Monthly Mortgage Payment Calculator

How the calculation works

Mortgage Payments: How the Monthly Amount Is Calculated

A mortgage payment is the amount a borrower pays the lender each month for the length of the loan. In most US home loans, the payment is set so that interest and principal together bring the balance to zero by the last payment. Its size depends on three things: the amount borrowed, the interest rate and the number of payments. Knowing how the formula produces the number makes it easier to compare offers, test scenarios and understand what a lender is proposing.

The level-payment formula

The calculator uses this formula:

P = C × [r × (1+r)^n] / [(1+r)^n − 1]

C is the loan amount, r is the monthly interest rate and n is the total number of monthly payments. The rate r comes from the annual nominal rate, NR, divided by 1200. Dividing by 1200 turns a percentage into a decimal and an annual rate into a monthly one in a single step. For a 6.5% rate, r is about 0.00542. The term is entered in years, and n is the term multiplied by 12, so a 30-year loan has 360 payments.

The bracketed expression is an annuity factor. It converts a lump sum into the equal payment that, made every month at rate r, exactly repays the loan by the final payment. This is why the payment does not change over the life of a fixed-rate loan, even though the mix of interest and principal does.

Why the split between interest and principal changes

Each month the lender charges interest on the balance still owed, and the rest of the payment reduces that balance. Early in the loan the balance is large, so interest takes a large share of each payment. As the balance falls, the interest charge falls too, and a bigger share of the same payment reduces principal. In the 30-year example at 6.5%, the first month's interest is about 0.54% of the loan amount, which is the monthly rate applied to the full balance. Principal makes up the rest of that first payment. Near the end of the term, almost the entire payment reduces principal.

How the rate is built: index plus margin

The calculator asks for an index rate and a margin, and adds them to give the nominal rate. The index is a benchmark that moves with market conditions. Adjustable-rate mortgages commonly tie to SOFR, the Secured Overnight Financing Rate published by the Federal Reserve Bank of New York, and some products use the prime rate. The margin is a fixed percentage the lender adds on top of the index, and it is written into the loan note. Lenders set it using the borrower's credit profile, the loan-to-value ratio, the product and the market at the time of the offer. Two borrowers with the same index can therefore be offered different margins.

For a fixed-rate loan, the simplest approach is to enter the agreed rate as the index and set the margin to zero. The result is the same as entering that rate directly into the formula.

Term length and total cost

Term has a larger effect on total cost than most borrowers expect. At the same 6.5% rate, a 15-year loan has a monthly payment about 38% higher than a 30-year loan. Its total interest, however, is about 57% of the amount borrowed, compared with about 128% over 30 years. The longer term lowers the monthly obligation while increasing the cost of borrowing over time. The right balance depends on income stability, other debts, savings and how long the borrower expects to stay in the home.

Edge cases the formula handles differently

• A zero nominal rate makes the bracketed fraction undefined, because the numerator and the denominator both reach zero. In that case the calculator uses P = C ÷ n, which splits the loan evenly across the payments.
• The loan amount and the term must both be greater than zero. A term of zero leaves no payments to divide the loan across.
• Lenders round each payment to the cent, so the final payment on a real loan can differ by a few cents from the others.
• The formula assumes one rate for the whole term. An adjustable-rate loan changes its payment at each reset, so the calculator shows the payment at the rate you enter, not a forecast of future payments.

When to use this calculator

Use it to compare term options, test how a change in index or margin moves the payment, and check the payment implied by each offer before requesting formal quotes. It also helps with prepayment planning. To estimate the effect of an extra principal payment, enter the remaining balance as the loan amount and the remaining years as the term. The result is the payment a re-amortized loan would need, which shows how much the monthly cost falls if the loan is recalculated over the remaining period.

When not to use it

This calculator is not designed for every loan type. It does not model interest-only loans, where the scheduled payments do not reduce principal, and it does not model home equity lines of credit, which are revolving balances with variable draws. It also does not compute the APR, property taxes, homeowners insurance or mortgage insurance, so it cannot produce the full monthly housing cost on its own. A reverse mortgage follows different rules and needs its own calculation.

Common mistakes

Several input errors produce misleading results:

• Entering the home price instead of the loan amount. The loan amount is the purchase price minus the down payment.
• Entering the rate as 0.065 instead of 6.5. The calculator expects the percentage.
• Entering the term in months rather than years.
• Treating the nominal rate as the APR. The APR is usually higher because it includes certain fees.
• Forgetting escrow. The payment on a monthly statement can be well above the principal and interest result.
• Assuming an adjustable loan will keep its starting rate. Test higher index values before choosing one.

Regulatory and disclosure context

In the United States, the Truth in Lending Act and its implementing rule, Regulation Z, require lenders to disclose the APR and the finance charge in a standard format. Under the TILA-RESPA Integrated Disclosure rule, known as TRID, lenders provide a Loan Estimate shortly after an application and a Closing Disclosure before closing. Those forms show the note rate, the APR, the projected monthly payment and the estimated escrow amounts, so they are the reference to check against this calculator's results. The Consumer Financial Protection Bureau supervises consumer lending rules and publishes guidance for borrowers. The Federal Reserve influences the benchmark rates that feed many adjustable mortgages through its monetary policy decisions.

Consulting a professional

The result is an estimate. Before signing, review the Loan Estimate and Closing Disclosure, compare offers from several lenders, and consider speaking with a licensed mortgage broker, a loan officer or a HUD-approved housing counselor. Each can check the figures against the actual terms of the loan you are being offered.