FA-58631 / Loan amortization schedules / Open access
Rule of 78s early payoff rebate: minimum rebate threshold · case 01
A rebate exactly at the minimum is suppressed.
ROOT CAUSE
The threshold comparison is inclusive.
VERIFIED REPAIR
Suppress rebates strictly below the minimum.
Unsuccessful approach: Testing the rebatable charge instead of the rebate keeps tiny rebates.
Case contract
x = {'term' n, 'paid' k, 'finance_charge', 'acq_fee' (fully earned up front), 'payment', 'min_rebate'}. Rebatable charge = finance_charge - acq_fee; remaining r = n - k; rebate = round_half_up(rebatable * r(r+1) / (n(n+1))), set to 0 when below min_rebate. Payoff = payment*r - rebate; earned = finance_charge - rebate. Return {'rebate', 'payoff', 'earned'}.
Why this case matters
Amortization engines drive borrower statements, payoff quotes and investor remittances; a misplaced rounding step, boundary or ordering rule compounds across hundreds of periods.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
def rnd(n, d):
q, r = divmod(n, d)
return q + (1 if 2 * r >= d else 0)
n = x['term']
k = x['paid']
fc = x['finance_charge'] - x['acq_fee']
rem = n - k
rebate = rnd(fc * rem * (rem + 1), n * (n + 1))
if rebate <= x['min_rebate']:
rebate = 0
remaining = x['payment'] * rem
return {'rebate': rebate, 'payoff': remaining - rebate, 'earned': x['finance_charge'] - rebate}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 100}, {'rebate': 100, 'payoff': 155456, 'earned': 0}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 36, 'paid': 35, 'finance_charge': 50000, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 25000, 'earned': 50000}], ['control 1', {'term': 36, 'paid': 35, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 180, 'payoff': 9820, 'earned': 119820}], ['control 2', {'term': 24, 'paid': 23, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 25000, 'earned': 100}], ['control 3', {'term': 24, 'paid': 12, 'finance_charge': 50000, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 100}, {'rebate': 13000, 'payoff': 287000, 'earned': 37000}], ['control 4', {'term': 12, 'paid': 3, 'finance_charge': 100, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 100}, {'rebate': 0, 'payoff': 38889, 'earned': 100}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 12, 'paid': 11, 'finance_charge': 7777, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 100}, {'rebate': 100, 'payoff': 4221, 'earned': 7677}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 12, 'paid': 1, 'finance_charge': 100, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 110000, 'earned': 100}], ['control 1', {'term': 36, 'paid': 3, 'finance_charge': 7777, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 500}, {'rebate': 4445, 'payoff': 325555, 'earned': 3332}], ['control 2', {'term': 24, 'paid': 1, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 500}, {'rebate': 110400, 'payoff': 464600, 'earned': 9600}], ['control 3', {'term': 24, 'paid': 24, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 0, 'earned': 120000}], ['control 4', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 500}, {'rebate': 0, 'payoff': 900000, 'earned': 100}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 12, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 119900, 'earned': 0}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 12, 'paid': 11, 'finance_charge': 7777, 'acq_fee': 2500, 'payment': 4321, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 4321, 'earned': 7777}], ['control 1', {'term': 6, 'paid': 5, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 25000, 'earned': 100}], ['control 2', {'term': 24, 'paid': 3, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 2000}, {'rebate': 92400, 'payoff': 117600, 'earned': 27600}], ['control 3', {'term': 12, 'paid': 3, 'finance_charge': 50000, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 2000}, {'rebate': 28846, 'payoff': 10043, 'earned': 21154}], ['control 4', {'term': 6, 'paid': 3, 'finance_charge': 7777, 'acq_fee': 7500, 'payment': 4321, 'min_rebate': 0}, {'rebate': 79, 