Most people see a mortgage payment as one number from the lender. Behind it is a single formula, and once you understand it you can see why a longer term costs so much more, why early payments are mostly interest, and how much a small change in the rate really matters.
The standard formula
For a fixed-rate loan repaid in equal monthly instalments, the payment M is:
M = P × r × (1 + r)<sup>n</sup> ÷ ((1 + r)<sup>n</sup> − 1)
- P is the amount borrowed (the principal).
- r is the monthly interest rate: the annual rate divided by 12, written as a decimal.
- n is the total number of monthly payments: years × 12.
The payment covers principal and interest only. Property tax, insurance and any mortgage insurance are usually added on top, so a lender's quoted monthly figure can be higher.
Step 1: Convert the inputs
Take a $300,000 loan at 6% a year for 30 years.
- r = 0.06 ÷ 12 = 0.005
- n = 30 × 12 = 360
Step 2: Work through the formula
(1 + r)<sup>n</sup> = 1.005<sup>360</sup> ≈ 6.0226. Then:
M = 300,000 × 0.005 × 6.0226 ÷ (6.0226 − 1) = 1,500 × 6.0226 ÷ 5.0226 ≈ $1,798.65 a month.
Raising 1.005 to the 360th power by hand isn't realistic, and rounding it too early throws the answer off by several dollars. To check your working, or to try different rates and terms quickly, use the Mortgage Calculator and compare its result with yours. If they differ, the usual culprit is using the annual rate instead of the monthly one.
Step 3: See where the money goes
In the first month, interest is simply the balance times the monthly rate: 300,000 × 0.005 = $1,500. So only about $299 of the first $1,798.65 payment reduces the balance. Each month the balance falls slightly, so the interest share shrinks and the principal share grows. This schedule is called amortization. Over the full 30 years, total interest comes to roughly $347,500, more than the amount borrowed.
Step 4: Test the levers
- Shorter term: the same loan over 15 years costs about $2,532 a month, but total interest falls to around $155,700.
- Lower rate: at 5% over 30 years, the payment drops to about $1,610.
- Bigger deposit: every dollar you don't borrow saves interest at the loan's rate for the life of the loan.
A note on extra payments
Paying even a small amount above the required payment goes straight to principal. On the example loan, an extra $100 a month would clear it roughly four and a half years early and save tens of thousands of dollars in interest. Check first that your lender doesn't charge early repayment fees.
Before you commit
The formula gives the payment for a given rate, but it can't tell you what you can afford or which loan type fits you. The US Consumer Financial Protection Bureau's home-buying guides explain loan estimates, closing costs and how to compare offers. In other countries, check the equivalent regulator's guidance, as fees and rate structures differ.
Common mistakes to avoid
- Using the annual rate as r. A 6% loan uses 0.005 per month, not 0.06. This one slip makes the payment roughly ten times too high.
- Forgetting to convert years to months. A 30-year loan has 360 payments, not 30.
- Rounding (1 + r)^n too early. Keep at least four decimal places until the final step, or the answer drifts by several dollars.
- Comparing loans only by monthly payment. A lower payment over a longer term can cost far more in total interest, so compare the total repaid as well.
Quick recap
- Convert the annual rate to a monthly decimal and the term to months.
- Plug P, r and n into the formula.
- Check the result with a calculator.
- Remember taxes and insurance come on top.