Mortgage Calculator

A mortgage payment might look like a simple monthly bill, but underneath it is an amortization calculation that determines exactly how much of each payment goes toward interest versus paying down the actual loan balance (the principal). Understanding this calculation helps explain why early mortgage payments feel like they barely dent the balance, while later payments make rapid progress. The standard formula for a fixed-rate mortgage payment is: M = P × r × (1+r)ⁿ ÷ ((1+r)ⁿ − 1), where P is the loan principal, r is the monthly interest rate (the annual rate divided by 100 and then by 12), and n is the total number of monthly payments (the term in years multiplied by 12). This formula guarantees that if you make exactly this payment every month for n months, the loan balance reaches exactly zero at the end — no more, no less. It's derived from the mathematics of an annuity, treating the mortgage as a series of equal payments whose present value, discounted at the monthly interest rate, equals the original loan amount. What makes mortgages feel front-loaded with interest is that the interest portion of each payment is calculated on the *remaining* balance, which is largest at the very start of the loan. On a 30-year, £250,000 mortgage at 5.5%, the very first monthly payment is split roughly £1,144 interest and only £276 principal — over 80% interest. By year 15, that split has roughly reversed, and by the final years almost the entire payment goes to principal. This is why paying off a mortgage early saves disproportionately more interest than the raw numbers might suggest: eliminating a payment in year 2 avoids far more interest than eliminating one in year 28, because more of that early payment was interest to begin with. A worked example: borrow £250,000 at 5.5% annual interest over 30 years. The monthly rate r = 5.5 ÷ 100 ÷ 12 ≈ 0.004583, and n = 360 payments. Plugging into the formula gives a monthly payment of approximately £1,419. Over 360 months, total payments come to about £510,984, meaning total interest paid over the life of the loan is roughly £260,984 — more than the original loan amount itself. This is the single most surprising fact for most first-time buyers: on a typical 30-year mortgage, you often pay more in cumulative interest than you borrowed in principal, purely because of how long the loan is stretched out. A common misconception is that halving the interest rate halves the monthly payment, or that doubling the loan term halves the payment. Neither is true because of the compounding structure of the formula — the relationship between rate, term, and payment is non-linear. Shortening a 30-year mortgage to a 15-year mortgage at the same rate typically increases the monthly payment by 40-50%, not 100%, while cutting total interest paid by more than half, because so much less time is available for interest to compound against the outstanding balance. This is why comparing mortgage offers by monthly payment alone can be misleading — the total interest cost over the loan's life is often the more meaningful number for evaluating true affordability.