Credit Card Payoff Planner

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Finance, Economics & Business (educational only — never individualized investment, tax, or legal advice)

Tranche

tranche-4

Evidence ID

t4-056

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json