Guide
How mortgage payments are calculated (with a worked example)
A repayment mortgage charges the same monthly amount for the whole term (as long as the rate doesn’t change), yet the loan balance barely moves in the early years. Both facts come from one formula. Once you’ve seen it, you can check any lender’s quote yourself — and see how the mortgage calculator on this site arrives at its numbers.
Figures below were checked on 2026-10-10 against that calculator.
The formula
For a fixed-rate loan repaid in equal monthly instalments:
M = P × r × (1 + r)^n ÷ [(1 + r)^n − 1]
- M: the monthly payment
- P: the amount borrowed (price minus deposit)
- r: the monthly interest rate = annual rate ÷ 12 (3% a year → 0.0025)
- n: the number of payments = years × 12
If the rate is zero, the formula divides by zero, and the payment is simply P ÷ n.
This is the same annuity maths as compound interest run in reverse: M is the level payment whose present value, discounted at r, equals the loan. (See how compound interest works.)
Assumptions
The rate stays fixed for the whole term. Payments are monthly, interest compounds monthly, and the loan is fully amortising. An optional extra monthly payment can be applied to principal after the contractual split. The formula does not include fees, insurance, rate changes, a one-time prepayment, prepayment penalties, offset accounts, a stress test, a debt-servicing ratio, or a loan-to-value cap.
A worked example
Borrow 1,000,000 at 3% a year over 30 years — the same check the mortgage calculator documents. The rate is a round number for illustration, not a forecast. The currency doesn’t matter.
- r = 0.03 ÷ 12 = 0.0025
- n = 30 × 12 = 360
- (1.0025)^360 ≈ 2.4568
- M = 1,000,000 × 0.0025 × 2.4568 ÷ 1.4568 ≈ 4,216.04 a month
Over 360 payments you pay about 1,517,774.52 in total, of which 517,774.52 is interest. Enter loan 1,000,000, annual rate 3%, term 30 years in the mortgage calculator and you should see the same monthly payment and totals.
Why early payments are mostly interest
Each month the lender first charges interest on the balance you still owe, and whatever is left of your payment reduces the balance.
- Month 1 interest: 1,000,000 × 0.0025 = 2,500.00
- Month 1 principal: 4,216.04 − 2,500.00 = 1,716.04
Because the balance is largest at the start, interest takes most of the early payment. As the balance shrinks, the split slowly flips. In this example the principal part of the payment doesn’t overtake the interest part until month 84 (year 7), and you still owe more than half the loan until around month 220 (year 19).
| After year | Interest paid so far | Principal repaid so far | Balance owed |
|---|---|---|---|
| 1 | 29,714.48 | 20,878.00 | 979,122.00 |
| 5 | 142,026.05 | 110,936.37 | 889,063.63 |
| 10 | 266,122.93 | 239,801.91 | 760,198.09 |
| 15 | 369,392.97 | 389,494.29 | 610,505.71 |
| 20 | 448,470.21 | 563,379.47 | 436,620.53 |
| 30 | 517,774.52 | 1,000,000.00 | 0.00 |
That table is an amortization schedule. It’s why overpaying early in a loan saves far more interest than overpaying late, and why someone who sells after five years has repaid surprisingly little principal.
How principal reduction works (extra monthly payment)
Contractual split vs extra applied to principal
The contractual payment M is fixed by the formula above. Each month:
- Interest = opening balance × r
- Contractual principal = M − interest
- Any extra monthly payment X is then applied to principal (it is not added into M)
The last month pays only the remaining balance plus that month’s interest.
Months saved and interest saved
Compared with the same loan and no extra:
- Months saved = n − months actually paid
- Interest saved = (M × n − P) − total interest with the extra
Worked mini-example
Same loan as above: 1,000,000 at 3% for 30 years, plus an extra 500 each month.
- Contractual M stays 4,216.04
- The loan finishes in 303 months instead of 360 (57 months saved)
- Total interest falls from 517,774.52 to about 426,492.81 (91,281.71 interest saved)
Enter the same inputs, including Extra monthly payment 500, in the mortgage calculator to reproduce the months saved and interest saved figures. Whether paying extra is worthwhile depends on your cash flow, other debts, and any prepayment rules in your loan documents — the maths alone is not advice.
How a mortgage calculator uses this formula
A mortgage calculator maps the inputs you type — loan amount (or price minus deposit), annual rate, term in years, and an optional extra monthly payment — onto M, total paid, total interest, and a year-by-year summary. Under the hood it runs the same amortising formula and month-by-month schedule described here. It does not quote a bank offer or apply regional stress-test or loan-to-value rules.
