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The calculator's own fields, action and results arrive with the verified pack when you load it. Nothing is computed in this page.
Adjustable-rate mortgages · first adjustment
The instalment after an ARM adjustment, once the caps have had their say
Work out the instalment after an adjustable mortgage adjusts: the fully-indexed rate squeezed into the bands the note’s periodic and lifetime caps allow, then re-amortised over the balance and the term that are actually left.
Verified engine
What the engine returns
Read the applied rate against the fully-indexed rate on every run. On the first two the fully-indexed figure sits above the band and the applied rate is pinned at the band’s upper edge — in the second case a long way short of it, and the instalment reflects the pinned rate rather than the benchmark that would otherwise have driven it. On the third the fully-indexed figure is inside the band and the two rates coincide, so nothing has been held back and the next adjustment starts from a rate the market has already reached.
Inputs the result is built from
Balance at the adjustment
Remaining amortisation term
Note margin
Benchmark value at the adjustment
Periodic adjustment limit
Lifetime limit over the starting rate
Starting rate on the note
How the result is derived
MethodThe benchmark and margin summed, clamped into the periodic band around the starting rate, clamped again into the lifetime band, and the resulting rate applied to the outstanding balance over the remaining term through the standard annuity relation, with the zero-rate case handled separately.
StandardAdjustable-rate reset mechanics with periodic and lifetime rate limits
GuardThe balance must be greater than nothing, and the pack pins that with a declared refusal vector — a rebuilt schedule needs something left to repay.
Why the adjusted rate is so often not the fully-indexed one
The bounding happens in two passes, and their order is the whole subtlety. The fully-indexed rate is first squeezed into a narrow band the periodic limit draws around the starting rate, and the result of THAT is squeezed into the wide band the lifetime limit draws around the same starting rate. The narrow band is inside the wide one, so at a first adjustment the periodic limit is the one with teeth and the lifetime limit is an outer fence that rarely gets touched. The declared vectors bear this out exactly: the periodic band decides the outcome in two of the three computed cases, and the lifetime band changes nothing in any of them.
Watching the two rate outputs diverge is the point of the exercise. In the first two vectors the benchmark has moved far enough that the fully-indexed figure lands above the narrow band, and the applied rate is pinned to the top of that band, visibly short of the fully-indexed figure reported beside it — the note, not the market, is setting the instalment. In the third the fully-indexed figure falls comfortably inside the band and passes through untouched, applied rate equal to fully-indexed rate. Same relation, two entirely different stories about what the borrower is exposed to next time.
The bounding is symmetric, and borrowers rarely price that half. The same limit that stops a rate climbing more than a step also stops it falling more than a step: when a benchmark collapses, relief arrives at the pace the note allows and no faster. That behaviour is in the relation rather than in the declared vectors — all three computed cases sit at or above the starting rate — so it is worth testing with a low benchmark value before assuming a downturn passes straight through.
Re-amortisation is the second half of the answer and the half that surprises people. The instalment is not scaled up from the old one; it is rebuilt, from the balance that survives and the payments that remain. Two loans taking an identical rate step can therefore move by quite different amounts, because a schedule with two decades left and one with a quarter century left spread the same balance very differently — which is precisely why the declared vectors carry three different remaining terms rather than three balances at one term.
Past a certain benchmark level the instalment simply stops responding. The pack declares a chart that sweeps the benchmark across a wide range and traces the instalment: it climbs, and then it flattens the moment the periodic limit takes over, because every further point of benchmark movement is being absorbed by the cap. The pack also declares a reverse direction that solves for the benchmark from a target instalment, and the flat stretch is where that question stops having a single answer — a great many benchmark values produce the same capped instalment, so a solved value there is one member of a range rather than the only value that fits.
The benchmark and margin summed, clamped into the periodic band around the starting rate, clamped again into the lifetime band, and the resulting rate applied to the outstanding balance over the remaining term through the standard annuity relation, with the zero-rate case handled separately.
When this calculation is used
- Auditing the adjustment notice a servicer sends: does the note’s benchmark, margin and cap structure reproduce the instalment being demanded?
- Asking what the instalment becomes if the benchmark stands at a chosen level on the next adjustment date.
- Establishing whether the cap or the benchmark is what sets the next instalment — the difference between exposure that is bounded and exposure that is live.
- Budgeting the step at the end of an introductory period, using the balance and remaining term that will actually be in force by then.
- Comparing two notes with different cap structures at one common benchmark value.
