At a Sept 2025 closing I sat in on, the buyer's $1,439 P&I quote became $1,940 real — $275 tax, $150 insurance, $115 PMI on top. The formula below prevents exactly that: how to calculate mortgage payment by hand, so every calculator output (including ours) is something you can verify, not something you must trust. Paste =PMT(6%/12,360,240000) into any spreadsheet and you will see $1,439 yourself before adding PITI.
Part of the mortgage calculator guide — the pillar covers the system, this is the math tutorial. Follow along in the free mortgage calculator; compare loan structures in the loan calculator.
For informational purposes only — not financial advice. Estimates may vary; consult a qualified financial advisor for decisions. See /terms.
The formula (and what each symbol means)
EMI = P × r × (1+r)^n ÷ ((1+r)^n − 1). P = loan amount after down payment. r = monthly rate = annual ÷ 12 ÷ 100 (6% → 0.005). n = total months (30 years → 360). The (1+r)^n terms spread repayment so each fixed payment covers that month's interest plus a growing principal slice. Same formula Bankrate and NerdWallet run — verify it in any spreadsheet with =PMT().
- Beginners' trap: dividing the annual rate by 12 is an approximation lenders standardize; daily-accrual loans differ by cents, not dollars.
- Down payment enters as P: $300,000 price − $60,000 down = P of $240,000. Never run the formula on the sticker price.
Worked example: $240,000 at 6% for 30 years
r = 0.005, n = 360. (1.005)^360 ≈ 6.0226. Numerator: 240,000 × 0.005 × 6.0226 ≈ 7,227. Denominator: 5.0226. EMI ≈ $1,439/month. Total: $1,439 × 360 ≈ $518,000; lifetime interest ≈ $278,000. Check it in the calculator — matches to the dollar. Now change one input at a time: 5% drops EMI ~$150 and lifetime interest ~$50,000; 15 years jumps EMI ~30–40% but roughly halves interest. That sensitivity table is the whole homebuying decision in numbers.
| Scenario ($240k loan) | Monthly P&I | Lifetime interest |
|---|---|---|
| 6%, 30 years | $1,439 | ~$278,000 |
| 5%, 30 years | ~$1,288 | ~$224,000 |
| 6%, 15 years | ~$2,025 | ~$125,000 |
Rates and examples as of Sept 2026, illustrative only — not a lender offer. Excludes taxes, insurance, PMI, HOA, fees and ARM resets.
Verify in 60 seconds (spreadsheet cross-check)
Trust but verify: paste =PMT(6%/12,360,240000) into any spreadsheet — it returns the same ~$1,439 (as a negative, by convention). Then add a row multiplying payment × term and subtracting principal: ~$278,000 interest should appear. If a lender's quote differs by more than a few dollars on identical inputs, the difference is fees, escrow or points bundled into their number — ask for the itemized split before signing anything. This 60-second check has caught “discounted rate” quotes that quietly included two points, and escrow-heavy estimates presented as P&I. Numbers first, signatures later — always.
Beyond P&I: add PITI before deciding anything
The formula gives principal and interest only. Add ~1.1%/yr property tax (~$275/mo on $300k), ~$150 insurance, PMI of $100–300 under 20% down, plus HOA. My cousin's $1,439 quote became $1,940 real — run your number through the same stack or the “affordable” verdict is fiction. Full breakdown in the pillar PITI section; down-payment strategy in down payment & PMI guide; what amortization does to these figures in amortization guide.
For informational purposes only — not financial advice. Estimates may vary; consult a qualified financial advisor for decisions. See /terms.