Mortgage payment calculator

How the formula works

A fixed-rate mortgage is amortized: every month you pay the same amount \(M\), but its composition shifts. Interest is charged on the balance that remains, so early payments are mostly interest and late payments are mostly principal. The payment that exactly pays the loan off over \(N\) months is:

where \(L\) is the loan amount (price minus down payment), \(r\) the annual rate as a decimal and \(T\) the term in years. That covers principal and interest only. What you actually send each month usually escrows the rest of home ownership:

What each input means

Home price and down payment

The loan is the gap between them: \(L = \text{price} - \text{down}\). The down payment also sets whether you pay PMI — put down less than 20% and most conventional lenders charge it.

Interest rate — \(r\)

The note rate on the loan, not the APR. The APR folds fees into a single comparison number; the payment is computed from the note rate.

Term — \(T\)

How long the loan runs. A shorter term raises the payment but cuts total interest sharply, because the balance — the thing interest is charged on — falls faster.

Property tax and home insurance

Annual figures, usually collected monthly into escrow. Tax varies by county — around 1% of the home's value is a common national ballpark, but check the actual bill for the property.

PMI rate

Private mortgage insurance, charged while the down payment is under 20%. Typically 0.3–1.5% of the loan per year depending on credit score and loan size. It protects the lender, not you, and it can be removed once you reach 20% equity.

HOA dues

Monthly association dues, if any. Not part of the mortgage, but part of the payment you must budget for — lenders count it when qualifying you.

A worked example

The worksheet's defaults: a $400,000 home with $80,000 down (20%, so no PMI), at 6.5% for 30 years, with $4,800 a year of property tax and $1,800 of insurance.

• Loan amount: $400,000 − $80,000 = $320,000.
• Monthly rate: \(i = 0.065/12 = 0.005417\); over \(N = 360\) months the growth factor is \((1+i)^{360} = 6.9918\).
• Principal & interest: $320,000 × 0.005417 × 6.9918 / (6.9918 − 1) = $2,022.62.
• Add escrow: $4,800/12 + $1,800/12 = $550 a month, for a PITI of $2,573.

The first payment splits $1,733 interest / $289 principal — the balance barely moves. Over the full term the interest adds up to $408,142, more than the loan itself at this rate. That is not a trick; it is what borrowing $320,000 for three decades costs.

Assumptions and limits

• Fixed rate for the whole term. An ARM reprices; this model does not.
• Tax and insurance are today's figures held flat. In reality both rise over time, so the PITI shown is a floor, not a ceiling.
• PMI is shown at today's charge. On a conventional loan it can be removed at 20% equity on request and falls away automatically at 22%; the schedule here does not model that drop.
• No closing costs, points or extra payments — the payment is the contract payment. This is arithmetic, not advice: qualification depends on your whole financial picture, which only a lender can price.

Questions people ask

How much house can I afford on my income?

Lenders commonly cap the housing payment near 28% of gross monthly income and total debt payments near 36% (the 28/36 rule). On a $100,000 salary that is roughly a $2,333 housing payment — this calculator tells you what price and rate produce that number. The stricter test is your own budget: a lender approves the maximum, not the comfortable.

Why is my first payment almost all interest?

Interest is charged on the outstanding balance, and at the start the balance is the whole loan. In the worked example the first month's interest is $320,000 × 0.005417 ≈ $1,733, leaving only $289 of the $2,022.62 payment to reduce the balance. As the balance falls the split shifts — by the final years the same payment is nearly all principal.

What do extra payments do?

Every extra dollar goes straight to principal, which shrinks the base interest is charged on for every month that follows. Adding $200 a month to the worked example pays the loan off about 6.7 years early and saves roughly $105,430 in interest. There is no penalty on extra principal for standard US conforming loans.

When does PMI go away?

On a conventional loan you can request cancellation once the balance reaches 80% of the home's original value, and the lender must drop it automatically at 78%. FHA loans work differently: their mortgage insurance premium usually runs for the life of the loan unless you put 10% or more down, which is a common reason borrowers refinance out of FHA later.

Is the rate here the same as APR?

No. The payment is computed from the note rate — the rate on the loan documents. APR restates the loan's cost including origination fees and points as if they were interest, which makes it useful for comparing offers but wrong for computing the payment. APR is always the higher of the two on the same loan.