FA-58801 / Loan amortization schedules / Open access
Credit line average daily balance: minimum payment cap · case 01
The minimum payment due exceeds the total owed on small balances.
ROOT CAUSE
The minimum is not capped at the amount owed.
VERIFIED REPAIR
Cap the minimum at the balance plus interest.
Unsuccessful approach: Capping at the balance without interest leaves the cycle interest unpaid.
Case contract
x = {'rate_bp', 'basis', 'start_balance', 'cycle_days', 'events': [[day 1..cycle_days, signed amount]], 'min_bp', 'min_floor'}. Events take effect at the start of their day. Each day adds max(balance, 0) to the accumulator; interest = round_half_up(acc*bp/(10000*basis)) once per cycle. owed = end balance + interest. Minimum = 0 if owed <= 0 else min(owed, max(min_floor, interest + round_half_up(max(end balance, 0)*min_bp/10000))). Return {'interest', 'balance': owed, 'minimum', 'adb': acc // cycle_days}.
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)
bal = x['start_balance']
ev = sorted(x['events'])
i = 0
acc = 0
for day in range(1, x['cycle_days'] + 1):
while i < len(ev) and ev[i][0] == day:
bal += ev[i][1]
i += 1
acc += max(bal, 0)
interest = rnd(acc * x['rate_bp'], 10000 * x['basis'])
owed = bal + interest
if owed <= 0:
minimum = 0
else:
minimum = (max(x['min_floor'], interest + rnd(max(bal, 0) * x['min_bp'], 10000)))
return {'interest': interest, 'balance': owed, 'minimum': minimum, 'adb': acc // x['cycle_days']}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: minimum payment cap', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 30, 'events': [[12, 5000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 22, 'balance': 5022, 'minimum': 5022, 'adb': 3166}], ['control 1', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 31, 'events': [[4, 5000], [24, -20000], [10, 10000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 5129, 'balance': 1000129, 'minimum': 15079, 'adb': 1006451}], ['control 2', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[3, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 1447, 'balance': 151447, 'minimum': 10000, 'adb': 146666}], ['control 3', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 30, 'events': [[6, -80000], [30, -80000], [3, 10000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 10, 'balance': -149990, 'minimum': 0, 'adb': 1000}], ['control 4', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [], 'min_bp': 150, 'min_floor': 2500}, {'interest': 0, 'balance': 0, 'minimum': 0, 'adb': 0}], ['control 5', {'rate_bp': 850, 'basis': 365, 'start_balance': 30000, 'cycle_days': 28, 'events': [[27, 10000], [8, 50000], [10, -80000], [12, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 289, 'balance': 60289, 'minimum': 10000, 'adb': 44285}], ['control 6', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[9, 10000], [16, 10000], [22, -80000], [9, 10000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 105, 'balance': -49895, 'minimum': 0, 'adb': 11428}]], [['regression: minimum payment cap', {'rate_bp': 1200, 'basis': 365, 'start_balance': 30000, 'cycle_days': 31, 'events': [[30, -80000], [4, 50000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 713, 'balance': 713, 'minimum': 713, 'adb': 70000}], ['control 1', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 28, 'events': [[1, 50000], [6, 5000], [24, 10000], [18, -80000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 1146, 'balance': 86146, 'minimum': 2500, 'adb': 124464}], ['control 2', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 31, 'events': [[25, 10000], [7, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 5313, 'balance': 1065313, 'minimum': 15913, 'adb': 1042580}], ['control 3', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 30, 'events': [[25, 10000], [30, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 12, 'balance': -9988, 'minimum': 0, 'adb': 1666}], ['control 4', {'rate_bp': 1200, 'basis': 365, 'start_balance': 30000, 'cycle_days': 28, 'events': [[18, 10000], [3, -80000], [4, 5000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 20, 'balance': -34980, 'minimum': 0, 'adb': 2142}], ['control 5', {'rate_bp': 850, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[6, 50000], [1, -80000], [24, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 540, 'balance': 120540, 'minimum': 10000, 'adb': 74838}], ['control 6', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 28, 'events': [[24, 50000], [22, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 957, 'balance': 130957, 'minimum': 10000, 'adb': 103928}]], [['regression: minimum payment cap', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[3, 10000], [9, -80000], [6, 50000], [1, -80000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 61, 'balance': 61, 'minimum': 61, 'adb': 12333}], ['control 1', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[8, 5000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 4620, 'balance': 1009620, 'minimum': 14670, 'adb': 1003750}], ['control 2', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[3, 5000], [20, 5000], [25, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 44, 