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 $18,000 of PMI. The PMI calculator estimates the monthly add-on for your own figures, and the amortization schedule shows exactly when your balance crosses the threshold.
Try it instantly
Model your own purchase with the Mortgage Calculator. Related tools:
Worked example: PMI Calculator at its default inputs
A worked example is only useful if you can reproduce it. The defaults on PMI Calculator give exactly the figures in this section, with no rounding done by us.
| Input | Default |
|---|---|
| Home Price ($) | 300000 |
| Down Payment (%) | 10 |
| Annual PMI Rate (%) | 0.5 |
Result: PMI: $112.50/mo
The steps behind that answer
- Step 1: Down payment = 10% × $300,000 = $30,000
- Step 2: Loan = $300,000 − $30,000 = $270,000
- Step 3: Annual PMI = 0.5% × $270,000 = $1350
- Step 4: Monthly PMI = $112.50
Home Price ($) — three values, three answers
Home Price ($) is the first input worth testing, so here it is at three sizes.
| Home Price ($) | Result |
|---|---|
| 150,000 | PMI: $56.25/mo |
| 300,000 | PMI: $112.50/mo |
| 450,000 | PMI: $168.75/mo |
The middle row is the default. The outer two show how far the answer drifts when home price ($) is wrong by half or by a half in the other direction.
Related guides
Principal and interest is not the monthly cost
The payment this calculator returns covers principal and interest only. A real monthly outgo usually adds property tax, homeowners insurance, and — below a down-payment threshold — mortgage insurance, plus any association fee. Those extras can add 20-40% to the number on the screen.
Budget against the full figure. A payment that fits your income before escrow can fail to fit after it, and escrow amounts change every year as assessments and insurance premiums move.
Fixed and adjustable carry different risks
A fixed rate locks the interest for the whole term, so the risk is opportunity cost if rates fall. An adjustable rate starts lower and resets on a schedule, so the risk is the payment itself — and the reset usually arrives whether or not your income has kept up.
If you take an adjustable product, model the payment at the capped rate, not the teaser rate. The affordability question is whether you can carry the worst case for a few years, not the first year.
The term changes cost far more than the rate
Going from a 20-year to a 30-year term cuts the payment by roughly a fifth and raises total interest by well over half. Shortening the term does the reverse and raises the monthly obligation, which is where most affordability problems actually start.
A middle path is a longer term with deliberate extra principal payments. It keeps the required payment low while recovering much of the interest saving — provided the extra payments actually happen.
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.
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