gives you — price and your down payment (dollars and percent stay in sync) — plus the term and rate from a loan quote. The calculator computes the fixed principal-and-interest payment with the standard amortization formula, then layers on the costs that ride along with a real mortgage bill: property tax, homeowners insurance, PMI when the down payment is under 20%, and HOA dues. The donut shows where each month's money goes; the headline is the whole payment, not just the loan.

    Below the breakdown, the chart tracks three lines over the life of the loan — the falling balance, cumulative principal, and cumulative interest — and the year-by-year schedule shows the same amortization a servicer would print. PMI is handled the way the law works: it's charged until the scheduled balance reaches 80% of the original price, and the calculator reports the exact month that happens and what the payment drops to. If you're weighing extra payments, the early-payoff calculator continues where this one stops.

    The formula

    Monthly P&I   M = P · r(1+r)ⁿ / ((1+r)ⁿ − 1)
              P = price − down payment,  r = rate ÷ 1200,  n = years × 12

Each month    interest  = balance × r
              principal = M − interest      (final payment prorated)

Escrow-side   tax/mo = annual tax ÷ 12      insurance/mo = premium ÷ 12
              PMI/mo = loan × PMI% ÷ 1200   (until balance ≤ 80% of price)

Total monthly = M + tax + insurance + PMI + HOA

    M is the closed-form annuity payment used by every lender for fixed-rate loans — the derivation appears in any corporate-finance text. The PMI cancellation point follows the federal Homeowners Protection Act: a borrower can request cancellation at 80% of the original value and the servicer must auto-terminate at 78% — see the Consumer Financial Protection Bureau's guide "When can I remove private mortgage insurance?"(consumerfinance.gov). The CFPB also documents what sits inside a monthly payment and how escrow accounts are re-analyzed yearly. Property-tax and insurance defaults here are national ballparks only — the help tips say where to find your real numbers.

    Worked example

    A $400,000 home with 10% down — the calculator's default. Loan: 30 years at 6.5%, property tax 1.2%/yr, insurance $1,600/yr, PMI 0.5%/yr:

    1. Loan amount: 400,000 − 40,000 = $360,000
    2. P&I: r = 6.5/1200, n = 360 → M = 360,000 × r(1+r)³⁶⁰/((1+r)³⁶⁰−1) = $2,275.44
    3. Escrow side: tax $400.00/mo, insurance $133.33/mo, PMI = 360,000 × 0.5% ÷ 12 = $150.00/mo
    4. Total: 2,275.44 + 400.00 + 133.33 + 150.00 = $2,958.78 per month
    5. PMI ends after 95 payments (~8 years), when the balance crosses 80% of the price ($320,000) — the payment drops to $2,808.78 and total PMI paid is $14,250
    6. Over 30 years: $459,160 of interest, and the home's all-in cost — down payment, principal, interest, taxes, insurance, and PMI — is about $1,065,410

    Switch the down payment to 20% and watch the difference: no PMI at all, a $320,000 loan, and the payment falls to $2,555.95 — the donut and schedule update as you type.

    Assumptions & tips

    • Compare loans by P&I, budgets by the total. Rate shopping only moves the principal-and-interest line, so compare quotes on that number — but budget on the full payment, because taxes and insurance arrive on the same bill.
    • Taxes and insurance are the moving parts. The P&I on a fixed loan never changes; escrow almost always does. Expect a yearly escrow analysis and a payment that drifts with reassessments and premium renewals.
    • PMI can end early if the home appreciates. The schedule here reaches 20% equity by amortization alone, but rising value counts too — after a couple of hot years, a ~$500 appraisal that proves 20% equity can delete PMI years ahead of schedule.
    • Try 15 years before dismissing it. On the default loan, a 15-year term at a typical lower rate roughly halves total interest. If the higher payment fits, the wealth difference is enormous — flip the term above and compare.
    • The all-in number is the honest one. A "$400,000 home" costing over a million dollars across 30 years is normal — that's what financing and carrying costs do. Knowing it up front beats discovering it in retrospect.
    • Closing costs aren't in this number. Expect another 2–5% of the loan at closing for fees, points, and prepaid escrow — the home-sale and payoff calculators cover other stages of the journey.

    Frequently asked questions

    What is actually inside a monthly mortgage payment?

    Four things, abbreviated PITI: principal (the part that pays down the loan), interest (the lender's charge on what you still owe), taxes (property tax, usually collected monthly into an escrow account), and insurance (your homeowners policy, plus PMI if you put less than 20% down). HOA dues are a fifth cost for condos and some neighborhoods, paid to the association rather than the lender. Only the principal builds equity — everything else is a carrying cost.

    What is PMI and when does it go away?

    Private mortgage insurance protects the lender when your down payment is under 20%. It typically costs 0.2% to 1.5% of the loan amount per year. Under the federal Homeowners Protection Act you can request cancellation once the balance reaches 80% of the home's original value, and the lender must cancel it automatically at 78%. This calculator removes PMI at the 80% point on the scheduled amortization. If your home appreciates quickly, you may reach 20% equity years earlier — a new appraisal can prove it.

    Do I really need 20% down?

    No. Conventional loans go as low as 3% down, FHA loans 3.5%, and VA and USDA loans can be 0% for eligible borrowers. What 20% buys you is no PMI and a smaller loan. The calculator shows the trade-off directly: lower the down payment slider and watch the PMI line appear and the payment rise. For many buyers, paying PMI for a few years beats waiting a decade to save the full 20%.

    Why is my lender's escrow payment different from this estimate?

    Escrow is the lender's running estimate of your taxes and insurance, recalculated every year — and they typically hold a cushion of up to two months on top. Property taxes also change when the assessor revalues your home or the local rate changes, and insurance premiums move at every renewal. The principal-and-interest part of a fixed-rate loan never changes; the escrow part almost always does.

    Does this work for adjustable-rate mortgages?

    It models the fixed period only. An ARM quoted as 6.125% (7/6 SOFR, for example) holds that rate for the first seven years, then adjusts every six months — the payment after year seven cannot be known today. Enter the initial rate to see the payment during the fixed period, and treat everything after the first adjustment as an unknown that could move up or down within the loan's caps.

    Sources

    1. 12 U.S.C. §4902, Termination of private mortgage insurance — Homeowners Protection Act of 1998; United States Code, 2024 edition, Office of the Law Revision Counsel. govinfo.govThe statute the PMI logic follows: borrower-requested cancellation at 80% of original value, automatic termination at 78%.
    2. When can I remove private mortgage insurance (PMI) from my loan? — Consumer Financial Protection Bureau. consumerfinance.govThe consumer-facing statement of the same 80%/78% thresholds, and the appraisal route to cancelling PMI early when the home appreciates.
    3. How do mortgage lenders calculate monthly payments? — Consumer Financial Protection Bureau. consumerfinance.govConfirms the fixed-rate amortization behind the closed-form principal-and-interest payment used above.
    4. On a mortgage, what's the difference between my principal and interest payment and my total monthly payment? — Consumer Financial Protection Bureau. consumerfinance.govThe PITI split the breakdown chart draws — which slice repays the loan and which slices are escrowed carrying costs.
    5. Regulation X, 12 CFR §1024.17, Escrow accounts — Consumer Financial Protection Bureau. consumerfinance.govThe annual escrow analysis and the cushion a servicer may hold, which is why this page's tax and insurance figures are estimates rather than a fixed bill.
    6. Why did my monthly mortgage payment go up or change? — Consumer Financial Protection Bureau. consumerfinance.govSupports the tip that reassessments and premium renewals move the total payment while principal and interest on a fixed loan never change.

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