Mortgage overpayment calculator — methodology

The month, in five steps — this is the contract

Every row of the table on the calculator page is produced by exactly these steps, in exactly this order:

1. open      = last month's closing balance (or the balance you entered)
2. interest  = open × (annual rate ÷ 12), rounded to whole pence
3. payment   = min(contractual payment, open + interest)
4. overpay   = min(your overpayment, open + interest − payment)
5. closing   = open + interest − payment − overpay

Steps 3 and 4 are each capped at what is actually owed, and that is the whole of the guarantee that no closing balance is ever below zero. Nothing in the loop can take out more than the balance has. Line 5 is a sum of whole pence, so the identity is exact rather than approximate — and it is asserted on every rendered row of the table by the page’s test suite, read back out of the page rather than out of the engine.

Why the overpayment lands after the interest, not before it

This single ordering decides whether the headline saving is honest, so it is worth stating rather than leaving to be inferred.

An overpayment made in month k reduces the balance that month k + 1’s interest is charged on. It does not reduce month k’s own interest: the money was owed for that month and the interest had already accrued by the time the payment arrived. Crediting the overpayment before the interest charge would hand the borrower one free month of interest on every overpayment they ever make — a fabricated saving that grows with the size of the overpayment, which is precisely the input the reader is varying.

The consequence is the thing that makes overpayment worth doing and worth showing: an overpayment saves the interest on itself for every remaining month. Measured on this calculator’s default mortgage — £250,000.00 at 5.40% over 25 years — a £10,000.00 lump sum in month 1 saves £26,348.72 and 1 year and 11 months, and the identical £10,000.00 in month 241 saves £2,815.94 and 8 months. Same money, 9.4× the effect, twenty years earlier. That ratio is asserted nowhere; it falls straight out of the ordering above.

The rate: divided by twelve, not compounded — and this is not a preference

Everywhere else on this site an annual rate is treated as an effective one, because a fund’s quoted return and a savings account’s AER compound to exactly the figure quoted. A mortgage rate is the other kind.

nominal   (a mortgage):    monthly = annual ÷ 12
effective (a fund, an AER): monthly = (1 + annual)^(1/12) − 1

A UK lender quoting 5.40% charges 5.40% ÷ 12 = 0.4500% a month on the balance outstanding, on a monthly-rest convention. Twelve of those compound to slightly more than 5.40% over a year, and that is not an error in the quote — it is what the contract says.

The cost of getting this wrong is measured rather than asserted. On £250,000.00 over 25 years at 5.40%, using the effective convention would understate the monthly payment by £19.13 and the total interest by £5,744.21, or 2.87%. Both errors run in the direction that matters: the wrong convention tells somebody their mortgage is cheaper than it is, on the figure they are budgeting against.

The investment comparison on the calculator page uses the effective convention, because it is about a fund rather than a mortgage. Two conventions on one page is two right answers, not an inconsistency, and both are stated where they are used.

The contractual payment, and the one figure not read off the schedule

Every headline figure on the calculator page is read back off the schedule: the total interest is a column sum, the term is the number of rows, and the interest saved is the difference between two column sums over two real schedules. There is exactly one exception and it is called out rather than hidden — the contractual monthly payment, which is an input to the loop rather than a product of it. It is the payment the lender fixed at the outset, computed once from the standard annuity formula:

payment = balance × p ÷ (1 − (1 + p)^−n)

  p = the monthly rate      n = months in the original term

At a rate of 0% that expression is 0 ÷ 0. A zero rate is a genuine input — an interest-free family arrangement, or simply a rate dragged to the bottom of its range — so it is short-circuited to balance ÷ n with no interest at all, rather than allowed to produce a NaN that would flow silently into every row and every total.

The two schedules being compared — with your overpayment and without it — share one contractual payment, because they must: the payment is fixed by the balance, the rate and the original term, none of which an overpayment changes. That is what makes them comparable at all, and it is the arithmetic statement of “the payment stays the same and the term gets shorter”.

The last payment is short, and a schedule that overshoots is the classic bug

The payment is rounded to whole pence and so is every month’s interest, so the payment multiplied by the number of months does not equal the debt plus its interest. Measured across 991 balances from £10,000 to £1,000,000, the final payment lands between £3.39 below and £3.39 above the scheduled one. Left alone that produces one of the two failures every naive amortisation table ships with: a final balance of −£3.39 — a mortgage the lender now owes you — or one extra row for £3.39.

