Comparison
The Cost of a Lower Payment Across Deferred Principal: What Leaving Part of the Advance Outstanding Removes From the Monthly Figure, and Adds to the Total
When an agreement lowers the monthly payment by leaving part of the advance outstanding at the end, how much of the payment does it remove, how much does it add to the total, and what does each unit of that payment relief cost?
The short answer
No. The lower payment is bought, not saved. Over 4 years at 9.0%, deferring 40% of the advance cuts every payment by 27.94% — and raises the total paid by 6.62% of the amount borrowed. The deferred part is never repaid during the term, so it accrues interest for the whole of it.
The useful figure is the price of that relief: every unit of monthly payment removed costs 19.83% extra in total at this term and rate. That price carries neither the amount borrowed nor the share deferred, so it is one number per agreement shape — 2.32% over 1 year at 5%, and 61.78% over 7 years at 13%.
- Who it applies to
- Any borrowing repaid by level payments that deliberately leaves part of the advance outstanding at the end — a balloon, a residual value, a guaranteed future value, or a deferred final instalment under any other name. It compares two structures at the same amount, the same rate and the same term.
- What this does not tell you
- It establishes what deferring principal does to the payment and to the total, and what each unit of payment relief costs. It does not establish that any such agreement is available, what any provider charges, or whether a lower payment is the right choice for anyone.
Outputs of Residual Amortisation v1.0, a locked calculation model, over the stated reference sets. No market data, no product terms and no forecast enter it, so nothing here goes out of date when rates or products do.
What is being compared
Two agreements that differ in exactly one respect: how much of the advance is still outstanding when the term ends. The amount, the rate, the term and the number of payments are identical in every row, and no amount of money appears anywhere on this page.
| Amount borrowed | One unit — every figure below is a share of it |
|---|---|
| Term | 4 years |
| Annual rate | 9.0%, nominal, charged monthly |
| Payments | 48 level monthly payments |
| Deferred share | Stated in the first column, from nothing deferred to 60% |
| Settlement | The deferred share is paid in full when the term ends |
| Not modelled | Fees, deposits, part-exchange, early settlement, mileage or condition charges |
Every rate, term and deferred share on this page is a stated level entered into a model, chosen so the shape can be read. None is a survey of what any provider offers, a claim that any of them is available, or a suggestion that any is typical.
Where the difference comes from
A level payment has to do two jobs: pay the interest as it accrues, and repay the advance by the end. Deferring part of the advance removes the second job for that part and leaves the first one running for the whole term. So the payment falls by what that part would have contributed to repayment, and the total rises by the interest the part goes on accruing.
Written once, per unit of principal deferred:
payment falls by δ = v^n ÷ a(n, i)
total rises by κ = 1 − n × δ
Both are properties of the term and the rate alone. Neither contains the amount borrowed and neither contains how much of it is deferred, which is why every figure on this page is a share rather than an amount: an agreement ten times the size has ten times every currency figure and exactly the same ratios.
The second identity is the first one read to the end. A deferred unit saves δ on each of n payments, so it buys n × δ of relief in total — and it is still owed when the term finishes, so it costs 1 − n × δ. The saving and the cost are the same fact counted at two moments, not two independent quantities that happen to point opposite ways.
What deferring more does, at one agreement
Seven stated shares of the advance, over 4 years at 9.0%. The second column falls and the fourth rises, in the same row, in every row.
| Share of the advance deferred | Monthly payment, against the ordinary agreement | Total paid, as a share of the advance | Of which the charge for deferring |
|---|---|---|---|
| 0% | 100.00% | 119.45% | 0.00% |
| 10% | 93.01% | 121.10% | 1.66% |
| 20% | 86.03% | 122.76% | 3.31% |
| 30% | 79.04% | 124.41% | 4.97% |
| 40% | 72.06% | 126.07% | 6.62% |
| 50% | 65.07% | 127.72% | 8.28% |
| 60% | 58.08% | 129.38% | 9.93% |
The top row is the comparison rather than a spacer. With nothing deferred the payment is 100.00% of itself and the charge is 0.00%, exactly — this model reproduces the ordinary amortisation it extends with no difference at all, which is what makes every row beneath it a like-for-like comparison rather than an approximation.
Both moving columns are linear in the share deferred, and that is the finding rather than an artefact of the levels chosen. Deferring 20% costs 3.31% and deferring40% costs 6.62%, which is twice as much for twice as much deferral. There is no level at which the trade becomes good and none at which it becomes suddenly worse — so there is no threshold to find, and this page publishes none.