'payoff': 12884, 'earned': 7698}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 36, 'paid': 35, 'finance_charge': 120000, 'acq_fee': 7500, 'payment': 10000, 'min_rebate': 500}, {'rebate': 0, 'payoff': 10000, 'earned': 120000}], ['control 1', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 500}, {'rebate': 0, 'payoff': 900000, 'earned': 100}], ['control 2', {'term': 12, 'paid': 12, 'finance_charge': 50000, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 0}, {'rebate': 0, 'payoff': 0, 'earned': 50000}], ['control 3', {'term': 12, 'paid': 0, 'finance_charge': 7777, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 2000}, {'rebate': 7777, 'payoff': 44075, 'earned': 0}], ['control 4', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 0}, {'rebate': 100, 'payoff': 359900, 'earned': 0}], ['control 5', {'term': 6, 'paid': 3, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 75000, 'earned': 100}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 899900, 'earned': 0}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 36, 'paid': 35, 'finance_charge': 50000, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 10000, 'earned': 50000}], ['control 1', {'term': 24, 'paid': 12, 'finance_charge': 120000, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 500}, {'rebate': 29250, 'payoff': 270750, 'earned': 90750}], ['control 2', {'term': 24, 'paid': 12, 'finance_charge': 100, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 500}, {'rebate': 0, 'payoff': 51852, 'earned': 100}], ['control 3', {'term': 36, 'paid': 0, 'finance_charge': 7777, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 900000, 'earned': 7777}], ['control 4', {'term': 6, 'paid': 5, 'finance_charge': 120000, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 100}, {'rebate': 5595, 'payoff': 4405, 'earned': 114405}]]]
for label, args, expected in fixtures[N-1]:
try:
actual = solve(args)
except Exception as exc:
actual = 'raised ' + type(exc).__name__
check(label, actual, expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: rebate exactly at minimum | {'earned': 7800, 'payoff': 10000, 'rebate': 0} | {'earned': 7700, 'payoff': 9900, 'rebate': 100} | Failed |
| regression: minimum rebate threshold | {'earned': 100, 'payoff': 155556, 'rebate': 0} | {'earned': 0, 'payoff': 155456, 'rebate': 100} | Failed |
| regression: minimum rebate threshold, partial-repair probe | {'earned': 50000, 'payoff': 25000, 'rebate': 0} | {'earned': 50000, 'payoff': 25000, 'rebate': 0} | Passed |
| control 1 | {'earned': 119820, 'payoff': 9820, 'rebate': 180} | {'earned': 119820, 'payoff': 9820, 'rebate': 180} | Passed |
| control 2 | {'earned': 100, 'payoff': 25000, 'rebate': 0} | {'earned': 100, 'payoff': 25000, 'rebate': 0} | Passed |
| control 3 | {'earned': 37000, 'payoff': 287000, 'rebate': 13000} | {'earned': 37000, 'payoff': 287000, 'rebate': 13000} | Passed |
| control 4 | {'earned': 100, 'payoff': 38889, 'rebate': 0} | {'earned': 100, 'payoff': 38889, 'rebate': 0} | Passed |
SHA-256 / 306b964612626748f0a287a07cdf5cc0b3db110eea8e829f6414b60dedea4e59
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
def rnd(n, d):
q, r = divmod(n, d)
return q + (1 if 2 * r >= d else 0)
n = x['term']
k = x['paid']
fc = x['finance_charge'] - x['acq_fee']
rem = n - k
rebate = rnd(fc * rem * (rem + 1), n * (n + 1))
if fc < x['min_rebate']:
rebate = 0
remaining = x['payment'] * rem
return {'rebate': rebate, 'payoff': remaining - rebate, 'earned': x['finance_charge'] - rebate}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 100}, {'rebate': 100, 'payoff': 155456, 'earned': 0}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 36, 'paid': 35, 'finance_charge': 50000, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 25000, 'earned': 50000}], ['control 1', {'term': 36, 'paid': 35, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 180, 'payoff': 9820, 'earned': 119820}], ['control 2', {'term': 24, 'paid': 23, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 25000, 'earned': 100}], ['control 3', {'term': 24, 'paid': 12, 'finance_charge': 