What moves the payment
Keeping everything else in the example fixed:
| Change | Monthly payment | Total interest |
|---|---|---|
| Base case: 3%, 30 years | 4,216.04 | 517,774.52 |
| Rate 1 point higher (4%) | 4,774.15 (+558.11) | 718,695.06 |
| Term 15 years instead of 30 | 6,905.82 | 243,046.95 |
A shorter term raises the monthly payment by about 64% here but cuts total interest by about 274,727.57. Whether that trade is worth it depends on your cash flow and what else the money could do. For the same comparison across 15, 20, 25 and 30 years, including investing the payment gap and prepaying a longer loan, see 15 vs 30 year mortgage.
What the formula leaves out
- Rate changes. Variable, tracker or adjustable-rate loans recalculate the payment when the rate moves. The formula only gives a snapshot at today’s rate.
- Compounding conventions. The formula assumes monthly compounding. Conventions differ by region; in some regions fixed-rate mortgages are compounded semi-annually, which gives a slightly different payment for the same quoted rate.
- Everything that isn’t principal and interest: property taxes, insurance, mortgage insurance, arrangement or legal fees, and stamp or transfer taxes. A lender’s “monthly cost” may bundle some of these in.
- Day-count and payment-date details, which can shift the result by small amounts.
- Approval rules such as a stress test, debt-servicing ratio, or loan-to-value cap — those affect how much you can borrow, not the payment formula itself.
Check it yourself in a spreadsheet
In Excel, Google Sheets or Numbers, =PMT(3%/12, 360, -1000000) returns about 4,216.04. For a schedule, each row’s interest is the previous balance × r, the principal is the payment minus that interest, and the new balance is the old balance minus the principal. To model an extra monthly payment, subtract X from the balance after the contractual principal step.
FAQ
What is the mortgage payment formula?
For a fixed-rate loan repaid in equal monthly instalments, M = P × r × (1 + r)^n ÷ [(1 + r)^n − 1]. P is the amount borrowed, r is the annual rate ÷ 12, and n is years × 12. If the rate is zero, the payment is simply P ÷ n.
How do I calculate a mortgage payment manually / by hand?
Divide the annual rate by 12 to get r, multiply the term in years by 12 to get n, then plug P, r and n into the amortising formula. You can check the arithmetic with a spreadsheet PMT function or the mortgage calculator.
How is the monthly mortgage payment calculated?
The payment is the fixed amount that is scheduled to bring the balance to zero on the last month at a constant monthly rate. Interest each month is the opening balance times r; whatever is left of the payment reduces principal.
How does a mortgage calculator work?
It takes a loan amount (or price minus deposit), an annual rate, a term in years, and an optional extra monthly payment. It applies the same amortising formula, then builds a month-by-month schedule for totals and a year-by-year summary. Fees and stress tests are not included.
How do I calculate principal reduction on a mortgage?
Each month, interest is charged on the balance first. Principal reduction is the contractual payment minus that interest, plus any extra amount applied to principal. Repeating that step produces the amortisation schedule.
What happens if I pay an extra amount each month?
The contractual payment M does not change. The extra comes off principal after the interest/principal split, so the balance falls faster, the term shortens, and total interest falls. Months saved and interest saved compare that result with the same loan and no extra.
Why is so much of my payment interest?
Interest is charged on the outstanding balance, which is largest at the start. Your payment is fixed, so the principal part starts small and grows over time.
Does a bigger deposit lower the payment proportionally?
Yes. The payment is directly proportional to the amount borrowed. Borrow 10% less and, at the same rate and term, you pay 10% less each month and 10% less interest overall.
Is a longer term always more expensive?
At the same rate, yes, in total interest. It gives a lower monthly payment and more breathing room, which can matter more for some borrowers.
Why doesn’t my lender’s figure match exactly?
Usually it’s fees or insurance included in the quote, a different compounding or day-count convention, or a first payment that covers more or fewer than 30 days.
Does the formula include fees, insurance, or tax?
No. It covers principal and interest only. Property taxes, insurance, mortgage insurance, arrangement or legal fees, and stamp or transfer taxes sit outside the formula.
Is this financial advice or a loan offer?
No. This article explains the maths for general education. It is not financial advice and not a loan offer. Check your lender’s documents for the real terms.
Run your own numbers in the mortgage calculator.
This article explains the maths for general education. It is not financial advice or a loan offer. Check your lender’s documents for the real terms. See the disclaimer.