'balance': -9956, 'minimum': 0, 'adb': 4821}], ['control 3', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[20, 5000], [17, 10000], [26, -20000], [10, -20000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 440, 'balance': 75440, 'minimum': 2500, 'adb': 89166}], ['control 4', {'rate_bp': 850, 'basis': 365, 'start_balance': 30000, 'cycle_days': 30, 'events': [[22, -80000], [1, -80000], [8, -20000], [6, -80000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 0, 'balance': -230000, 'minimum': 0, 'adb': 0}], ['control 5', {'rate_bp': 1200, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 30, 'events': [[29, 5000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 9866, 'balance': 1014866, 'minimum': 24941, 'adb': 1000333}], ['control 6', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[5, -80000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 0, 'balance': -80000, 'minimum': 0, 'adb': 0}]], [['regression: minimum payment cap', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[22, -80000], [2, -20000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 279, 'balance': 279, 'minimum': 279, 'adb': 56666}], ['control 1', {'rate_bp': 850, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[20, 50000], [29, -80000], [30, -80000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 773, 'balance': -9227, 'minimum': 0, 'adb': 110666}], ['control 2', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[23, 50000], [7, 10000], [8, 10000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 4723, 'balance': 1074723, 'minimum': 20773, 'adb': 1026071}], ['control 3', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[22, 5000], [2, 50000], [3, -80000], [3, 10000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 431, 'balance': 85431, 'minimum': 2500, 'adb': 84516}], ['control 4', {'rate_bp': 600, 'basis': 365, 'start_balance': 30000, 'cycle_days': 28, 'events': [], 'min_bp': 150, 'min_floor': 2500}, {'interest': 138, 'balance': 30138, 'minimum': 2500, 'adb': 30000}], ['control 5', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[6, -20000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 4527, 'balance': 984527, 'minimum': 19227, 'adb': 983571}], ['control 6', {'rate_bp': 1200, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 31, 'events': [], 'min_bp': 100, 'min_floor': 10000}, {'interest': 10192, 'balance': 1010192, 'minimum': 20192, 'adb': 1000000}]], [['regression: minimum payment cap', {'rate_bp': 1200, 'basis': 365, 'start_balance': 30000, 'cycle_days': 31, 'events': [[26, -20000], [20, -20000], [31, 10000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 207, 'balance': 207, 'minimum': 207, 'adb': 20322}], ['control 1', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[21, 10000], [25, -80000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 4563, 'balance': 934563, 'minimum': 13863, 'adb': 991428}], ['control 2', {'rate_bp': 600, 'basis': 365, 'start_balance': 0, 'cycle_days': 31, 'events': [[15, 50000], [8, -80000], [21, 5000], [31, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 0, 'balance': -45000, 'minimum': 0, 'adb': 0}], ['control 3', {'rate_bp': 1200, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 30, 'events': [[28, 50000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 9912, 'balance': 1059912, 'minimum': 25662, 'adb': 1005000}], ['control 4', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[5, -80000], [22, 5000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 0, 'balance': -75000, 'minimum': 0, 'adb': 0}], ['control 5', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[31, -20000], [27, -20000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 980, 'balance': 60980, 'minimum': 2500, 'adb': 96129}], ['control 6', {'rate_bp': 850, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[15, 10000], [15, -80000], [4, 10000], [10, -20000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 408, 'balance': 20408, 'minimum': 2500, 'adb': 56451}]]]
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: minimum payment cap | {'adb': 3166, 'balance': 5022, 'interest': 22, 'minimum': 10000} | {'adb': 3166, 'balance': 5022, 'interest': 22, 'minimum': 5022} | Failed |
| control 1 | {'adb': 1006451, 'balance': 1000129, 'interest': 5129, 'minimum': 15079} | {'adb': 1006451, 'balance': 1000129, 'interest': 5129, 'minimum': 15079} | Passed |
| control 2 | {'adb': 146666, 'balance': 151447, 'interest': 1447, 'minimum': 10000} | {'adb': 146666, 'balance': 151447, 'interest': 1447, 'minimum': 10000} | Passed |
| control 3 | {'adb': 1000, 'balance': -149990, 'interest': 10, 'minimum': 0} | {'adb': 1000, 'balance': -149990, 'interest': 10, 'minimum': 0} | Passed |
| control 4 | {'adb': 0, 'balance': 0, 'interest': 0, 'minimum': 0} | {'adb': 0, 'balance': 0, 'interest': 0, 'minimum': 0} | Passed |
| control 5 | {'adb': 44285, 'balance': 60289, 'interest': 289, 'minimum': 10000} | {'adb': 44285, 'balance': 60289, 'interest': 289, 'minimum': 10000} | Passed |
| control 6 | {'adb': 11428, 'balance': -49895, 'interest': 105, 'minimum': 0} | {'adb': 11428, 'balance': -49895, 'interest': 105, 'minimum': 0} | Passed |