50000, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 100}, {'rebate': 13000, 'payoff': 287000, 'earned': 37000}], ['control 4', {'term': 12, 'paid': 3, 'finance_charge': 100, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 100}, {'rebate': 0, 'payoff': 38889, 'earned': 100}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 12, 'paid': 11, 'finance_charge': 7777, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 100}, {'rebate': 100, 'payoff': 4221, 'earned': 7677}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 12, 'paid': 1, 'finance_charge': 100, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 110000, 'earned': 100}], ['control 1', {'term': 36, 'paid': 3, 'finance_charge': 7777, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 500}, {'rebate': 4445, 'payoff': 325555, 'earned': 3332}], ['control 2', {'term': 24, 'paid': 1, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 500}, {'rebate': 110400, 'payoff': 464600, 'earned': 9600}], ['control 3', {'term': 24, 'paid': 24, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 0, 'earned': 120000}], ['control 4', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 500}, {'rebate': 0, 'payoff': 900000, 'earned': 100}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 12, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 119900, 'earned': 0}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 12, 'paid': 11, 'finance_charge': 7777, 'acq_fee': 2500, 'payment': 4321, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 4321, 'earned': 7777}], ['control 1', {'term': 6, 'paid': 5, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 25000, 'earned': 100}], ['control 2', {'term': 24, 'paid': 3, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 2000}, {'rebate': 92400, 'payoff': 117600, 'earned': 27600}], ['control 3', {'term': 12, 'paid': 3, 'finance_charge': 50000, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 2000}, {'rebate': 28846, 'payoff': 10043, 'earned': 21154}], ['control 4', {'term': 6, 'paid': 3, 'finance_charge': 7777, 'acq_fee': 7500, 'payment': 4321, 'min_rebate': 0}, {'rebate': 79, 'payoff': 12884, 'earned': 7698}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 36, 'paid': 35, 'finance_charge': 120000, 'acq_fee': 7500, 'payment': 10000, 'min_rebate': 500}, {'rebate': 0, 'payoff': 10000, 'earned': 120000}], ['control 1', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 500}, {'rebate': 0, 'payoff': 900000, 'earned': 100}], ['control 2', {'term': 12, 'paid': 12, 'finance_charge': 50000, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 0}, {'rebate': 0, 'payoff': 0, 'earned': 50000}], ['control 3', {'term': 12, 'paid': 0, 'finance_charge': 7777, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 2000}, {'rebate': 7777, 'payoff': 44075, 'earned': 0}], ['control 4', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 0}, {'rebate': 100, 'payoff': 359900, 'earned': 0}], ['control 5', {'term': 6, 'paid': 3, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 75000, 'earned': 100}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 899900, 'earned': 0}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 36, 'paid': 35, 'finance_charge': 50000, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 10000, 'earned': 50000}], ['control 1', {'term': 24, 'paid': 12, 'finance_charge': 120000, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 500}, {'rebate': 29250, 'payoff': 270750, 'earned': 90750}], ['control 2', {'term': 24, 'paid': 12, 'finance_charge': 100, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 500}, {'rebate': 0, 'payoff': 51852, 'earned': 100}], ['control 3', {'term': 36, 'paid': 0, 'finance_charge': 7777, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 900000, 'earned': 7777}], ['control 4', {'term': 6, 'paid': 5, 'finance_charge': 120000, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 100}, {'rebate': 5595, 'payoff': 4405, 'earned': 114405}]]]
for label, args, expected in fixtures[N-1]:
try:
actual = solve(args)
except Exception as exc:
