How the payment formula works
A fixed-rate mortgage promises one thing: the same payment every month until the loan is gone. The formula that produces that payment is:
Payment = P × r × (1+r)ⁿ ÷ ((1+r)ⁿ − 1)
where P is the amount borrowed, r the monthly interest rate (annual rate divided by 12), and n the number of payments. The formula balances two forces: every month interest accrues on the remaining balance, and every payment must clear that interest plus enough principal for the balance to hit exactly zero on the final payment.
Worked example
$400,000 home, 20% down ($80,000), leaving a $320,000 loan at 6.5% for 30 years. Monthly rate r = 0.065 ÷ 12 = 0.005417; n = 360. Payment = 320,000 × 0.005417 × 1.005417³⁶⁰ ÷ (1.005417³⁶⁰ − 1) = $2,022.62 per month. Over the full term that is $728,141 paid, $408,141 of it interest.
Where each payment goes
The payment is constant; its composition is not. Month one of the example above: $1,733 interest, $289 principal. Year 15: roughly $1,280 interest, $740 principal. The final year: almost all principal. This is why the amortization table below the calculator is worth a look, the crossover point where principal overtakes interest lands in month 233, early in year 20, on a 30-year loan at these rates, later than most borrowers guess.
It is also why extra payments early in the loan are so powerful, and late ones barely matter, see the early payoff calculator for exactly what an extra $100–500 a month does.
The four levers you control
| Lever | Effect on the $320k example |
|---|---|
| Rate: 6.5% → 6.0% | Payment falls $104/month; $37,500 less interest over the term |
| Term: 30 → 15 years | Payment rises $766/month; interest falls by $226,000 |
| Down payment: 20% → 25% | Payment falls $126/month; $25,500 less interest |
| Extra $200/month | Loan ends 6+ years early; ~$96,000 less interest |
The rate is negotiable more often than people think, lenders compete, and discount points let you buy it down when you plan to stay long. The term decision is really a cash-flow decision; the comparison calculator puts any two structures side by side.
Rules of thumb that hold up
- 28/36: housing costs under 28% of gross income, all debt payments under 36%. Lenders still underwrite near these numbers because they work.
- Rate shopping is free money. Multiple mortgage enquiries within a short window count as one credit check. The spread between lenders on the same borrower is routinely 0.25–0.5%.
- The payment is the floor, not the cost. Tax, insurance, maintenance (~1% of home value yearly) and utilities sit on top. A payment that fits exactly leaves no room for the roof.