How to Calculate a Mortgage Payment — Formula & Example
What a mortgage payment actually is
A mortgage is an amortizing loan: every payment covers the month's interest plus a slice of the principal. Early payments are mostly interest; near the end they are mostly principal. The monthly principal-and-interest amount stays fixed for a fixed-rate loan.
The mortgage payment formula
Where:
- M = monthly principal & interest payment
- P = loan amount (home price − down payment)
- r = monthly rate = annual rate ÷ 12 ÷ 100
- n = number of payments = years × 12
Note this is the same amortization formula as the EMI formula — a mortgage is simply a large, long EMI loan.
Worked example
$300,000 loan at 6% for 30 years
Step 1 — monthly rate: r = 6 ÷ 12 ÷ 100 = 0.005
Step 2 — payments: n = 30 × 12 = 360
Step 3 — growth factor: (1.005)360 ≈ 6.0226
Step 4 — payment: M = 300,000 × 0.005 × 6.0226 ÷ (6.0226 − 1) = 9,033.9 ÷ 5.0226 ≈ $1,799/month
Total paid: 360 × $1,799 ≈ $647,515 → interest ≈ $347,515 — more than the loan itself.
What PITI means (the real payment)
The formula gives only principal + interest. Your actual monthly housing cost is usually PITI:
- Principal — loan repayment
- Interest — cost of borrowing
- Taxes — property tax (often escrowed monthly)
- Insurance — homeowner's policy (+ PMI if down payment is under 20%)
On top of that, HOA fees may apply. Always budget with PITI, not just the formula result.
How rate and term change everything
- Rate: on the same $300k/30yr loan, 7% raises the payment to about $1,996 (+$197/month, ~$70,800 over the term).
- Term: a 15-year loan at 6% costs about $2,532/month (more monthly) but total interest drops to roughly $155,700 — less than half.
- Down payment: 20% down on a $375k home keeps the loan at $300k and usually removes PMI from the payment.
15 vs 30 years: the computed trade-off
Term choice is the biggest lever on a mortgage, and it deserves exact numbers rather than folklore. On a $400,000 loan at 7%:
| Term | Monthly P&I | Total paid | Total interest |
|---|---|---|---|
| 15 years | $3,595.31 | $647,156 | $247,156 |
| 30 years | $2,661.21 | $958,036 | $558,036 |
The 30-year loan costs $934 less per month but $310,880 more in lifetime interest — roughly the original principal again. The honest comparison, though, is not loan vs loan: it's whether you would invest the $934/month difference at more than 7%. If yes, the 30-year with invested savings wins mathematically; if the money would simply be spent, the 15-year is the enforced discipline. The rate is the same for both terms at some lenders and lower for 15-year at others — price both before deciding.
Prepayment as a middle path: take the 30-year and add $200/month. The loan closes at month 291 instead of 360 and total interest drops to about $432,600 — capturing a third of the 15-year saving while keeping the lower required payment as option value.
PMI: the cost of a small down payment
Put down less than 20% and most US lenders add Private Mortgage Insurance — an insurance policy that protects the lender, paid by you. It's not small: on a $360,000 loan (10% down) at a typical 0.6% annual premium, PMI is $180/month. It doesn't fall off automatically the day you cross 20% equity either — by the amortization math, the balance first reaches 80% of the home's value at around month 101, by which point you'd have paid roughly $18,000 of PMI. The PMI calculator estimates the monthly add-on for your own figures, and the amortization schedule shows exactly when your balance crosses the threshold.
Try it instantly
Model your own purchase with the Mortgage Calculator. Related tools:
Frequently asked questions
What is the mortgage payment formula?
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), with P the loan amount, r the monthly rate (annual ÷ 12 ÷ 100), and n the total monthly payments.
What does PITI mean?
Principal, Interest, Taxes and Insurance — the four parts of a real housing payment. The formula only computes principal and interest; taxes and insurance are added on top, often via escrow.
How much does a 1% rate change affect payment?
On a $300,000 30-year loan, going from 6% to 7% raises the payment from about $1,799 to about $1,996 — roughly $197 more per month.
How does a bigger down payment help?
It shrinks the principal, lowering both the monthly payment and total interest, and a 20% down payment typically removes PMI.