What each unit of payment relief costs
The ladder above answers how much, at one agreement. This answers the question a reader comparing two offers actually has: what am I paying for the relief?
Divide what the deferral costs by what it buys — κ ÷ (n × δ) — and both the amount borrowed and the share deferred cancel out. What is left is a single figure per term and rate: the extra total paid for each unit of monthly payment removed.
| Term | 5% a year | 9% a year | 13% a year |
|---|---|---|---|
| 1 year | 2.32% | 4.23% | 6.18% |
| 2 years | 4.94% | 9.12% | 13.51% |
| 3 years | 7.65% | 14.31% | 21.51% |
| 4 years | 10.45% | 19.83% | 30.26% |
| 5 years | 13.34% | 25.71% | 39.82% |
| 6 years | 16.34% | 31.95% | 50.30% |
| 7 years | 19.44% | 38.60% | 61.78% |
Read down a column and the price rises with the term, because a deferred unit accrues for longer. Read across a row and it rises with the rate, for the same reason. The two compound: the cheapest corner of this table charges 2.32% for a unit of relief and the dearest charges 61.78%, which is more than 26 times as much for the identical thing.
This is the figure a monthly payment cannot show, and it is why two agreements offering the same reduction are not the same offer. The reduction is what is advertised; the price of it is what is being decided.
At the end of the axis, an agreement that repays nothing
The ladder stops at 60% because the columns are linear and nothing changes character further along. The end of the axis does change character, and it has a name.
Defer the whole advance and every payment is interest: the balance never moves, and the entire amount falls due at the end. Over 4 years at 9.0% the payment is 30.14% of the ordinary agreement's — the largest reduction available — and the total paid is 136.00% of the advance, of which 16.55% is the charge for having repaid none of it.
The model names that state on the agreement rather than inferring it from an output, and this page keeps the name attached to the figures. It is not an eighth rung: the other seven differ in degree, and this one differs in kind. An arrangement that repays nothing is a different arrangement, not an aggressive version of the same one.
A higher total is not automatically a worse decision
Everything above is a price, and a price is not a verdict. Payment relief buys something, and what it buys does not appear in any of this arithmetic: money that stays in a household each month is available for everything else that month, and an agreement that is affordable is not obviously worse than one that is not.
What this page establishes is that the relief has a price and what the price is, so the comparison can be made on both numbers rather than on the visible one. Two readers with identical agreements can reasonably decide differently depending on:
- what the payment relief is being used for, and what that use is itself worth
- whether the money freed each month is spent, saved or earning a return
- how likely the reader is to keep the agreement to the end of its term
- what settling the deferred share will actually require when it falls due
- whether an agreement with a lower payment is affordable when one with a higher payment is not
No structure is presented here as sensible or reckless, and nothing on this page is a reason to enter, avoid, refinance or settle any agreement.
What this comparison does not determine
The figures on this page are outputs of a locked calculation model applied to the stated reference sets. They are not quoted terms, market conditions, offers or a forecast of anything. The comparison cannot determine:
- whether any agreement of this shape is available anywhere, at any rate or term
- what any lender, dealer, broker or platform charges, offers or requires
- whether the deferred share will be paid, refinanced, or settled by handing something back
- what an asset the advance was used for will be worth when the term ends
- whether a lower payment is worth its total cost for any particular reader
- the effect of any fee, charge or deposit, none of which is in this arithmetic
It also holds the agreement still. A rate that changes during the term, a payment that is missed, a settlement taken early and a deferred share that is refinanced rather than paid all move the arithmetic, and none of them is modelled here — the comparison is between two schedules that both run to their stated end.
None of this is financial, legal or tax advice, and no product, provider, lender or platform is recommended, ranked or named anywhere on this page.
Where these figures come from
Every number above is produced at build time by Residual Amortisation v1.0, run over the two reference sets in the comparison set. Nothing on this page is typed by hand and nothing on this page is computed by this page.
The model is an extension of the amortisation the mortgage reference publishes, adding exactly one capability: a balance that is still outstanding when the term ends. Its canonical vectors RA-1, RA-3, RA-6 are recalculated by an independently written 60-digit verifier rather than by the implementation itself, and all three sit at the term and rate this page's first ladder is read at — which is why that agreement was chosen rather than invented.
The build refuses to publish a ladder whose first row is not the ordinary agreement exactly, or whose two moving columns ever point the same way. The first is the parity claim this model was accepted on; the second is the finding this page exists to state, and a build that could not reproduce either would be publishing something other than what it says.