Mortgage payment formula
- M = monthly principal and interest (P&I)
- P = loan amount = home price − down payment
- r = monthly rate = annual rate ÷ 12 ÷ 100
- n = number of payments = years × 12
The full monthly payment adds the extras on top: P&I + property tax ÷ 12 + insurance ÷ 12 + HOA + PMI. In the US this is often called PITI (principal, interest, taxes, insurance).
Worked example
A $400,000 home with 10% down ($40,000) leaves a $360,000 loan. At 6.5% over 30 years, r = 0.0054167 and n = 360:
- Principal and interest: $2,275.44 a month.
- Property tax of $4,800 a year adds $400. Insurance of $1,500 a year adds $125.
- The loan is 90% of the price, so PMI applies. At 0.5% a year that is $150 a month.
- Total monthly payment: $2,950.44.
The first payment is $1,950.00 interest and only $325.44 principal. Over 30 years you pay about $459,160 in interest, more than the loan itself.
How PMI works
Private mortgage insurance (PMI) protects the lender, not you. US lenders usually require it on conventional loans when you put down less than 20%, that is, when the loan-to-value (LTV) ratio is above 80%. The calculator follows the US rule of thumb:
- You can ask to remove PMI once the balance reaches 80% of the home's original value.
- Under the Homeowners Protection Act, the lender must cancel it automatically when the balance is scheduled to reach 78%, if you're up to date on payments.
In the example, the balance reaches 80% after 95 payments and 78% after 109 payments. The calculator stops PMI after payment 109, for a total of $16,350. If you ask at 80%, you could save 14 payments of $150. Paying extra principal reaches both points sooner. FHA, VA and other government-backed loans follow different rules.
Down payment and term compared
| $400,000 home at 6.5% | P&I | PMI | Total interest |
|---|---|---|---|
| 10% down, 30 years | $2,275.44 | $150 for 109 months | $459,160 |
| 20% down, 30 years | $2,022.62 | None | $408,142 |
| 20% down, 15 years | $2,787.54 | None | $181,758 |
A 15-year term costs about $765 more a month than 30 years, but saves over $226,000 in interest on the same loan. In practice, 15-year loans often have a lower rate too.
Outside the US
The P&I formula works for any repayment mortgage in any currency. Property tax, home insurance, HOA fees and PMI are US-centric: leave them at zero if they don't apply, or enter your local equivalents. For Indian home loans, where the monthly payment is called an EMI, use the EMI calculator.
Tips before you borrow
- Compare offers by APR, which includes fees, not just the headline rate.
- Property tax and insurance usually rise over time, so treat them as estimates.
- Keep a cash buffer after the down payment for repairs and closing costs.
Frequently asked questions
How is a monthly mortgage payment calculated?
When does PMI stop?
Is a 15-year or 30-year mortgage better?
Does this work for mortgages outside the US?
Why is my lender's figure slightly different?
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