SHA-256 / 2e44e5d6097ff3b1f236a40cd95bf81b48cb00e82c76fc795b7e41fe79b2c1af
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)
bal = x['start_balance']
ev = sorted(x['events'])
i = 0
acc = 0
for day in range(1, x['cycle_days'] + 1):
while i < len(ev) and ev[i][0] == day:
bal += ev[i][1]
i += 1
acc += max(bal, 0)
interest = rnd(acc * x['rate_bp'], 10000 * x['basis'])
owed = bal + interest
if owed <= 0:
minimum = 0
else:
minimum = min(bal, max(x['min_floor'], interest + rnd(max(bal, 0) * x['min_bp'], 10000)))
return {'interest': interest, 'balance': owed, 'minimum': minimum, 'adb': acc // x['cycle_days']}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: minimum payment cap', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 30, 'events': [[12, 5000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 22, 'balance': 5022, 'minimum': 5022, 'adb': 3166}], ['control 1', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 31, 'events': [[4, 5000], [24, -20000], [10, 10000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 5129, 'balance': 1000129, 'minimum': 15079, 'adb': 1006451}], ['control 2', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[3, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 1447, 'balance': 151447, 'minimum': 10000, 'adb': 146666}], ['control 3', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 30, 'events': [[6, -80000], [30, -80000], [3, 10000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 10, 'balance': -149990, 'minimum': 0, 'adb': 1000}], ['control 4', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [], 'min_bp': 150, 'min_floor': 2500}, {'interest': 0, 'balance': 0, 'minimum': 0, 'adb': 0}], ['control 5', {'rate_bp': 850, 'basis': 365, 'start_balance': 30000, 'cycle_days': 28, 'events': [[27, 10000], [8, 50000], [10, -80000], [12, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 289, 'balance': 60289, 'minimum': 10000, 'adb': 44285}], ['control 6', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[9, 10000], [16, 10000], [22, -80000], [9, 10000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 105, 'balance': -49895, 'minimum': 0, 'adb': 11428}]], [['regression: minimum payment cap', {'rate_bp': 1200, 'basis': 365, 'start_balance': 30000, 'cycle_days': 31, 'events': [[30, -80000], [4, 50000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 713, 'balance': 713, 'minimum': 713, 'adb': 70000}], ['control 1', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 28, 'events': [[1, 50000], [6, 5000], [24, 10000], [18, -80000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 1146, 'balance': 86146, 'minimum': 2500, 'adb': 124464}], ['control 2', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 31, 'events': [[25, 10000], [7, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 5313, 'balance': 1065313, 'minimum': 15913, 'adb': 1042580}], ['control 3', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 30, 'events': [[25, 10000], [30, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 12, 'balance': -9988, 'minimum': 0, 'adb': 1666}], ['control 4', {'rate_bp': 1200, 'basis': 365, 'start_balance': 30000, 'cycle_days': 28, 'events': [[18, 10000], [3, -80000], [4, 5000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 20, 'balance': -34980, 'minimum': 0, 'adb': 2142}], ['control 5', {'rate_bp': 850, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[6, 50000], [1, -80000], [24, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 540, 'balance': 120540, 'minimum': 10000, 'adb': 74838}], ['control 6', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 28, 'events': [[24, 50000], [22, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 957, 'balance': 130957, 'minimum': 10000, 'adb': 103928}]], [['regression: minimum payment cap', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[3, 10000], [9, -80000], [6, 50000], [1, -80000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 61, 'balance': 61, 'minimum': 61, 'adb': 12333}], ['control 1', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[8, 5000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 4620, 'balance': 1009620, 'minimum': 14670, 'adb': 1003750}], ['control 2', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[3, 5000], [20, 5000], [25, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 44, 'balance': -9956, 'minimum': 0, 'adb': 4821}], ['control 3', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[20, 5000], [17, 10000], [26, -20000], [10, -20000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 440, 'balance': 75440, 'minimum': 2500, 'adb': 89166}], ['control 4', {'rate_bp': 850, 'basis': 365, 'start_balance': 30000, 'cycle_days': 30, 'events': [[22, -80000], [1, -80000], [8, -20000], [6, -80000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 0, 'balance': -230000, 'minimum': 0, 'adb': 0}], ['control 5', {'rate_bp': 1200, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 30, 'events': [[29, 5000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 9866, 'balance': 1014866, 'minimum': 24941, 'adb': 1000333}], ['control 6', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[5, -80000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 