Mortgage Calculator
Calculate the fixed monthly principal-and-interest payment on a home loan, the total repaid and a month-by-month amortization schedule.
Common Scenarios
Updated Formula covered by automated tests
A home loan is usually the largest debt a household ever takes on, and the number that matters month to month is the principal-and-interest payment. Enter the amount you plan to borrow, the annual interest rate on the offer and the term in years, and this tool returns the fixed monthly payment, the total you will hand the lender over the life of the loan, and how much of that total is interest.
House hunters use it to turn a listing price into a monthly figure before talking to a lender, and current owners use it to see how a shorter term or a lower rate would change their costs. The amortization schedule shows, month by month, how each payment is split between interest and paying down the balance, which explains why equity builds so slowly in the first years of a 30-year mortgage.
The formula
- M
- Monthly principal-and-interest payment in dollars
- P
- Amount borrowed: purchase price minus down payment, in dollars
- r
- Monthly interest rate as a decimal, so 6.5% a year becomes 0.065 ÷ 12 = 0.0054167
- n
- Total number of monthly payments, 360 for a 30-year loan and 180 for a 15-year loan
A fixed-rate mortgage is an annuity: the lender hands you P today in exchange for n equal payments. The formula picks the one payment size whose present value, discounted at the monthly rate, equals the loan amount. Each month the lender first charges interest on the remaining balance (balance × r), and whatever is left of M reduces the principal. Because the balance is highest at the start, early payments are mostly interest.
US lenders quote mortgage rates as nominal annual rates compounded monthly, which is why the annual figure is simply divided by 12 rather than converted with an exponent. At a 0% rate the standard equation becomes 0 ÷ 0, so the calculator switches to plain division of the balance by the number of payments.
Worked example
The Garcias are buying a $400,000 house with 20% down, so they need to borrow $320,000. Their lender offers a 30-year fixed rate of 6.5%.
- 1 Monthly rate: 0.065 ÷ 12 = 0.0054167. Number of payments: 30 × 12 = 360.
- 2 Growth factor: (1.0054167)³⁶⁰ = 6.9918.
- 3 Payment: 320,000 × 0.0054167 × 6.9918 ÷ (6.9918 − 1) = 320,000 × 0.037872 ÷ 5.9918 = $2,022.62.
- 4 Total paid: 2,022.62 × 360 = $728,142.36, so total interest is 728,142.36 − 320,000 = $408,142.36.
- 5 First month: interest is 320,000 × 0.0054167 = $1,733.33, leaving only $289.28 of the first payment to reduce the balance.
Result: The Garcias would pay $2,022.62 a month for principal and interest. Over 30 years they would pay about $408,000 in interest, more than the amount they borrowed.
Before you rely on the result
- Assumes a fixed rate for the whole term. Adjustable-rate mortgages reset after the initial period and need a different projection.
- Excludes property tax, insurance, mortgage insurance, HOA dues and closing costs, and the result is rounded to the cent, so a lender’s schedule may differ by a few cents on the final payment.
- This is an estimate for planning, not a loan offer. Compare official Loan Estimates from several lenders and consider a HUD-approved housing counselor before committing.
Frequently asked questions
Why is my lender’s monthly figure higher than this result?
This tool calculates principal and interest only. Most lenders collect property tax and homeowners insurance through an escrow account, and loans with less than 20% down usually add private mortgage insurance or an FHA premium. Those items can add several hundred dollars a month and change from year to year.
How much does a 15-year term save compared with 30 years?
On the Garcias’ $320,000 at 6.5%, a 15-year term raises the payment to about $2,787.54 but cuts total interest to about $181,758, a saving of roughly $226,000. In practice 15-year loans are often offered at a lower rate too, which widens the gap further.
Is the interest rate the same thing as the APR on my Loan Estimate?
No. The note rate drives the payment and is what you should enter here. The APR folds in points and certain closing costs to make offers comparable, so it is usually a little higher and would overstate the payment if used in this formula.
What happens to the schedule if I pay extra toward principal?
Any extra amount goes straight to the balance, so the next month’s interest charge is smaller and the loan ends early. The required payment on a standard fixed-rate loan does not drop unless you ask the lender to recast it. Check that your loan has no prepayment penalty first.
Sources
- Consumer Financial Protection Bureau: Buying a House (consumerfinance.gov)
- Consumer Financial Protection Bureau: Ask CFPB, mortgages (consumerfinance.gov)