How the monthly payment is calculated
A fixed-rate mortgage is repaid in equal monthly installments. Each installment first pays the interest that built up on the outstanding balance during the month, and whatever is left reduces the balance. Because the balance shrinks every month, the interest part shrinks too, and a growing share of the same payment goes to principal. This pattern is called amortization, and the table above shows it for every month of the loan.
The level payment that brings the balance to exactly zero at the end of the term is:
M = P × r ÷ (1 − (1 + r)^−n)
Mis the monthly principal and interest payment.Pis the amount borrowed (the principal).ris the monthly interest rate: the annual rate divided by 100 and then by 12. A 6% annual rate is 0.005 per month.nis the number of monthly payments: the term in years times 12.
When the rate is 0%, the formula reduces to the amount borrowed divided by the number of payments. The calculator rounds each month's interest to the cent and lets the final payment absorb the few cents of rounding so that the last balance is exactly zero. That is why the last row of the schedule can differ slightly from the other payments.
Worked example: a published Loan Estimate
The U.S. Consumer Financial Protection Bureau publishes a completed sample Loan Estimate (form H-24(B)) for a $162,000.00 loan over 30 years at a fixed 3.875% rate. Working through it step by step:
- Monthly rate: 3.875 ÷ 100 ÷ 12 = 0.00322917.
- Number of payments: 30 × 12 = 360.
- Growth factor: (1 + r)^n = 3.191934, so (1 + r)^−n = 0.313290.
- Payment: $162,000.00 × 0.00322917 ÷ (1 − 0.313290) = $761.78 a month.
The published form shows the same monthly principal and interest of $761.78. In the first month, interest is $523.13 and only $238.65 goes to principal. After five years (60 payments) the borrower has paid off $15,773.00 of principal, which matches the $15,773 the form reports under “In 5 Years”. Over the full term the interest adds up to $112,243.70, and the final payment of $764.68 leaves a balance of $0.00.
The form also reports a Total Interest Percentage of 69.45%. That figure adds the $262 of prepaid interest due at closing to the scheduled interest and divides by the loan amount: ($112,243.70 + $262) ÷ $162,000.00 = 69.45%.
What changes the cost of a loan
Starting from the calculator's default of $300,000.00 at 6.5% over 30 years, the payment is $1,896.20 and total interest is $382,636.71. Changing one input at a time shows which lever matters most.
A shorter term
Over 15 years instead of 30, the payment rises to $2,613.32, but total interest falls to $170,398.28. You pay more each month and far less overall, because the balance is outstanding for half as long.
A higher rate
One percentage point more (7.5%) raises the payment to $2,097.64 and total interest to $455,155.25. On a long loan, small rate differences compound into large differences in total cost, which is why comparing offers on the same term and amount is useful.
Borrowing less
Borrowing $270,000.00 instead of $300,000.00, for example by putting more money down, lowers the payment to $1,706.58 and total interest to $344,372.91. The payment scales in direct proportion to the amount borrowed, so 10% less principal means a payment about 10% lower.
What this calculator leaves out
The result is principal and interest only. Many home loans also collect property tax and home insurance through an escrow or impound account, and some require mortgage insurance. Those amounts depend on where you live and on your lender, so add them separately to estimate a full monthly housing cost. Adjustable-rate loans change payment when the rate resets; this calculator describes only a rate that stays fixed for the whole term.
Frequently asked questions
Does the monthly payment include taxes and insurance?
No. It covers principal and interest only. Property tax, home insurance, mortgage insurance and association fees vary by country and property, and lenders often add them to the monthly bill on top of the amount shown here.
Why does most of an early payment go to interest?
Interest is charged on the outstanding balance, and the balance is largest at the start. In the worked example, the first payment is $761.78, of which $523.13 is interest. As the balance falls, the interest part falls and the principal part grows, while the payment itself stays the same.
Does changing the currency convert the amounts?
No. The currency menu changes only the symbol and number format so that the figures read naturally. The arithmetic is identical in every currency, so enter the loan amount in the currency you borrow in. Your choice is saved in this browser only.
Why is my lender's figure a few cents different?
Rounding conventions differ: a lender may round the payment differently, or charge interest on a daily rather than a monthly basis, and fees or a first payment date that is not exactly one month after closing also change the figures. This calculator rounds each month's interest to the cent and settles the leftover cents in the final payment.
Can I use this for a car loan or a personal loan?
Yes, as long as the loan has a fixed rate and equal monthly payments. The same formula applies to any fully amortizing installment loan; only the amount, rate and term change.
Sources
- Consumer Financial Protection Bureau, Loan Estimate sample for a fixed-rate loan (form H-24(B)) — the loan amount, rate, monthly payment, five-year principal and Total Interest Percentage used in the worked example.
- Consumer Financial Protection Bureau, Loan Estimate and Closing Disclosure forms and samples
- Regulation Z, Appendix H to Part 1026: closed-end model forms and clauses
- Regulation Z, official interpretation of § 1026.37 (Total Interest Percentage includes prepaid interest)