Source: https://guthlabs.ai/docs/instruments/credit-card-payoff-planner/mechanism/

instrument mechanism / verified-clean

# Credit Card Payoff Planner mechanism

The inspectable method record for Credit Card Payoff Planner, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The underlying standard amortization mathematics is valid under the stated assumptions, but the instrument specification is incomplete. It needs explicit recurrence, rate convention, payment timing, target-payment formula, zero-rate handling, impossible-payoff handling, rounding policy, and a precise definition of months to payoff before it can receive PASS.

- The specification says “same recurrence as amortization” but does not state the recurrence explicitly, including whether payments occur at the end or beginning of each month.

- The formula for solving payoff time n given balance, APR, and payment is not written explicitly.

- The formula for solving the required payment given a target number of months is omitted.

- The specification does not define whether “months to payoff” means the fractional analytical result or the integer number of scheduled payments after rounding up.

- The specification does not define how the final partial payment and total interest are calculated when the analytical payoff time is fractional.

## Units and conventions

- APR is a nominal annual percentage rate compounded monthly, so the monthly rate is r = APR/12; APR must be supplied as a decimal or explicitly converted from percent.

- Payments are assumed to occur at the end of each month.

- For fixed-payment payoff, the balance recurrence is B_(k+1) = B_k(1+r) - P.

- For r > 0 and P > rB, the analytical payoff time is n = ln(P/(P-rB)) / ln(1+r).

- For a target of N months and r > 0, the required payment is P = Br(1+r)^N / ((1+r)^N - 1).

- For APR = 0, payoff time is B/P and target-month payment is B/N.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "balance": 1000,
    "apr": 0.12,
    "monthly_payment": 100
  },
  "expected_outputs": {
    "analytical_months_to_payoff": 10.5886,
    "scheduled_months_to_payoff": 11,
    "total_interest": 58.9849,
    "min_payment_trap_warning": false
  },
  "working": "Monthly rate: r = 0.12/12 = 0.01. Interest accrued each month initially: 1000 x 0.01 = 10, so P = 100 > 10. Analytical months: n = ln(100/(100 - 0.01 x 1000)) / ln(1.01) = ln(100/90) / ln(1.01) = 0.1053605/0.00995033 = 10.5886. After 10 full payments: B10 = 1000(1.01)^10 - 100[((1.01)^10 - 1)/0.01] = 58.4009. Final payment after one more month of interest: 58.4009 x 1.01 = 58.9849. Total paid = 10 x 100 + 58.9849 = 1058.9849. Total interest = 1058.9849 - 1000 = 58.9849."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The literal logarithmic payoff formula breaks at APR = 0 through a 0/0 expression, and the under-minimum-payment branch produces no finite payoff. The specification also leaves APR convention ambiguous, allowing materially different results.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/credit-card-payoff-planner/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/credit-card-payoff-planner/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/credit-card-payoff-planner/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`