actual = 'raised ' + type(exc).__name__
check(label, actual, expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: rebate exactly at minimum | {'earned': 7700, 'payoff': 9900, 'rebate': 100} | {'earned': 7700, 'payoff': 9900, 'rebate': 100} | Passed |
| regression: minimum rebate threshold | {'earned': 0, 'payoff': 155456, 'rebate': 100} | {'earned': 0, 'payoff': 155456, 'rebate': 100} | Passed |
| regression: minimum rebate threshold, partial-repair probe | {'earned': 49936, 'payoff': 24936, 'rebate': 64} | {'earned': 50000, 'payoff': 25000, 'rebate': 0} | Failed |
| control 1 | {'earned': 119820, 'payoff': 9820, 'rebate': 180} | {'earned': 119820, 'payoff': 9820, 'rebate': 180} | Passed |
| control 2 | {'earned': 100, 'payoff': 25000, 'rebate': 0} | {'earned': 100, 'payoff': 25000, 'rebate': 0} | Passed |
| control 3 | {'earned': 37000, 'payoff': 287000, 'rebate': 13000} | {'earned': 37000, 'payoff': 287000, 'rebate': 13000} | Passed |
| control 4 | {'earned': 42, 'payoff': 38831, 'rebate': 58} | {'earned': 100, 'payoff': 38889, 'rebate': 0} | Failed |
SHA-256 / 0b588f20d54606a25f1c6d4985b54e614ad26fd4bc1a3c0c026526b7f5b0a403
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
def rnd(n, d):
q, r = divmod(n, d)
return q + (1 if 2 * r >= d else 0)
n = x['term']
k = x['paid']
fc = x['finance_charge'] - x['acq_fee']
rem = n - k
rebate = rnd(fc * rem * (rem + 1), n * (n + 1))
if rebate < x['min_rebate']:
rebate = 0
remaining = x['payment'] * rem
return {'rebate': rebate, 'payoff': remaining - rebate, 'earned': x['finance_charge'] - rebate}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 100}, {'rebate': 100, 'payoff': 155456, 'earned': 0}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 36, 'paid': 35, 'finance_charge': 50000, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 25000, 'earned': 50000}], ['control 1', {'term': 36, 'paid': 35, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 180, 'payoff': 9820, 'earned': 119820}], ['control 2', {'term': 24, 'paid': 23, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 25000, 'earned': 100}], ['control 3', {'term': 24, 'paid': 12, 'finance_charge': 50000, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 100}, {'rebate': 13000, 'payoff': 287000, 'earned': 37000}], ['control 4', {'term': 12, 'paid': 3, 'finance_charge': 100, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 100}, {'rebate': 0, 'payoff': 38889, 'earned': 100}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 12, 'paid': 11, 'finance_charge': 7777, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 100}, {'rebate': 100, 'payoff': 4221, 'earned': 7677}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 12, 'paid': 1, 'finance_charge': 100, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 110000, 'earned': 100}], ['control 1', {'term': 36, 'paid': 3, 'finance_charge': 7777, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 500}, {'rebate': 4445, 'payoff': 325555, 'earned': 3332}], ['control 2', {'term': 24, 'paid': 1, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 500}, {'rebate': 110400, 'payoff': 464600, 'earned': 9600}], ['control 3', {'term': 24, 'paid': 24, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 0, 'payoff': 0, 'earned': 120000}], ['control 4', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 500}, {'rebate': 0, 'payoff': 900000, 'earned': 100}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 12, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 119900, 'earned': 0}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 12, 'paid': 11, 'finance_charge': 7777, 'acq_fee': 2500, 'payment': 4321, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 4321, 'earned': 7777}], ['control 1', {'term': 6, 'paid': 5, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 25000, 'earned': 100}], ['control 2', {'term': 24, 'paid': 3, 'finance_charge': 120000, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 2000}, {'rebate': 92400, 'payoff': 117600, 'earned': 27600}], ['control 3', {'term': 12, 'paid': 3, 'finance_charge': 