Mortgage payment calculator: what the monthly number is made of

A mortgage payment calculator answers one narrow question: given a purchase price, a down payment, an interest rate and a term, what leaves your account every month, and what does the loan cost in total by the time it is paid off?

The monthly figure has two very different halves. Principal and interest is fixed by contract at closing and does not change for the life of a fixed-rate loan. Property tax, insurance, mortgage insurance and HOA dues are estimates that drift year to year, and they are often the reason a payment quoted from a listing feels wrong when the first statement arrives.

This page explains the amortization formula the calculator uses, works one payment out by hand, and shows how far the answer moves when the rate, the term or the down payment changes. The rate you enter is your assumption -- lenders quote rates individually, based on the loan, the property and your credit file.

#The amortization formula

A fixed-rate mortgage is an ordinary annuity. The lender advances a principal today and receives an identical payment each month until the balance reaches zero. The payment is whatever amount makes the present value of that stream equal the amount borrowed.

Formula: M = L * r * (1 + r)^n / ((1 + r)^n - 1) where M is the monthly principal-and-interest payment, L is the loan amount (price minus down payment), r is the monthly interest rate (the annual rate divided by 12, as a decimal), and n is the number of monthly payments (years x 12).

Two details matter. The rate is divided by 12 rather than converted to an equivalent monthly compounding rate, which is the standard US convention. And n counts payments, not years, so a 30-year loan is 360 periods.

The full monthly outlay adds the escrowed and recurring items:

Formula: Total monthly = M + annual property tax / 12 + annual insurance / 12 + monthly HOA + PMI

The calculator adds a mortgage insurance estimate whenever the loan is more than 80% of the price. It uses 0.75% of the loan amount per year, divided by 12, as a mid-range placeholder. Real mortgage insurance pricing depends on the loan program, the loan-to-value ratio and your credit score, and your quote will state the actual figure.

#A worked example, done by hand

Take a price of $380,000 with 20% down, a 30-year term, and an assumed rate of 6.5%.

1. Down payment: 380,000 x 0.20 = $76,000. Loan amount: 380,000 - 76,000 = $304,000.
2. Monthly rate: 0.065 / 12 = 0.0054166667. Number of payments: 30 x 12 = 360.
3. Growth factor: (1.0054166667)^360 = 6.991798.
4. Numerator: 304,000 x 0.0054166667 x 6.991798 = 1,646.67 x 6.991798 = 11,513.16.
5. Denominator: 6.991798 - 1 = 5.991798.
6. Payment: 11,513.16 / 5.991798 = $1,921.49 a month in principal and interest.

Now the rest of the payment. Property tax of $4,600 a year is $383.33 a month. Insurance of $1,800 a year is $150.00 a month. With 20% down there is no mortgage insurance and, in this example, no HOA.

Worked example: 1,921.49 + 383.33 + 150.00 = $2,454.82 a month in total. Over 360 payments the principal-and-interest side totals 1,921.49 x 360 = $691,735.24, of which $387,735.24 is interest -- more than the $304,000 borrowed.

#Why the payment is constant but the split shifts

Interest each month is charged on the balance that is actually outstanding: interest = balance x r. Whatever is left of the fixed payment reduces the balance. Because the balance falls, the interest portion falls, and the principal portion rises by exactly the same amount.

In month one, interest is 304,000 x 0.0054166667 = $1,646.67, so only $274.82 of the $1,921.49 payment touches the debt. The curve is slow at first and then accelerates.

Halfway through the term in time, at payment 180, the balance is still $220,579.79 -- about 73% of the original loan. That asymmetry is the single most misunderstood feature of a mortgage, and it is why selling early leaves less equity than people expect. The rent vs buy calculator uses the same schedule to work out what is left after selling costs.

#PITI and the parts of the payment

Lenders describe the housing payment as PITI: principal, interest, taxes and insurance. Only the first two come from the loan contract. The others are collected because the lender has a claim on the property and wants the tax bill and the hazard policy paid on time.

• Principal and interest. Fixed for a fixed-rate loan. This is the only line the amortization formula produces.
• Property tax. Set by the local assessor as a rate applied to an assessed value. It is reassessed periodically and generally rises over time.
• Home insurance. A separate contract with an insurer, repriced at each renewal.
• Mortgage insurance. Protects the lender, not you, and applies when the down payment is small.
• HOA dues. Paid directly to an association, not usually escrowed, and outside the lender's calculation of your payment.

Most lenders escrow the tax and insurance items: one-twelfth of the annual bills is added to the payment, held, and disbursed when the bills fall due. When an escrow analysis finds a shortfall after a tax increase, the monthly payment changes even though the loan terms did not.