Two rules together make both impossible:

• Every payment is capped at what is owed, and the overpayment is capped again at what remains. No step can take out more than the balance has, so no closing balance in any schedule this page can produce is ever below zero.
• The final scheduled payment settles the balance in full, in both directions — short when the rounding ran your way, slightly over when it did not. This is what a real lender does, and it is the “your final payment may differ” line on every UK mortgage illustration.

The loop also stops the moment the balance reaches zero, so it never emits a row of a mortgage that has already been repaid. That is what makes the number of rows the honest answer to “how long did it actually take?” without a special case anywhere.

Where each payment actually goes

On the default mortgage the first payment is £1,520.32, of which £1,125.00 is interest and £395.32 comes off the debt — 74.00% of the money leaving the account buys nothing. By the final payment of the same mortgage the interest is £6.82. The whole of the case for overpaying early is in those two numbers, and the calculator page shows the proportion moving between them year by year.

An overpayment is different in kind from a payment: every penny of it comes off the balance, because the interest has already been charged and the contractual payment already taken by the time it lands. That is why £47,200.00 of overpayments removes £49,509.24 of interest on the default figures.

Early repayment charges and the 10% allowance, and why they are not here

Almost every fixed-rate UK deal caps penalty-free overpayments at 10% of the balance a year and charges an early repayment fee above it, often a percentage of the amount repaid.

That is a product term, not arithmetic. It varies by lender, by product and by which year of the deal you are in, and there is no published figure anywhere that a calculator could look up and cite. Hard-coding one would mean this page asserting something about your contract that it cannot know — and it would give the engine behind it the statutory-figure problem it deliberately does not have: a number that goes stale, with no authority to check it against and no verification log to record it in.

So every figure on the calculator page assumes no charge is made, the page says so next to the answer rather than here, and your mortgage offer or annual statement is the only place your real allowance is written down. If you would exceed it, your saving is smaller than the figure shown, and it can be negative.

What else it does not model

• Rate changes part-way through. One rate for the whole schedule. A two-year fix followed by a reversion rate is two schedules, and this page draws one — so if your fixed deal is shorter than your remaining term, every figure is conditional on a rate you have not been offered yet.
• “Reduce my payment” rather than “reduce my term”. Overpaying can be taken either way and lenders default to different ones. This implements term reduction only: the contractual payment is fixed for the life of the schedule and the debt clears sooner. Mixing the two readings would produce a saving that is partly a shorter term and partly a smaller payment — two answers wearing one number.
• Fees, and interest accrued daily rather than at monthly rest. No arrangement, valuation or product fee. Daily accrual moves the answer by pennies a month and would cost the exact per-row whole-penny identity that makes the table checkable.
• Offset mortgages, mortgage terms in months, and part-and-part. The term is whole years, because a part-year would need a part-month and there is no honest way to charge a month’s interest on one.
• Tax, anywhere. No tax is charged on interest you were not charged, and the investment comparison is shown before any tax on the investment. Neither figure has a statutory rate in it.

The investment comparison, and what it puts on each side

The panel below the answer compares the monthly overpayment only, invested for the mortgage’s remaining term at a rate you supply, through the same package. Four things about it are deliberate:

• Contributions land at the end of the month, because that is when the overpayment lands — step 4 of the month, after the interest and the payment. Crediting the investment at the start would give it one extra month of growth the overpayment never had.
• A lump sum is excluded. The projection has no dated one-off contribution: money either starts in the pot or arrives every month. Treating a lump sum paid in month 12 as invested today would flatter the investment by eleven months of growth on the largest single figure on the page.
• Both money-in figures are shown, not just the two outcomes. The overpayments stop when the mortgage clears; the investment keeps receiving money for the full term. On the defaults that is £47,200.00 against a full-term £60,000.00, and a panel that showed the outcomes without the inputs would be quietly comparing different amounts of money and letting the bigger number win.
• The investment figure is gross and the overpayment figure is net. No platform fee is charged on interest you were not charged and no tax is due on it; the investment side is before both, and both make it smaller.

The comparison that decides it is a rate, not a total. Overpaying returns exactly your mortgage rate, certainly, for as long as that is your rate. Investing returns whatever the investment returns, which nobody can promise. That asymmetry is the honest answer, and this page does not resolve it for you: it is information, not advice.