50000, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 2000}, {'rebate': 28846, 'payoff': 10043, 'earned': 21154}], ['control 4', {'term': 6, 'paid': 3, 'finance_charge': 7777, 'acq_fee': 7500, 'payment': 4321, 'min_rebate': 0}, {'rebate': 79, 'payoff': 12884, 'earned': 7698}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 36, 'paid': 35, 'finance_charge': 120000, 'acq_fee': 7500, 'payment': 10000, 'min_rebate': 500}, {'rebate': 0, 'payoff': 10000, 'earned': 120000}], ['control 1', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 500}, {'rebate': 0, 'payoff': 900000, 'earned': 100}], ['control 2', {'term': 12, 'paid': 12, 'finance_charge': 50000, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 0}, {'rebate': 0, 'payoff': 0, 'earned': 50000}], ['control 3', {'term': 12, 'paid': 0, 'finance_charge': 7777, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 2000}, {'rebate': 7777, 'payoff': 44075, 'earned': 0}], ['control 4', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 0}, {'rebate': 100, 'payoff': 359900, 'earned': 0}], ['control 5', {'term': 6, 'paid': 3, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 75000, 'earned': 100}]], [['regression: rebate exactly at minimum', {'term': 12, 'paid': 11, 'finance_charge': 7800, 'acq_fee': 0, 'payment': 10000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 9900, 'earned': 7700}], ['regression: minimum rebate threshold', {'term': 36, 'paid': 0, 'finance_charge': 100, 'acq_fee': 0, 'payment': 25000, 'min_rebate': 100}, {'rebate': 100, 'payoff': 899900, 'earned': 0}], ['regression: minimum rebate threshold, partial-repair probe', {'term': 36, 'paid': 35, 'finance_charge': 50000, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 10000, 'earned': 50000}], ['control 1', {'term': 24, 'paid': 12, 'finance_charge': 120000, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 500}, {'rebate': 29250, 'payoff': 270750, 'earned': 90750}], ['control 2', {'term': 24, 'paid': 12, 'finance_charge': 100, 'acq_fee': 0, 'payment': 4321, 'min_rebate': 500}, {'rebate': 0, 'payoff': 51852, 'earned': 100}], ['control 3', {'term': 36, 'paid': 0, 'finance_charge': 7777, 'acq_fee': 7500, 'payment': 25000, 'min_rebate': 2000}, {'rebate': 0, 'payoff': 900000, 'earned': 7777}], ['control 4', {'term': 6, 'paid': 5, 'finance_charge': 120000, 'acq_fee': 2500, 'payment': 10000, 'min_rebate': 100}, {'rebate': 5595, 'payoff': 4405, 'earned': 114405}]]]
for label, args, expected in fixtures[N-1]:
try:
actual = solve(args)
except Exception as exc:
actual = 'raised ' + type(exc).__name__
check(label, actual, expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| regression: rebate exactly at minimum | {'earned': 7700, 'payoff': 9900, 'rebate': 100} | {'earned': 7700, 'payoff': 9900, 'rebate': 100} | Passed |
| regression: minimum rebate threshold | {'earned': 0, 'payoff': 155456, 'rebate': 100} | {'earned': 0, 'payoff': 155456, 'rebate': 100} | Passed |
| regression: minimum rebate threshold, partial-repair probe | {'earned': 50000, 'payoff': 25000, 'rebate': 0} | {'earned': 50000, 'payoff': 25000, 'rebate': 0} | Passed |
| control 1 | {'earned': 119820, 'payoff': 9820, 'rebate': 180} | {'earned': 119820, 'payoff': 9820, 'rebate': 180} | Passed |
| control 2 | {'earned': 100, 'payoff': 25000, 'rebate': 0} | {'earned': 100, 'payoff': 25000, 'rebate': 0} | Passed |
| control 3 | {'earned': 37000, 'payoff': 287000, 'rebate': 13000} | {'earned': 37000, 'payoff': 287000, 'rebate': 13000} | Passed |
| control 4 | {'earned': 100, 'payoff': 38889, 'rebate': 0} | {'earned': 100, 'payoff': 38889, 'rebate': 0} | Passed |
SHA-256 / 48bcf449744e232dc7fa34aa099aaa1b30ff116b3d7edfc92d64d53584078070
Verification & scope
A deterministic bounded teaching model with stipulated toy lending rules stated in the contract; money is integer cents and rates are basis points; it makes no claim of conformance to any regulation, servicing standard or product. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:46:28.517035+00:00.
Case digest / 1567ae93bd711a90724e65b00378bf5ee2b351fbd1f25529f8f6ec57bd453a09