On this page15 sections
- 01Where the extra money actually goes
- 02Concepts to hold first
- 03Why the extra unit is the mightiest one
- 04Two schedules, one difference
- 05Where the reward bends
- 06The fine print that eats savings
- 07How the method works
- 08Try it, verified
- 09What each input represents
- 10Worked example
- 11Reading the result
- 12Common mistakes
- 13Questions readers arrive with
- 14When this calculation is used
- 15Assumptions and guards
Where the extra money actually goes
The scheduled payment already covers the interest each period accrues; that is what makes it a workable payment at all. So an extra amount added on top has nowhere to go but the principal — none of it is consumed by interest. A smaller principal accrues less interest the very next period, which frees more of the unchanged scheduled payment to attack the principal in turn. Acceleration compounds, in the borrower’s favour, by the same mechanism that made the debt expensive in the first place.
The method is a comparison, not a new formula: the payoff-time relation evaluated at the scheduled payment gives the baseline horizon, the same relation at the boosted payment gives the revised one, and the interest on each path is the total money paid along it minus the principal. The difference between the two interest totals is the saving — money that under the baseline schedule would have been accrued and paid, and under the accelerated one simply never comes into existence.
The reward is not linear in the extra amount. The first increment of overpayment does disproportionate work, especially when the scheduled payment sits close to the interest-only level, and each further increment buys a little less time than the one before. The chart on this page sweeps the revised horizon across a range of extra amounts so that bend is visible before any commitment is made — the point where more acceleration stops buying much is a fact worth seeing, not guessing.
What is modelled is a recurring extra: the same additional amount every period, from now until the debt ends. A one-off lump sum is a different action — it resets the balance once rather than boosting every payment — and answering it honestly means re-running the baseline with a reduced principal instead. The distinction matters because a windfall and a raise feel similar and behave completely differently over a schedule.
The workspace also offers the reverse direction: name the horizon the debt should have — the revised payoff target — and it solves for the recurring extra that achieves it. That turns a finish date into a required top-up, the acceleration question asked from the calendar’s side instead of the wallet’s.
Concepts to hold first
Paying a recurring amount above the scheduled payment, every period, until the debt ends. It leaves the contract untouched and the payment voluntary — the schedule simply finishes early, having accrued less interest along the way.
What the loan does if nothing extra is ever paid: the horizon and lifetime interest of the scheduled payment alone. Every claim about savings is a comparison, and the baseline is the thing compared against.
The gap between the interest the baseline schedule would have handed over and the interest the accelerated one actually does. It is not a rebate or a payout — it is money that under acceleration simply never comes into existence.
Two actions that feel similar and behave differently. A recurring extra boosts every payment from now on; a lump sum resets the balance once and leaves the payments alone. This page models the first; the second is the baseline re-run at a smaller principal.
Why the extra unit is the mightiest one
The scheduled payment already has a job: it covers the period’s interest and retires a slice of principal, in whatever proportion the balance dictates. An extra amount added on top arrives after the interest is already settled — so it has nowhere to go but principal. None of it is consumed by interest. Unit for unit, the extra money is more effective at reducing debt than the scheduled money it rides along with.
And the effect does not stop at the period it is paid in. A smaller principal accrues less interest next period, which leaves more of the unchanged scheduled payment free to retire principal, which shrinks the accrual again. Acceleration recruits the loan’s own compounding and turns it around — the same mechanism that made the debt expensive now runs in the borrower’s favour, period after period, without any further action.
This is why the savings figure routinely surprises people who expected the extra money to come back at face value. It comes back with everything the untouched balance would have accrued on top — and on a long-dated loan, where the balance would otherwise have sat large for years, that multiple is at its greatest.
Extra money lands on principal, the balance shrinks, less interest accrues, and more of the next payment reaches principal
The acceleration loop. Each pass around it is a period; the loop tightens itself, which is why the reward compounds without any further effort.
Two schedules, one difference
The method is a comparison, not a new formula. The payoff-time relation from the previous lesson is evaluated twice: once at the scheduled payment, giving the baseline horizon, and once at the boosted payment, giving the revised one. Interest on each path is everything paid along it minus the principal, and the difference between the two interest totals is the saving.
Keeping both schedules in view is what makes the answer trustworthy. A claim like “a small top-up saves years” is meaningless without stating the baseline it is measured against — the same top-up saves dramatically on a payment near the interest-only line and modestly on one far above it. The comparison prints both horizons so the claim carries its own evidence.