Worked example
The pack declares three adjustments that differ in every input that matters: balances in the middle six figures, remaining terms of two decades, a quarter century and a little beyond, starting rates spread across several points, and benchmark values ranging from modest to elevated. All three carry the same cap structure, which is what makes the comparison between them clean.
Read the applied rate against the fully-indexed rate on every run. On the first two the fully-indexed figure sits above the band and the applied rate is pinned at the band’s upper edge — in the second case a long way short of it, and the instalment reflects the pinned rate rather than the benchmark that would otherwise have driven it. On the third the fully-indexed figure is inside the band and the two rates coincide, so nothing has been held back and the next adjustment starts from a rate the market has already reached.
Every figure is produced by the certified engine when the calculator loads; this page stores none. The pack also declares a refusal on a balance of nothing: with nothing outstanding there is no schedule to rebuild, so the request is declined rather than answered with an instalment of nought.
What each input represents
Balance at the adjustment
What is still owed on the adjustment date, not the amount originally borrowed. Using the original figure overstates the instalment, because an amortising schedule has been retiring principal the whole time — the amortisation-balance calculator exists precisely to supply this number for a date in the future.
Remaining amortisation term
How long the rebuilt schedule has to clear the balance, in years — the original term less the time already served. It is the shortening of this figure, as much as the rate, that moves an adjusted instalment: the same balance at the same rate costs more per month the less time is left to repay it.
Note margin
The fixed spread the note adds to the benchmark. It does not adjust and is not capped — the caps bound the sum, never the spread — so it sets the floor under every fully-indexed rate this note will ever construct.
Benchmark value at the adjustment
The published value the note reads on the date its look-back rule names. Supplied by the reader from the note and the published series, never fetched or assumed here; a modestly negative value is accepted, since published benchmarks have printed below nought.
Periodic adjustment limit
How far the rate may move at a single adjustment, in percentage points either side of the starting rate. This is the limit that usually decides the answer, and notes state it in their own terms — sometimes with a different limit on the first adjustment than on later ones. The pack ships an illustrative value so the field is never empty; the limit that governs is the one in the disclosure.
Lifetime limit over the starting rate
The outer fence: how far above the starting rate the note may ever go, whatever the benchmark does. Applied here after the periodic limit, so it changes the answer only when a single adjustment would otherwise clear the whole lifetime allowance — which it does not in any of the pack’s declared cases. Read it from the disclosure rather than trusting the field as it arrives.
Starting rate on the note
The rate the loan began at — the anchor both limits are measured from. It matters after the introductory period is over, and it is why two loans facing the same benchmark on the same day can be permitted very different adjusted rates.
Assumptions and limits
- Both limits are measured from the starting rate, which frames this as a single adjustment rather than a chain: notes that cap each move against the rate then in force are not modelled by repeating this step.
- No rounding increment is applied. The fully-indexed figure enters the bounding unrounded, so a note that rounds before capping will differ slightly — that rounding is its own calculation.
- The rebuilt schedule is fully amortising and monthly, with the balance reaching nought on the final payment; interest-only periods, recasts and negative amortisation are outside it.
- The periodic rate is the annual rate divided by the payments in a year — the nominal convention notes quote.
- Only principal and interest are computed. Property taxes, insurance premiums, mortgage insurance and any escrow shortfall sit outside this instalment.
- The benchmark value supplied is a question, not a prediction: nothing here claims where a published series will stand on a future adjustment date.
What the guards protect against
- The balance must be greater than nothing, and the pack pins that with a declared refusal vector — a rebuilt schedule needs something left to repay.
- The remaining term must be greater than nothing and is bounded above at a length beyond any ordinary amortisation, which catches a term entered in months where years belong.
- Both limits must be non-negative and are bounded above. A limit of nothing is legitimate and meaningful rather than an error: it pins the adjusted rate to the starting rate exactly, which is how a note with no permitted movement behaves.
- The benchmark is bounded to a band reaching a little below nought and well above any ordinary quoted rate; the margin may not be negative, because a spread is added to a benchmark and never subtracted from it.
Provenance
Adjustable-rate reset mechanics with periodic and lifetime rate limits
The benchmark and margin summed, clamped into the periodic band around the starting rate, clamped again into the lifetime band, and the resulting rate applied to the outstanding balance over the remaining term through the standard annuity relation, with the zero-rate case handled separately.
Educational reference, not financial advice. Every convention here — benchmark, margin, both limits and the starting rate — is an input taken from the reader’s own note and disclosure, and the note’s terms govern what actually happens at an adjustment. 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.