The math behind mortgage amortization
A standard repayment mortgage uses a fixed monthly payment calculated so that, after the exact number of scheduled payments, the balance reaches zero. That fixed payment is derived from the standard amortization formula:
M = P × [ r(1+r)^n ] / [ (1+r)^n − 1 ]
where M is the monthly payment, P is the principal (starting balance), r is the monthly interest rate (your annual rate divided by 12), and n is the total number of monthly payments (years × 12).
Each month, interest is charged on the current remaining balance (interest = balance × r), and whatever portion of your fixed payment exceeds that interest amount goes toward reducing the principal (principal_paid = M − interest). This is why amortization schedules front-load interest: early on, when the balance is largest, more of each payment is consumed by interest, leaving less to reduce principal; as the balance shrinks, interest shrinks with it, so more of each fixed payment goes toward principal in later years, even though the payment amount itself doesn’t change.
Why overpayments have outsized leverage early in a mortgage
An overpayment doesn’t just reduce your balance by the amount you paid — it reduces the balance that every future month’s interest calculation is based on, for as long as the loan would otherwise have run. A £5,000 overpayment made in year 1 of a 25-year mortgage removes that £5,000 (plus all the interest it would have accrued) from 24 more years of compounding; the same £5,000 overpayment made in year 20 only affects 5 remaining years. This is the single most important intuition for using this calculator effectively: the same overpayment amount is worth meaningfully more the earlier it’s made, purely because of how much time remains for the reduced balance to keep saving you interest.
A worked example
Suppose you have a mortgage with a £200,000 balance, a 5% annual interest rate, and 20 years (240 months) remaining, with no overpayments. The monthly rate is 5% / 12 ≈ 0.4167%. Plugging into the formula above gives a required monthly payment of approximately £1,319.91, and over the full 20 years you’d pay a total of about £316,778, meaning roughly £116,778 of that is interest.
Now suppose you add a £200/month overpayment on top of that required payment, starting immediately. Each month, that extra £200 goes straight to principal. Running the full amortization month-by-month (which is exactly what this calculator does, rather than using an approximation), the loan is paid off in roughly 15 years and 9 months instead of 20 years — a savings of about 4 years and 3 months — and total interest paid drops to approximately £85,600, a saving of around £31,000 in interest, for a total of about £51,000 in extra payments made (200 × ~189 months). The overpayment costs you £51,000 out of pocket over that shorter period, but it saves you £31,000 in interest you would otherwise have paid — a real, guaranteed return that doesn’t depend on any market performance.
A one-off £10,000 lump sum applied today instead, with the required payment unchanged, would shorten the same mortgage by roughly 14 months and save approximately £14,000 in interest — smaller in total than the sustained monthly overpayment above, because it only removes one chunk of principal rather than compounding a reduction every month, but with no ongoing commitment required.
Reading the amortization comparison chart
The chart plots remaining balance against time for both your original schedule and your overpaid schedule on the same axes. The gap between the two lines is the visual representation of how much faster the overpaid balance disappears — it starts at zero (since both start at the same balance) and widens steadily until the overpaid line hits zero months before the original line does. Where the two lines diverge fastest is exactly where your overpayments are doing the most work, which — per the compounding effect described above — is usually earliest in the term.
Practical considerations before you overpay
Before committing to an overpayment plan, confirm three things with your actual lender: whether overpayments reduce your term or your monthly payment by default (this calculator assumes term reduction, which usually saves more interest), whether there’s an annual overpayment cap tied to an Early Repayment Charge, and whether you have higher-interest debt (credit cards, personal loans) that would benefit more from being paid down first, since their rates are typically much higher than a mortgage rate and carry no comparable tax or long-term-planning considerations.