How mortgages really work — and what your bank's calculator doesn't show you

The formula is the easy bit

For a fixed-rate, capital-and-interest mortgage, the monthly payment is set by the standard amortisation formula: P × r × (1+r)^n / ((1+r)^n − 1), where P is the principal, r is the monthly interest rate (annual rate ÷ 12), and n is the total number of monthly payments. That formula gives the same payment every month for the life of the deal, and it is the formula every bank's calculator uses. The point of the formula is not cleverness. It is the unique payment amount that exactly amortises the loan to zero at the end of the term, assuming the rate never changes.

What the bank's calculator doesn't tell you

Three things, mostly.

1. The interest front-loads the payment

Because the loan balance is highest in month 1, interest is highest in month 1. The first payment of a typical 25-year mortgage is something like 65–80% interest. By year 15, that same payment is something like 30% interest. The balance isn't a straight line; it is a curve that flattens out. That is why the loan balance in year 5 can feel like it has barely moved. It has. The bank is just charging you interest on a much larger number than you owe today.

2. The "headline rate" is rarely the rate you pay

Almost no UK or US mortgage is fixed for the full 25–30 year term. A typical UK deal is 2, 3, or 5 years fixed, then reverts to the lender's standard variable rate (SVR), then you re-mortgage. The payment the calculator shows you is the payment during the fix, not the payment over the life of the loan. Worst case: you stay on SVR for the rest of the term, which is usually higher than any fixed deal you have ever seen. Realistic case: you re-fix every 2–5 years, your payment fluctuates, and your total interest paid is higher than the calculator implied.

3. Overpayments cut the term, not the payment

If you overpay by £100/month on a 25-year mortgage at 5%, you don't reduce your monthly payment — the bank reduces the term, because you have shortened the time needed to clear the balance. The interest saved is close to 40% of the overpayment over the remaining term, depending on when you start. Most lenders let you overpay by 10% of the balance per year without penalty. After that, an early-repayment charge (ERC) kicks in during the fix.

The honest way to use a mortgage calculator

Open the calculator and put in three things: the amount you are actually borrowing (purchase price minus deposit, plus any fees rolled in), the real rate (not the headline — if the deal is 5 years fixed at 4.5%, and you expect to re-fix at 5.5% after that, model the loan at 4.5% for 5 years and 5.5% for 20), and the term you actually want to be done by, not the maximum the lender will give you. Then ask: if I overpaid by £200/month, what does the term shorten to? That single number often decides whether the overpayment is worth it.

What a "mortgage" actually costs over its life

On a £250,000 loan at 4.5% over 25 years, the monthly payment is around £1,389. Over 25 years, you pay £416,556 — so £166,556 of that is interest. On a 30-year term at the same rate, the payment drops to about £1,267, but the total interest paid rises to about £206,000. Stretching the term by 5 years costs you £40,000 of extra interest for a £122/month saving. That is the part the bank's calculator never shows you in the summary box. It is the most important number on the page.