The same formula, run two ways
A savings balance grows because interest is added to it, and next period’s interest is charged on the larger figure. A loan balance shrinks because you pay more than the interest, and next period’s interest is charged on the smaller figure.
That is one mechanism, not two:
next balance = balance x (1 + rate) - payment
With a payment of zero and a positive balance, that equation is a savings account compounding. With a payment larger than the interest, it is a loan amortising. Nothing else changes.
Which is why the early years look wrong
- Interest57.2557.3%
- Off the balance42.7542.8%
The single most common surprise about a mortgage: after three years of payments the balance has barely moved.
Interest is charged on what you still owe. At the start you owe nearly all of it, so nearly all of a level payment is consumed by interest and only a sliver touches the principal. As the balance falls, the interest falls with it, and because the payment stays level, a larger slice reaches the principal every month.
The schedule is therefore not linear and never was. It is the same curve as compound growth, upside down. A repayment table is worth looking at for exactly this reason — it shows the crossover point where more of the payment goes to the debt than to the lender, which on a typical twenty-five year term arrives much later than people assume.
Why overpaying early is worth so much more than overpaying late
A pound of principal removed today stops accruing interest for the entire remaining term. A pound removed in the final year stops accruing it for a year.
The two are not comparable, and the difference is the whole reason overpayment calculators exist. It is also why the order matters more than the amount: an irregular overpayment made early beats a larger one made late.
Two practical caveats. Many fixed-rate deals cap annual overpayments or charge for exceeding them, and an early-repayment charge can wipe out the saving entirely. And an overpayment that reduces the term is a different product from one that reduces the payment, even though both remove the same principal.
Nominal, effective and APR
Three figures that all describe the same loan and differ on purpose.
Nominal rate. The headline number per year, before any question of how often it is applied.
Effective rate. What the nominal rate actually amounts to once compounding frequency is taken into account. 12% compounded monthly is not 12% a year; it is 12.68%.
APR. The effective rate plus the compulsory fees, expressed as one annual figure. It exists so two loans can be compared, and lenders are required to quote it precisely because the nominal rate can be made to look better than the deal is.
The conversion between the first two is worth having to hand, because the gap grows faster than the rate: at 2% it is two hundredths of a point and at 24% it is nearly three points. APR and APY is the tool for it, and it also settles the daily-compounding question — at 12% nominal, monthly compounding captures 91% of everything available all the way out to the continuous limit.
When a calculator asks for a rate, it matters which of the three you are typing. Entering an APR as a nominal rate overstates the cost; entering a nominal rate where an APR belongs understates it.
The revolving case, where the payment moves too
Before you read on
A 3,000 credit card balance at 22.9%. Which clears it faster — paying the 2% minimum, which starts at 117.25, or paying a flat 100 every month?
The flat 100, in 45 months against 112. The minimum starts at 117.25 and falls every month as the balance falls, so it removes less and less; the flat payment does not move, so it removes more and more. Nine years and four months against three years and nine months, and 1,003.03 more in interest.
Everything above assumes a level payment against a shrinking balance. A credit card breaks that assumption in the one way that matters: the minimum payment is a percentage of the balance, so it falls as the balance falls.
That inverts the mechanism. On a mortgage, a level payment means a growing share reaches the principal every month and the payoff accelerates. On a percentage minimum, a shrinking payment means a shrinking share reaches the principal, and the balance approaches zero without arriving. What eventually clears the card is the fixed floor underneath the percentage, not the percentage.
Every value
| Monthly payment | Time to clear | Interest paid |
|---|---|---|
| 60 | 13 years 8 months | 6,784.48 |
| 70 | 7 years 7 months | 3,306.27 |
| 80 | 5 years 7 months | 2,321.81 |
| 90 | 4 years 6 months | 1,813.18 |
| 100 | 3 years 9 months | 1,495.48 |
| 110 | 3 years 3 months | 1,276.63 |
| 120 | 2 years 11 months | 1,115.87 |
| 130 | 2 years 7 months | 992.4 |
| 140 | 2 years 4 months | 894.4 |
| 150 | 2 years 2 months | 814.94 |
| 160 | 2 years | 748.86 |
| 170 | 1 year 10 months | 693.11 |
| 180 | 1 year 9 months | 645.43 |
| 190 | 1 year 7 months | 603.94 |
| 200 | 1 year 6 months | 568.09 |
| 210 | 1 year 5 months | 536.32 |
| 220 | 1 year 4 months | 507.94 |
| 230 | 1 year 4 months | 482.88 |
| 240 | 1 year 3 months | 460.47 |
| 250 | 1 year 2 months | 439.81 |
| 260 | 1 year 2 months | 421.07 |
| 270 | 1 year 1 month | 404.33 |
| 280 | 1 year 1 month | 388.34 |
| 290 | 1 year | 374.38 |
| 300 | 1 year | 360.97 |
Two things are worth noticing on that control. The months fall steeply at first and then flatten — the first extra 50 a month is worth far more than the fifth. And the interest falls faster than the months do, because a shorter debt is charged interest fewer times and on a smaller balance.
The size of that difference is hard to believe until it is computed. On 3,000 at 22.9%, a 2% minimum starts at 117.25 — more than a fixed payment of 100 — and still takes 112 months against 45, because it does not stay there. Freezing the payment at that same first figure clears the card in 36 months.
Solving for the payment instead of the balance
The other direction people arrive from is a target rather than a plan: not “what does this become” but “what do I have to put in”. That is the same annuity equation solved for the contribution rather than the future value, which is what a savings goal works out.
Two things fall out of it that are worth knowing before running the numbers. Halving the time more than doubles the monthly amount, because there are half as many payments and each compounds for half as long. And over a short horizon the contributions do nearly all the work — over five years at 4%, the return supplies about a tenth of the total, so the assumed rate barely matters. Over thirty years the ratio reverses completely.
Money is never a float
One implementation note that belongs in a guide rather than in a footnote, because it affects every figure above.
Binary floating point cannot represent 0.1 exactly, so a schedule computed in it drifts — a few pence over three hundred payments, which is enough for a total to disagree with the sum of its own rows. Every money tool here uses decimal arithmetic instead, and the tests sweep every penny across every rate to prove the columns reconcile.
Common questions
Why is my early mortgage payment almost all interest?
Because interest is charged on what you still owe, and at the start you still owe nearly everything. The payment is a fixed amount, so whatever the interest does not consume goes to the balance — a small slice at first, growing every month as the balance falls. Nothing is being withheld from you; it is the arithmetic of a level payment against a shrinking debt.
What is the difference between a nominal rate and an APR?
A nominal rate is the headline percentage per year, ignoring how often it compounds and any fees. An APR folds in the compounding frequency and most compulsory charges, which is exactly why it is the figure lenders are required to advertise: two loans with the same nominal rate can have different APRs, and the APR is the one you can compare.
Does paying extra early really save that much?
More than most people expect, because every pound of principal removed early stops accruing interest for the whole remaining term. The same overpayment made in year one and in year twenty of a twenty-five year mortgage are not remotely equivalent. Check for early-repayment charges first, which can cancel the benefit outright.
Why does a small rate change move the total so much?
Because it applies to a large balance for a long time, and compounding multiplies rather than adds. On a twenty-five year mortgage the interest paid is a sizeable fraction of the loan itself, so a change of half a percentage point moves a number that is already large. The effect grows with both the balance and the term.