The comparison also degrades gracefully. Set the extra amount to nought and the two schedules collapse into one — the revised horizon equals the baseline and the saving vanishes. That degenerate case is worth running once deliberately: it confirms the machinery agrees with itself before you trust it with a decision.
Principal retired accumulates faster under the boosted payment, crossing the full balance well before the baseline schedule would
The accelerated schedule reaches the clearance line early. Everything to the right of the crossing — the periods the baseline would still be paying — is where the saved interest lives.
Where the reward bends
The reward is not linear in the extra amount. The first increment of overpayment does disproportionate work, especially when the scheduled payment sits close to the interest-only level — exactly the steep zone the previous lesson mapped. Each further increment buys a little less time than the one before, because the schedule it is shortening has already been shortened.
That bend is a planning fact, not a disappointment. It means a household does not need to find a heroic extra amount to capture most of the benefit; a sustainable modest top-up, held without fail, typically outperforms an ambitious one abandoned after a difficult season. Sweeping the extra amount through the calculator and watching where the horizon stops improving quickly is how the sustainable figure is found — the point where more acceleration stops buying much is worth seeing before committing, not guessing.
The fine print that eats savings
Three real-world conditions stand between this arithmetic and a bank account. The first is application: the extra must actually reach the principal, in the period it is paid — some lenders hold overpayments in a separate balance or apply them to future instalments unless told otherwise, which blunts the mechanism entirely. A single instruction to the lender usually fixes this, but it must be given.
The second is penalties. Where an agreement levies overpayment or early-settlement charges, they come straight out of the saving reported here, and a large enough charge can invert the decision. The third is recasting: if the lender responds to overpayment by lowering the scheduled payment instead of shortening the term, the cash-flow relief is real but the time-and-interest reward this page computes is traded away. The calculator models the term-shortening convention; make sure your loan does too.
How the method works
The payoff-time relation is evaluated at the scheduled payment, giving the baseline horizon; a scheduled payment at or below the interest-only amount is refused first, because a baseline that never ends has no horizon to improve.
The same relation is evaluated at the scheduled payment plus the recurring extra, giving the revised horizon.
Interest on each path is the total money paid along it minus the principal; the saving is the difference between the two totals.
The answer is reported in both currencies — periods removed from the schedule and interest never accrued — and the reverse direction solves for the extra amount a chosen finish date requires.
The certified engine performs this calculation. This page explains what it does; it does not reproduce it, because a second implementation of a specified method is a second answer waiting to disagree with the first.
Try the worked scenario
The engine below arrives pre-filled with the journey’s anchor: the long-dated home loan whose scheduled payment exactly amortises it over the full term, boosted by a modest recurring extra on every monthly payment. Try nought extra first and confirm the two schedules agree. Then sweep the extra upward in small steps and watch both outputs — the horizon pulling years inside the original term, and the interest saved growing fastest on the earliest increments.
Read the two results together: the revised payoff time is the schedule the extra amount buys, and the interest saved is money that never comes into existence under it. Both are computed live by the verified engine from your inputs — this page stores neither.
What each input represents
The balance owed today, from which both schedules — baseline and accelerated — are run. A loan part-way through its life enters at its current balance, so acceleration can be priced at any point in the term, not only at the start.
The nominal annual rate as a percentage, divided by the payments per year to get the periodic rate both schedules share. The higher the rate, the more each unit of principal removed early is worth, and the larger the saving the comparison reports.
How many payments fall in a year — twelve for monthly, the default. Both horizons come back in these periods, and the extra amount is per period too: an extra amount on a fortnightly schedule recurs far more often than the same figure monthly.
The contractual payment each period — the baseline the acceleration is measured against. It must be a payment that amortises the debt on its own; the comparison needs a finite baseline horizon to subtract from.
The recurring top-up added to every scheduled payment. Nought is allowed and collapses the comparison onto its baseline — a useful sanity check that the two schedules agree before any acceleration is applied.
Worked example
The scenario
The pack’s anchor vector takes a long-dated home loan whose scheduled payment exactly amortises it over the full term, then adds a modest recurring extra to every monthly payment; companion vectors do the same for a mid-sized balance and a small one.
Two outputs come back. The revised payoff time lands years inside the original term — the schedule the extra amount buys. The interest saved is the gap between what the baseline schedule would have paid in interest and what the accelerated one does, and on the anchor it amounts to a substantial slice of the whole interest bill. Read together they are the price tag of acceleration, stated in the two currencies it pays out in.
