One deal, three events, and the dates nobody wrote down

The deal

Tax and fee treatment varies by state; here they are simply lines on the order like any other. The note is sized on the $15,402 average amount financed reported for buy-here-pay-here paper (Federal Reserve, FEDS Notes, May 2026).

The terms

• 91 biweekly payments of $235.35 on Fridays, first 30 January 2026, last 13 July 2029
• 19.90% APR, simple interest on outstanding principal, no compounding
• Day count actual/365; interest is computed per interval and rounded half up to the cent before it posts
• A payment is applied to accrued interest first, then to principal
• When the balance changes: the payment holds and the term moves

Every line above is an input. The dental example runs the same engine on 30/360, monthly dates, and the opposite rule on change — there the dates hold and the instalment moves. Here the payment is the thing that has to keep fitting a paycheck, so the term absorbs everything instead.

What happened

• 3 July — payment 12 is deferred to the end of the term under the contract's skip clause. $25 fee, financed
• 7 August — the customer cancels the service contract, 203 days into 730. The administrator refunds the unearned premium to the dealer: $1,245.84, received 28 August
• 2 October — the vehicle is a total loss. The insurer pays actual cash value of $9,850.00 on 24 October; the GAP waiver covers the deficiency

Event 1 — the deferral

One payment moves to the back of the contract. The customer is not delinquent and the payment never changes — but a simple-interest note does not stop accruing because a payment did, and the engine says exactly where that lands:

That is the honest price of the skip clause, and it is the number a collector should be able to read out loud on the phone.

Event 2 — the cancelled service contract, and the fork

The service contract comes off the deal after 203 of its 730 days. The administrator computes the unearned premium pro rata and sends it to the dealer, because on this deal the dealer is the lender:

The contract says refunds are applied to the account. It does not say as of when — and there are two candidate dates twenty-one days apart: the day the coverage stopped, and the day the cheque arrived.

Twenty-one days of float on $1,245.84 is $14.26 of interest on the day it happens. By the end of the contract it is $23.98, because every payment after it splits differently — a knock-on the engine does not estimate, it replays. The customer's payment never changes in any column; what moves is when the paper stops earning, and that is 10 payments of difference against not crediting it at all.

Event 3 — the total loss, and which balance the waiver covers

The car is destroyed on 2 October. The last payment collected was 25 September, and this example assumes none is collected after the loss. That is an assumption of this example and nothing more: a contract that keeps collecting produces a different balance from the same log, which is the point. The insurer pays actual cash value of $9,850.00 twenty-two days later, on 24 October.

What the waiver covers has to be written down before any of this means anything, so here it is, synthetic and explicit: the unpaid balance as of the date of loss, less any amount added to the balance after origination, and less any instalment due but unpaid when the loss occurred. Published waivers say more — the Northwest Federal Credit Union addendum also carves out refunds of cancelled ancillary products and caps the benefit. Which set of exclusions is right is not the question; every one of them names a date and a base, and the ledger has to be able to produce both on demand. (NWFCU GAP waiver addendum, as a real example of the wording.)

Both numbers are right; they answer different questions. The waiver written above names the first, so it relieves the account of the deficiency as at the date of loss, less the $25 deferral fee that its own exclusion carves out as an amount added after origination: $2,298.19 waived. A waiver forgives debt rather than paying it — the only payment here is the insurer's $9,850.00.

Which leaves the account at $170.46:

Under the assumptions of this example, $170.46 remains on the borrower's account. Any further waiver or adjustment is a separate event and has to be recorded as one — which is the whole discipline. The engine's job is not to invent it: it is to produce the balance on either date, name the rule that produced it, and still be able to show that eighteen months later, to somebody who was not there.

What this example is actually about

Not the arithmetic. Interest on a declining balance is a solved problem, and any DMS that has been in this business for a decade computes it correctly.

It is about the fact that a deal keeps changing after it is signed, that every change carries two dates and at least two defensible readings, and that whichever reading ran has to still be legible when somebody asks eighteen months later. That is what an event log plus a deterministic replay buys: the answer, plus the rule that produced it, plus the ability to run the other reading and see the difference in dollars before choosing.

Check it yourself

The engine is a pure function of the terms and the event log: same inputs, same numbers, on any machine, including for periods already past. The block below is a summary of the state you are looking at. bhph.json is the whole of it — the deal line by line, every convention named, the posting log, and the expected outputs for all four policy sets these controls select. That file is generated from the same engine this page runs; the page does not read it back, so it is a published input, not a source of truth about itself. What makes it worth anything is verify.py: a second implementation written from the specification rather than shared with the engine. Save it next to the file and run python3 verify.py; it checks whichever of the two specifications it finds beside it, and either one on its own is enough.

{
  "terms": {
    "apr": "0.1990",
    "day_count": "actual/365",
    "compounding": "none",
    "payments": 91,
    "every_days": 14,
    "first_due": "2026-01-30",
    "amount_financed": "15,398.69",
    "payment": "235.35",
    "on_change": "payment holds, term moves",
    "allocation": "accrued interest, then principal"
  },
  "events": [
    { "on": "2026-07-03", "type": "payment_deferred",
      "fee": "25.00", "fee_financed": true, "moved_to": "2029-07-27" },
    { "on": "2026-08-07", "type": "service_contract_cancelled",
      "pro_rata_on": "elapsed days", "used": "203", "of": "730",
      "refund": "1,245.84", "received": "2026-08-28", "effective": "POLICY FORK" },
    { "on": "2026-10-02", "type": "total_loss",
      "acv": "9850.00", "insurer_paid": "2026-10-24" }
  ],
  "expected": {
    "payoff_at_date_of_loss": "12,173.19",
    "payoff_at_date_of_insurer_payment": "12,318.65",
    "deficiency_at_date_of_loss": "2,323.19",
    "deficiency_at_date_of_payment": "2,468.65",
    "daily_interest_at_loss": "6.61",
    "ends_not_credited":             { "date": "2029-08-24", "payment_no": 93, "final": "8.59" },
    "ends_credited_at_cancellation": { "date": "2029-04-06", "payment_no": 83, "final": "169.47" },
    "ends_credited_on_receipt":      { "date": "2029-04-06", "payment_no": 83, "final": "193.45" }
  }
}

If your numbers come out differently, the disagreement is in a named rule — the day count, the allocation order, the effective date, the rounding step — and that is a conversation worth having before anyone integrates anything.