#Where each input comes from

Home price. The contract price, not the list price. Seller concessions reduce your cash to close but do not usually reduce the recorded price.

Down payment. Enter it as a percentage. The 80% loan-to-value line is the one that matters: above it, the calculator adds mortgage insurance.

Interest rate. Use a quote you have been given, or run the page at several rates to see the range. Never treat any single figure as current; rates move daily and differ by borrower and loan type.

Loan term. The dropdown covers 30, 25, 20, 15 and 10 years. Shorter terms raise the payment and cut total interest sharply.

Property tax per year. The county assessor or the listing usually shows the last billed amount. A reassessment after sale can change it materially.

Home insurance per year. Use a written quote for the specific property. Location, roof age and construction drive the price more than the purchase amount does.

HOA dues per month. From the association's disclosure. Special assessments are separate and are not part of the monthly figure.

The answer is most sensitive to the rate and the loan amount, in that order. Tax and insurance change the monthly total but barely touch the lifetime interest.

#How rate and term move the payment

Both change the payment, but they do very different things to the lifetime cost. Each row below holds the $304,000 loan and the 30-year term constant and varies only the rate.

Each half point costs roughly $95 to $105 a month here, and roughly $35,000 in interest over the full term. Now hold the rate at 6.5% and change the term instead.

A 15-year term costs $726.68 more a month and removes $215,065.29 of interest. The trade is liquidity for total cost, and the arithmetic favors the shorter term only if the higher payment is comfortable in a bad month as well as a good one.

#The 80% threshold and PMI

Mortgage insurance is priced off the loan, so it shrinks as the down payment grows -- and then disappears entirely at 20% down. The table below keeps the $380,000 price, the 6.5% assumed rate, the 30-year term, $4,600 of tax and $1,800 of insurance.

The step from 15% to 20% down is the only discontinuity in the table: $19,000 more cash removes $321.97 a month, because it removes both interest on $19,000 and the whole mortgage insurance line. Mortgage insurance is not permanent -- borrowers can generally request cancellation once the loan is paid down far enough relative to value, and federal rules require automatic termination later in the schedule. The Consumer Financial Protection Bureau describes the mechanics.

#How to read the result

The headline number is a monthly cash-flow figure, useful for comparing properties and for testing whether a price is workable against your take-home pay. It is not the full cost of owning: it excludes maintenance, utilities and the cash you spend at closing.

The total interest line is the price of borrowing over the whole term, assuming you keep the loan that long. Most people do not. If you expect to move or refinance within a decade, the interest actually paid is far less than the total interest shown, but so is the equity built -- look at the balance column in the amortization table for the year you expect to sell.

#What this model leaves out

• Points and lender credits. Paying points buys a lower rate for cash up front; the calculator sees only the rate you type.
• Closing costs. Origination, title, appraisal, recording and prepaid escrow are real cash and are not in any line here. The loan calculator shows how an up-front fee changes an effective rate.
• Adjustable-rate loans. The formula assumes one rate for the whole term. An ARM reprices at set intervals, and the payment recomputes on the balance remaining.
• Flood, wind and umbrella coverage. These are separate policies in many areas, often required and sometimes larger than the base premium.
• Underwriting. Nothing here checks debt-to-income limits, reserves, loan limits or program eligibility. Only a lender's decision does that.
• Extra payments. The schedule assumes the exact contractual payment every month.
• Taxes. No tax treatment of mortgage interest or property tax is modeled.

#Common mistakes

Comparing a P&I figure to a rent figure. Rent usually includes the landlord's tax and insurance. Compare the full PITI total instead.

Assuming the tax line is stable. Many jurisdictions reassess on sale, so the seller's last bill can understate what you will pay.

Reading a total line as the cost of the house. The calculator shows two of them. "Total principal and interest paid" is the payment multiplied by the number of months, $691,735.24 on the default loan. "Total cash over the term, including the down payment and escrow" adds the $76,000 down payment and thirty years of escrowed tax and insurance, reaching $959,735.24. Neither figure includes maintenance, utilities or closing costs.

Treating a 15-year loan as strictly better. It costs far less in interest, but the higher payment is contractual. Some people prefer a 30-year loan and pay extra voluntarily, keeping the lower payment as a fallback.

Forgetting that money has other uses. Cash used for a larger down payment stops being available for anything else. The compound interest calculator shows what that same cash would need to earn elsewhere to keep up.

Ignoring the escrow reset. A payment quoted at closing can change at the first escrow analysis without any change to the loan itself. Browse the full set of calculators if you want to test the surrounding numbers.