Mortgage Calculator

Monthly total = A + annual tax ÷ 12 + annual insurance ÷ 12, where A = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)

P

Loan amount: the home price minus the down payment

r

Monthly interest rate: the annual rate divided by twelve

n

Number of payments: the mortgage term counted in months

A

The principal and interest part of the payment, rounded to the cent

T

Annual property tax, divided by twelve and rounded to the cent

I

Annual home insurance premium, divided by twelve and rounded to the cent

Use it before you look at houses, not after you have fallen for one: the monthly total decides which price band you can shop in, and it is usually a bigger constraint than the loan amount a lender will approve. Then use it to price the two decisions you actually control. The down payment trades cash today against cost over the whole term — moving from five percent to twenty on the same house cuts both the payment and the interest, and the reference chart below shows how much. The term moves the payment much less than people expect and the total interest a great deal more. Tax and insurance are the two fields people leave at zero and then get surprised by at closing: they are collected monthly whatever their size, and they rise over time even when the loan does not.

1. A 400,000 house, 20% down, 6.5% over thirty years

   1. Down payment: 400,000 × 20% = 80,000, so the loan amount is 400,000 − 80,000 = 320,000
   2. Monthly rate: 6.5 ÷ 12 = 0.541667% a month, which is 0.00541667 as a decimal
   3. Principal and interest: 320,000 × 0.00541667 × 1.00541667^360 ÷ (1.00541667^360 − 1) = 2,022.62
   4. Property tax: 4,800 ÷ 12 = 400.00 a month
   5. Insurance: 1,800 ÷ 12 = 150.00 a month
   6. Monthly total: 2,022.62 + 400.00 + 150.00 = 2,572.62
   7. Total interest over the term: 728,140.64 paid − 320,000 borrowed = 408,140.64

   This is the page's default. The loan payment is 2,022.62 but 2,572.62 leaves the account, and the 550 difference is not optional — it is collected with the payment. Note also that the interest over thirty years, 408,140.64, is larger than the amount borrowed.

2. A 250,000 house, 10% down, 6% over fifteen years

   1. Down payment: 250,000 × 10% = 25,000, so the loan amount is 225,000
   2. Monthly rate: 6 ÷ 12 = 0.5% a month, which is 0.005 as a decimal
   3. Principal and interest: 225,000 × 0.005 × 1.005^180 ÷ (1.005^180 − 1) = 1,898.68
   4. Property tax and insurance: 3,600 ÷ 12 = 300.00 and 1,200 ÷ 12 = 100.00 a month
   5. Monthly total: 1,898.68 + 300.00 + 100.00 = 2,298.68
   6. Total interest: 341,761.75 − 225,000 = 116,761.75

   Compare this with the example above: a smaller loan, but the payment is nearly as large, because the term is half as long. The interest, though, falls from 408,140.64 to 116,761.75 — the term is doing almost all of that work, not the rate or the price.

3. The same 400,000 house with 5% down

   1. Down payment: 400,000 × 5% = 20,000, so the loan amount is 380,000
   2. Principal and interest: 380,000 × 0.00541667 × 1.00541667^360 ÷ (1.00541667^360 − 1) = 2,401.86
   3. Monthly total: 2,401.86 + 400.00 + 150.00 = 2,951.86
   4. Extra interest against the 20% down case: 484,667.97 − 408,140.64 = 76,527.33

   The same house, the same rate, the same term — and 15,000 less cash down costs 379.24 a month and 76,527.33 more in interest over the life of the loan. This is the trade the down payment field exists to price, and it is the row the reference chart below is built around.

The loan arithmetic is exact; the monthly total is only as complete as the fields you fill in. Mortgage insurance is not here, and it is the big omission on low down payments — in the United States a down payment under twenty percent usually carries a monthly premium on top, which can add well over a hundred a month to the figure above. HOA or condo fees, ground rent and any special assessments are also excluded, and in some places they rival the tax. Closing costs are excluded because they are paid once rather than monthly. The two annual fields are entered by you and the page trusts them: property tax varies by state, county and city, is reassessed on its own schedule, and often changes the year after a sale, while insurance depends on the property and the cover. Moving from a thirty year to a fifteen year term usually raises the payment and always cuts the interest, and nothing here models an adjustable rate, an offset account or overpaying. If you are outside the United States, put the annual figures your lender actually collects with the payment, and leave both at zero where the property tax is a one-off at purchase and the insurance is not collected monthly. The amounts carry no currency symbol, so they are right in whatever currency you typed them in and meaningless in any other.

What is included in a monthly mortgage payment?

Principal, interest, property tax and home insurance — usually shortened to PITI. The principal and interest part is the loan; the tax and insurance parts are annual bills the lender collects in twelfths and holds in an escrow account until they are due. This page reports the loan payment, the two escrow figures and the total, which is the amount that actually leaves your account.

How much difference does the down payment make?

On a 400,000 house at 6.5% over thirty years, going from 5% down to 20% down raises the cash you need by 60,000, cuts the monthly payment by 379.24 and cuts the total interest by 76,527.33. It is the largest lever most buyers have, and it is also the one that decides whether mortgage insurance applies, which this page does not include.

Why are property tax and insurance part of the payment at all?

Because the lender has an interest in them being paid — an unpaid tax bill becomes a lien on the property that outranks the mortgage. Rather than trusting the borrower to find the money each year, the lender collects one twelfth a month into an escrow account and pays the bills itself. It also means the monthly figure can change even when the loan does not: reassess the tax or renew the insurance and the collected amount follows.

Is a shorter mortgage term always better?

It is always cheaper in total interest and always harder on the monthly budget. On 320,000, thirty years at 6.5% costs 408,140.64 in interest; fifteen years at the same rate costs far less but the payment rises by roughly a third. Whether that is better depends on whether you can carry the higher payment without straining, and whether the money would earn more somewhere else.

What down payment percentage should I enter?

Enter what you are actually putting in, as a percentage of the price: twenty percent for a fifth down, five for a twentieth. If you know the cash amount instead, divide it by the price — 60,000 on a 400,000 house is 15%. Do not enter 100%, which means paying cash and taking no loan at all; that is not a mortgage and the page will not calculate one.

Does this include closing costs and fees?

No. Application fees, appraisal, title insurance, legal costs and any points paid to buy the rate down are one-off charges at completion and are not part of the monthly payment or the total interest. They are real money and worth comparing between offers, but they belong on a different sheet — a lower rate bought with points is only cheaper after enough years.

• Property taxes — how the annual property tax behind the escrow figure is levied and collected — New York State Department of Taxation and Finance (United States)
• Home buying assistance — an overview of what a home purchase involves beyond the loan — USAGov, U.S. General Services Administration (United States)
• Mortgage Debt Outstanding — the size of the mortgage market the payment is measured against — Board of Governors of the Federal Reserve System (United States)