Stress-tested qualifying payment against income

Pricing the loan you were not quoted

One loan is priced twice. The contract rate produces the payment that will appear on the statement; the contract rate plus a buffer produces the payment the household is being asked to prove it could carry. Both are level, fully amortising instalments over the same principal and the same term, so the only thing that differs between them is the rate — and the distance between the two is a direct measure of how exposed this particular schedule is to a rate it did not expect.

The buffer is added in percentage points and the whole schedule is rewritten as though it had been struck at the higher rate from the first payment. That is deliberately more severe than most futures: it is not a forecast that rates will move, nor a model of when a reset might arrive, but a standing question about resilience. The size of the buffer is the reader’s to set, and the pack’s default is described in its own help text as a commonly cited figure rather than a required one.

The ceiling on the other side of the comparison is income multiplied by a maximum qualifying share — and here the page owes the reader a warning it would be easy to leave out. A maximum debt-to-income share is ordinarily meant to cover everything a household owes each month, while the payment tested against it here is principal and interest alone. Property taxes, insurance, mortgage insurance, association dues and every non-housing debt sit outside the figure and inside the ceiling’s intent. Whatever headroom appears is therefore an upper bound on the real thing, and often a generous one.

When the stressed payment does clear the ceiling, the pack raises a declared warning and still returns every figure. Nothing is withheld and nothing is decided. That is the right behaviour for an explanatory instrument: the reader who is over the line usually needs to see by how much, and against which of the two payments, far more than they need a refusal.

The share-of-income output is the reading that travels best between situations. An instalment means little without the income beneath it, whereas the stressed payment stated as a percentage of gross income can be compared across households, across property markets and against whatever guidance is being used — including guidance that is stricter than the ceiling entered in the box.

Term is the hidden variable in how much the buffer hurts. On a long schedule most of an early instalment is interest, so lifting the rate lifts nearly the whole payment; on a short one much of the instalment is principal being returned, and principal does not care what the rate is. The same buffer therefore produces a much smaller proportional shock on a short loan — one of the least intuitive facts in mortgage arithmetic, and one the declared vectors demonstrate directly.

When this calculation is used

• Seeing what the same loan would cost if the rate were meaningfully higher than the one on the offer.
• Sizing the headroom between a stressed payment and a stated qualifying share of income.
• Comparing a short, expensive schedule against a long, cheap one on resilience rather than on the instalment.
• Finding how large a buffer a household budget absorbs before the qualifying ceiling is crossed.
• Reading an adjustable or resetting arrangement as though the reset had already happened, before committing to it.

Worked example

The pack declares three vectors chosen to move the levers independently: a long-dated loan at a moderate rate with the larger buffer, a smaller long-dated loan at a higher rate with a smaller buffer, and a large loan over half the term at a low rate, carrying the larger buffer and held to the strictest qualifying share of the three.

Every declared vector clears its ceiling — in each of the three the stressed payment lands below the qualifying maximum, so none of them trips the pack’s warning. The interesting differences are in how much room is left and in what the buffer cost. The short-dated vector has the highest income of the three and the least headroom of the three, because a large principal compressed into half the term produces an instalment that eats most of a stricter ceiling. And of the two vectors sharing the larger buffer, the long-dated one has its payment lifted by close to a quarter again, while the half-length one is lifted by little more than half as much — the same buffer, a very different shock, because principal repayment is indifferent to the rate. The vector with the smallest buffer shows the smallest lift of all, as it should.

The pack also declares a refusal: an income of nothing is declined as a bad input, since both the ceiling and the share-of-income reading are built on it. Exceeding the ceiling, by contrast, is a declared warning and not a refusal — the figures are still returned. Every number shown is produced by the certified engine at mount, and none of it is a credit decision.

What each input represents

Assumptions and limits

• Both payments price principal and interest only. Property taxes, insurance, mortgage insurance and association dues are outside them, as is every non-housing debt.
• The qualifying ceiling is gross income multiplied by a share the reader supplies, and it is compared with a principal-and-interest payment — so any other obligation that share is meant to cover reduces the real headroom below the headroom shown.
• The buffer is added to the contract rate and the schedule repriced as if it had been written at the higher rate from the start; this is a resilience test, not a projection that any rate will move.
• Both schedules are fixed-rate, level-payment and fully amortising, with the periodic rate taken as the annual rate divided by the payments in a year — the nominal convention lenders quote.
• Income is gross, steady and continuing; no other income test, credit assessment or lender criterion is modelled.
• A stressed payment above the ceiling raises a declared warning rather than a refusal, and the pack returns all four figures either way.

What the guards protect against

• An income of nothing or less is refused rather than answered — the range excludes its lower bound, and the pack pins the behaviour with a declared refusal vector, because both the ceiling and the share-of-income reading divide by it.
• The principal and the term must each be greater than nothing, so that the two payments describe a schedule that actually exists rather than an arithmetic accident.
• The contract rate, the buffer, the term and the qualifying share are each bounded to bands that span realistic lending practice. A value outside any of them is refused rather than repriced, because the resulting payment would belong to no arrangement a reader could be offered.
• A contract rate of nothing is admitted rather than refused and handled on its own branch — the instalment becomes the principal spread evenly across the payments — while the stressed side still carries whatever buffer was set.

Provenance

Rate-stress qualifying test against a debt-to-income ceiling

The level instalment computed at the contract rate and again at the contract rate plus the buffer, both under the nominal monthly convention, with the stressed instalment expressed as a share of gross income and compared against gross income multiplied by the qualifying share.

Educational reference, not financial advice, and not a lending decision: no lender applies this test to an application on the strength of this page, and clearing the ceiling here is not an approval. Both the buffer and the qualifying share are inputs, so no threshold is asserted. 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.