How a Mortgage Calculator Works: The Formula, Shown
A mortgage calculator is not doing anything mysterious. It is solving a single equation — the annuity formula — and then repeating one subtraction for every month of the term.
Knowing the formula matters for a practical reason: it tells you exactly which four inputs move the answer, and it makes obvious why a bank’s figure will not match yours.
The formula#
For a standard repayment loan, the monthly payment is fixed for the whole term and is calculated so that the final payment clears the debt exactly. Written out: payment equals P times i, divided by one minus (one plus i) to the power of minus n. P is the amount borrowed, i is the monthly interest rate — the annual nominal rate divided by twelve — and n is the number of months.
- P — the amount borrowed, which is the price minus your deposit, not the price.
- i — the monthly rate. A 4.8% annual nominal rate is 0.004 per month.
- n — months, not years. A 25-year term is 300.
- If the rate is zero the formula divides by zero; the payment is simply P divided by n.
Note what is missing from that list. Your income does not appear, and neither does the property value except through the deposit. Those affect which rate you are offered, not the arithmetic once you have one.
A worked example#
Borrow 200,000 at 4.8% nominal over 25 years. The monthly rate is 0.004 and the term is 300 months. The formula returns a payment of about 1,146. Multiply by 300 and you have repaid roughly 343,800 — about 143,800 of it interest, which is more than seventy per cent of the amount borrowed added on top.
| Input | Value | Effect of changing it |
|---|---|---|
| Amount borrowed | 200,000 | Payment moves in exact proportion |
| Rate | 4.8% | Strongly non-linear — the effect grows with the term |
| Term | 25 years | Longer term, lower payment, much more total interest |
| Deposit | Reduces P | Also usually buys a lower rate band |
The single most surprising figure for most first-time borrowers is the total interest. It is not printed on any advertisement, and it is the number that makes the term decision real.
What happens month by month#
The payment is constant, but its composition is not. Each month the interest is charged on the balance outstanding at that moment; whatever is left of the payment reduces the balance. Early on the balance is large so the interest share is large, and progress feels slow. Late on it reverses.
| Point in a 25-year loan | Interest share of the payment | Balance cleared |
|---|---|---|
| Month 1 | About 70% | Almost none |
| Year 5 | About 60% | Roughly 12% |
| Year 12 | About 45% | Roughly 35% |
| Year 20 | About 20% | Roughly 75% |
| Final year | Under 5% | The rest |
This is why overpaying early is worth so much more than overpaying late: an early overpayment removes interest from every remaining month.
What most calculators leave out#
The formula gives you the loan repayment. It does not give you the cost of buying a house, and in several markets the gap is enormous — purchase taxes and fees can add a tenth of the price, and they are almost never lendable, which means they must be found in cash on top of the deposit.
- Purchase taxes — transfer tax, stamp duty, registration tax. The largest single line in most European markets.
- Notary and registry fees, which are fixed by law in several countries rather than negotiable.
- Arrangement or product fees charged by the lender, sometimes addable to the loan and sometimes not.
- Compulsory insurance — mortgage insurance below a deposit threshold, or borrower insurance priced into the offer.
- Mandatory amortisation rules, which raise the monthly payment above the pure annuity figure in some markets.
Our calculator adds these per market, because a payment you can afford on a house you cannot complete on is not a useful answer.
Why the bank’s number will differ#
- The bank quotes APR, which includes fees; the formula uses the nominal rate.
- Compulsory insurance is added to the payment in several markets.
- Day-count and rounding conventions differ slightly between lenders.
- The rate you were quoted online is the best band; the rate you are offered depends on your deposit, income and credit history.
- Some products are not pure annuities — interest-only periods, stepped payments, or mandatory amortisation schedules.
A calculator gives you the shape of the deal and the questions to ask. Only a lender’s binding illustration gives you the deal.
Frequently asked questions
What formula does a mortgage calculator use?
The standard annuity formula: monthly payment equals the amount borrowed multiplied by the monthly interest rate, divided by one minus (one plus the monthly rate) raised to the power of minus the number of months. The monthly rate is the annual nominal rate divided by twelve, and the number of months is the term in years multiplied by twelve. If the rate is zero the formula breaks down and the payment is simply the amount borrowed divided by the number of months.
Why does more of my early payment go to interest?
Because interest is charged on the balance outstanding, and at the start the balance is at its largest. The payment itself is constant, so if the interest portion is large the portion left to reduce the debt is small. As the balance falls the interest charge falls with it and more of the same payment goes to capital. On a typical 25-year loan the first payment can be around seventy per cent interest, and the last is almost entirely capital. It is also why an overpayment early in the term saves far more than the same overpayment late.
Does a mortgage calculator include fees and taxes?
Most do not, and in many markets that omission is larger than any difference in the rate. Purchase taxes, notary and registry fees, agent commission and lender fees can add anywhere from two to ten per cent of the price depending on the country, and they usually cannot be borrowed, so they have to be found in cash alongside the deposit. Our calculator itemises them per market for exactly this reason.
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