Every figure is produced by the certified engine when the calculator loads; the prose holds none. The pack also declares a refusal: a scheduled payment at or below the period’s interest-only amount is declined before any extra is considered, because a baseline that never ends has no horizon to improve.
Reading the result
The saving is carved directly out of the loan’s lifetime interest bill — the figure the next lesson totals — so a large saving is as much a statement about how expensive the baseline was as about how clever the extra is.
Time removed and interest saved move together but not in proportion: on a long, low-payment schedule the early increments of extra remove time spectacularly; on a short or heavily overpaid schedule the same increments buy little, because there is little left to buy.
A one-off windfall is not this calculation. Applying it means re-running the baseline at a reduced balance — the distinction matters because a raise and a bonus feel similar and behave completely differently over a schedule.
Common mistakes
Expecting the saving to equal the extra amounts paid. The saving is the interest the untouched balance would have accrued — usually a different and larger figure on long-dated debt.
Overpaying without instructing the lender to apply the extra to principal immediately. Held in a holding balance or applied to future instalments, the extra buys none of what this page prices.
Ignoring prepayment charges. Where they exist they come straight out of the reported saving, and the comparison should be re-judged with them in mind.
Confusing a recurring extra with a lump sum, or letting the lender recast the loan onto a lower payment and still expecting the shortened term — each swap silently changes which question is being answered.
Questions readers arrive with
Why is the interest saved so much larger than the extra I would pay in?
Because each extra unit removes principal that would otherwise have sat accruing interest for the rest of the schedule. On a long-dated loan that remainder is measured in decades, and the accrual avoided across it is what the saving totals. The extra comes back with the interest it forestalled on top.
Is it better to pay a lump sum now or a recurring extra?
They are different instruments. A lump sum resets the balance once and lets compounding work on the reduction from today; a recurring extra applies steady pressure every period. To compare them honestly, price the lump sum by re-running the baseline at the reduced balance, and price the recurring extra here — then compare the two revised schedules, not the feelings.
Does a small extra really matter on a large loan?
Most where the scheduled payment sits closest to the interest-only line, which is where large, long loans tend to live. The first increments of extra do disproportionate work there; the sweep in the calculator shows exactly how much before any commitment is made.
Why does the calculator refuse when I lower the scheduled payment far enough?
Because below the interest-only line the baseline schedule never ends, and a comparison needs a finite baseline to subtract from. The refusal belongs to the previous lesson’s law: no payment at or under the period’s accrual can end a debt, so no acceleration against it can be priced.
Should I overpay the loan or invest the extra instead?
That is a genuine decision with more inputs than this page holds — expected returns, risk, tax, liquidity, temperament. What this calculator contributes is one side of it stated precisely: the saving that overpaying this particular debt secures, fixed by the loan’s own terms rather than by any market. Weighing that against an uncertain alternative is yours to do, ideally with advice this educational page does not give.
When this calculation is used
Pricing a recurring overpayment before committing to it — what this much extra per period buys in months removed and interest never accrued.
Comparing the accelerated schedule against the baseline when deciding what a monthly surplus should do.
Using the reverse direction to find the extra amount a chosen finish date requires.
Checking a claim that a small top-up saves years — the sweep chart shows exactly when that is true and when it flattens.
Separating the effect of a recurring top-up from a one-off lump sum before mixing the two up.
Assumptions and guards
The extra amount is paid every period without fail and is applied to the principal immediately, in the same period it is paid.
The lender levies no prepayment penalty or overpayment charge — where one exists, it comes straight out of the saving reported here.
The scheduled payment stays unchanged after overpaying: the loan is not recast onto a new, lower payment, which would trade the time saving for cash-flow relief.
The rate is fixed across both schedules, and the periodic rate follows the nominal convention of the annual rate divided by the payments per year.
The comparison models a recurring top-up, not a one-off lump sum — a windfall applied once needs the baseline re-run at a reduced balance instead.
A scheduled payment at or below the interest-only amount for the period is refused: the baseline schedule would never end, so neither the revised horizon nor the saving against it can be stated.
The balance and the scheduled payment must both be greater than nought, and the extra amount cannot be negative — a withdrawal from the payment is not an acceleration.
The rate is bounded to a realistic range and the payments per year must be at least one, so both schedules describe actual repayment arrangements.