The gap between an introductory instalment and a fully-indexed one

What the introductory rate is holding back

The design is a controlled comparison rather than a simulation, and its restraint is what makes it trustworthy. No caps intervene, no balance is drawn down, no adjustment timetable is assumed and no benchmark is forecast. One loan is costed twice at two rates on one schedule. What comes out is the pure rate effect — the unbuffered distance between the two worlds — which is the honest starting point before the note’s limits are allowed to soften it.

The proportional reading is the one that travels. Money per month is what a household actually feels, but it cannot be compared between loans of different sizes; the share of the introductory instalment can. Across the pack’s declared cases the two long-dated ones land just under half again on top of what is being paid — an instalment rising by nearly half is not a rounding of the household budget, it is a different budget — while the short-dated case lands at around a fifth, less than half the proportional shock of either long one.

The term, not just the rate distance, is what governs that spread. Early in a long schedule almost the whole instalment is interest, so moving the rate moves nearly the whole instalment. On a short schedule the instalment is dominated by principal repayment, which no rate change can shrink — the same borrowed amount still has to be returned in the same number of months — so a rate rise moves a much smaller share of it. A short term is genuinely, structurally, less exposed to a rate shock, and it buys that protection with a higher instalment from the outset.

The most instructive coincidence in the pack’s cases is easy to miss. Two of them open at essentially the same instalment — the figures agree to within a hair, one a larger amount borrowed over a long term at a low introductory rate, the other a smaller amount over half that term at a slightly higher one. Identical opening cost; proportional exposure differing by more than a factor of two. The instalment a borrower is quoted at signing carries almost no information about the shock behind it, and no amount of staring at that opening figure would ever reveal which of the two loans it is.

This is the number a budget should be tested against, not the introductory one. Whether a lender underwrote at the discounted rate or at the fully-indexed one is a matter of programme and jurisdiction, and this page does not decide it — but a household that can meet the introductory instalment and not the fully-indexed one has bought a timer, and the gap reported here is the size of what it is counting down to.

When this calculation is used

• Testing a household budget against the fully-indexed instalment before committing to a discounted one.
• Comparing two adjustable offers of different sizes on the proportional shock each implies, where the money figures are not comparable.
• Deciding between a shorter term at a higher opening instalment and a longer one at a lower one, with the exposure of each made explicit.
• Sizing how much room a refinance or a sale would need to create, if the plan is to be gone before the discount ends.
• Reading the discount as a benefit with a price: what it saves each month now, and what it defers to later.

Worked example

The pack declares three loans: two long-dated ones of different sizes, each opening at a deeply discounted rate against a fully-indexed rate several points higher, and one short-dated loan at half the term with a narrower rate distance.

Take the proportional output first on all three. The two long-dated loans both land just short of half again on top of the opening instalment, despite differing in amount borrowed and in both rates — the proportional reading is remarkably stable across loan size, which is what makes it the comparable one. The short-dated loan lands at roughly a fifth: less than half the proportional exposure, on a schedule dominated by principal that no rate change can touch. Then look at the opening instalments themselves and notice that one long-dated loan and the short-dated one open at effectively the same figure — the clearest possible demonstration that the instalment on offer says nothing about the exposure behind it.

Every figure is produced by the certified engine when the calculator loads; this page stores none. The pack also declares a refusal on a term of no length: with no schedule there are no instalments to compare and no gap between them to report.

What each input represents

Assumptions and limits

• Both instalments are computed on the same amount borrowed and the same term, so the comparison isolates the rate — it does not model the balance the loan will actually have reached when the discount ends.
• No caps are applied. The gap shown is the unbuffered distance; a note’s per-adjustment limit can stop the charged rate reaching the fully-indexed one at a given adjustment, and the reset calculation is where that is tested.
• The fully-indexed rate is supplied, not derived: nothing here reads a benchmark, applies a margin or forecasts where a published series will stand when the discount lapses.
• Both schedules are fully amortising and monthly, at the nominal convention — the annual rate divided by the payments in a year.
• Only principal and interest are compared. Taxes, insurance, mortgage insurance and escrow changes move independently of the rate and are outside both figures.
• The proportional output is measured against the introductory instalment, so it answers “by how much would what I pay now rise”, not “what share of my income is this”.

What the guards protect against

• The term must be greater than nothing, pinned by a declared refusal vector — two instalments cannot be compared where no schedule exists to pay them into.
• The amount borrowed must be greater than nothing and is bounded above beyond any residential loan, which catches a figure entered in the wrong currency scale.
• Both rates are bounded to the band of plausible quoted mortgage rates, which declines a figure entered as a count of basis points; a rate typed as a decimal fraction, by contrast, sits inside the band and is answered, producing a gap that looks reassuringly small for no good reason.
• Nothing forces the fully-indexed rate to exceed the introductory one. Entering the lower of the two is permitted and reports a negative gap, which is the correct answer to a question about a discount that was never a discount.

Provenance

Adjustable-rate payment-shock comparison on a single amortisation schedule

The standard annuity relation applied twice to one amount borrowed and one term, once at the introductory rate and once at the fully-indexed rate, with the zero-rate case handled separately; the difference reported in money and as a share of the introductory instalment.

Educational reference, not financial advice, and not an underwriting or affordability determination. Both rates and the term are inputs taken from the reader’s own note and disclosure, whose terms govern what is charged and when. The signed pack carries its own citation, which displays from the verified leaf once the calculator loads; the page reports the verification state of the release it mounted rather than asserting one.