Mortgage Calculator: Monthly Payment & Interest
Calculate a mortgage payment from the loan amount, interest rate, and term. See the monthly, biweekly, or weekly payment and total interest paid over the loan.
Mortgage Calculator
Documentation
Mortgage Calculator
A mortgage calculator estimates the regular payment on a home loan from three numbers: the loan amount, the interest rate, and the loan term. It also shows the total interest paid over the life of the loan.
What the calculator does
Enter the loan amount (the amount borrowed, not the home price), the annual interest rate, the loan term in years, and how often payments are made: monthly, bi-weekly (every two weeks), or weekly. The calculator returns the payment amount for that schedule and the total interest paid over the full term.
The loan amount can be between 10,000,000. The interest rate can be 0% to 20%. The loan term can be 1 to 50 years.
How to calculate a mortgage payment
A mortgage is paid off with equal payments. Each payment covers that period's interest plus a growing share of the principal (the amount still owed). The standard formula is:
M = P × [r(1 + r)ⁿ] / [(1 + r)ⁿ − 1]
- M is the payment for one period.
- P is the principal, the amount borrowed.
- r is the interest rate for one period.
- n is the total number of payments over the loan term.
The period rate and the number of payments both depend on how often payments are made:
| Frequency | Payments per year | Period rate (r) | Number of payments (n) |
|---|---|---|---|
| Monthly | 12 | annual rate ÷ 12 | years × 12 |
| Bi-weekly | 26 | annual rate ÷ 26 | years × 26 |
| Weekly | 52 | annual rate ÷ 52 | years × 52 |
This formula comes from setting the loan amount equal to the present value of all future payments, then solving for M. If the interest rate is 0%, the payment is simply the loan amount divided by the number of payments.
How payment frequency changes the calculation
Switching from monthly to bi-weekly payments is not just a matter of taking the monthly payment and multiplying it by 12/26. The calculator instead recalculates the period rate and the number of payments for the new schedule, then applies the formula above directly. This gives a slightly different, more accurate result than scaling the monthly figure.
Example calculation
For a $200,000 loan at a 3.5% annual interest rate over 30 years, the calculator gives:
| Frequency | Payments per year | Number of payments | Payment amount | Total interest paid |
|---|---|---|---|---|
| Monthly | 12 | 360 | $898.09 | $123,312.18 |
| Bi-weekly | 26 | 780 | $414.32 | $123,168.87 |
| Weekly | 52 | 1,560 | $207.12 | $123,107.43 |
Total interest is the sum of every payment made, minus the original loan amount. Paying more often lowers total interest slightly, because each payment is applied a little sooner, which reduces the balance that interest is charged on.
15-year vs. 30-year loans
A shorter loan term raises the payment amount but lowers total interest, because interest has less time to accumulate. For a $300,000 loan at 6% interest, paid monthly:
| Term | Monthly payment | Total interest paid |
|---|---|---|
| 15 years | $2,531.57 | $155,682.69 |
| 30 years | $1,798.65 | $347,514.57 |
The 15-year loan costs about 192,000 in interest over the life of the loan.
What this calculator does not include
The calculator computes principal and interest only. It does not add property taxes, homeowners insurance, private mortgage insurance, or closing costs, all of which are often part of an actual monthly mortgage bill. It also assumes a fixed interest rate for the full term; it does not model adjustable-rate mortgages, where the rate can change partway through the loan.
If the entered values produce an invalid result, such as a rate and term combination that cannot be solved, the calculator shows a generic input error rather than a specific warning.
Frequently asked questions
How is a mortgage payment calculated? It is calculated with the formula M = P × [r(1 + r)ⁿ] / [(1 + r)ⁿ − 1], where P is the loan amount, r is the interest rate for one payment period, and n is the total number of payments.
Why isn't a bi-weekly payment just half the monthly payment? A bi-weekly schedule has 26 payments a year, not 24, so it is not simply half of 12 monthly payments. The extra two payments a year (equivalent to one extra monthly payment) are why bi-weekly schedules pay off a loan faster and with less total interest.
What is included in a monthly mortgage payment? This calculator's payment covers principal and interest only. A real mortgage bill often also includes property taxes and homeowners insurance, and, if the down payment is under 20%, private mortgage insurance.
Is a 15-year or 30-year mortgage better? Neither is better in every case. A 15-year loan has a higher monthly payment but far less total interest. A 30-year loan has a lower monthly payment, which can make it more affordable month to month, but costs more in interest overall.
Does a bigger down payment lower the payment? Yes. A larger down payment reduces the loan amount, which lowers both the periodic payment and the total interest, since P appears directly in the formula.
What happens if the interest rate is 0%? The payment is simply the loan amount divided by the number of payments, since there is no interest to add.
References
- "Mortgage Calculator." Investopedia, https://www.investopedia.com/mortgage-calculator-5084794.
- "Mortgage Formulas." The Mortgage Professor, https://www.mtgprofessor.com/formulas.htm.