0, 'balance': -80000, 'minimum': 0, 'adb': 0}]], [['regression: minimum payment cap', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[22, -80000], [2, -20000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 279, 'balance': 279, 'minimum': 279, 'adb': 56666}], ['control 1', {'rate_bp': 850, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[20, 50000], [29, -80000], [30, -80000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 773, 'balance': -9227, 'minimum': 0, 'adb': 110666}], ['control 2', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[23, 50000], [7, 10000], [8, 10000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 4723, 'balance': 1074723, 'minimum': 20773, 'adb': 1026071}], ['control 3', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[22, 5000], [2, 50000], [3, -80000], [3, 10000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 431, 'balance': 85431, 'minimum': 2500, 'adb': 84516}], ['control 4', {'rate_bp': 600, 'basis': 365, 'start_balance': 30000, 'cycle_days': 28, 'events': [], 'min_bp': 150, 'min_floor': 2500}, {'interest': 138, 'balance': 30138, 'minimum': 2500, 'adb': 30000}], ['control 5', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[6, -20000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 4527, 'balance': 984527, 'minimum': 19227, 'adb': 983571}], ['control 6', {'rate_bp': 1200, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 31, 'events': [], 'min_bp': 100, 'min_floor': 10000}, {'interest': 10192, 'balance': 1010192, 'minimum': 20192, 'adb': 1000000}]], [['regression: minimum payment cap', {'rate_bp': 1200, 'basis': 365, 'start_balance': 30000, 'cycle_days': 31, 'events': [[26, -20000], [20, -20000], [31, 10000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 207, 'balance': 207, 'minimum': 207, 'adb': 20322}], ['control 1', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[21, 10000], [25, -80000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 4563, 'balance': 934563, 'minimum': 13863, 'adb': 991428}], ['control 2', {'rate_bp': 600, 'basis': 365, 'start_balance': 0, 'cycle_days': 31, 'events': [[15, 50000], [8, -80000], [21, 5000], [31, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 0, 'balance': -45000, 'minimum': 0, 'adb': 0}], ['control 3', {'rate_bp': 1200, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 30, 'events': [[28, 50000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 9912, 'balance': 1059912, 'minimum': 25662, 'adb': 1005000}], ['control 4', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[5, -80000], [22, 5000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 0, 'balance': -75000, 'minimum': 0, 'adb': 0}], ['control 5', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[31, -20000], [27, -20000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 980, 'balance': 60980, 'minimum': 2500, 'adb': 96129}], ['control 6', {'rate_bp': 850, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[15, 10000], [15, -80000], [4, 10000], [10, -20000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 408, 'balance': 20408, 'minimum': 2500, 'adb': 56451}]]]
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: minimum payment cap | {'adb': 3166, 'balance': 5022, 'interest': 22, 'minimum': 5000} | {'adb': 3166, 'balance': 5022, 'interest': 22, 'minimum': 5022} | Failed |
| control 1 | {'adb': 1006451, 'balance': 1000129, 'interest': 5129, 'minimum': 15079} | {'adb': 1006451, 'balance': 1000129, 'interest': 5129, 'minimum': 15079} | Passed |
| control 2 | {'adb': 146666, 'balance': 151447, 'interest': 1447, 'minimum': 10000} | {'adb': 146666, 'balance': 151447, 'interest': 1447, 'minimum': 10000} | Passed |
| control 3 | {'adb': 1000, 'balance': -149990, 'interest': 10, 'minimum': 0} | {'adb': 1000, 'balance': -149990, 'interest': 10, 'minimum': 0} | Passed |
| control 4 | {'adb': 0, 'balance': 0, 'interest': 0, 'minimum': 0} | {'adb': 0, 'balance': 0, 'interest': 0, 'minimum': 0} | Passed |
| control 5 | {'adb': 44285, 'balance': 60289, 'interest': 289, 'minimum': 10000} | {'adb': 44285, 'balance': 60289, 'interest': 289, 'minimum': 10000} | Passed |
| control 6 | {'adb': 11428, 'balance': -49895, 'interest': 105, 'minimum': 0} | {'adb': 11428, 'balance': -49895, 'interest': 105, 'minimum': 0} | Passed |
SHA-256 / c288c1264b84cc0704a97535dbfbf84d9233a22416343b874563a58ce3ddc53a
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)
bal = x['start_balance']
ev = sorted(x['events'])
i = 0
acc = 0
for day in range(1, x['cycle_days'] + 1):
while i < len(ev) and ev[i][0] == day:
bal += ev[i][1]
i += 1
acc += max(bal, 0)
interest = rnd(acc * x['rate_bp'], 10000 * x['basis'])
owed = bal + interest
if owed <= 0:
minimum = 0
else:
minimum = min(owed, max(x['min_floor'], interest + rnd(max(bal, 0) * x['min_bp'], 10000)))
return {'interest': interest, 'balance': owed, 'minimum': minimum, 'adb': acc // x['cycle_days']}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: minimum payment cap', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 30, 'events': [[12, 5000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 22, 'balance': 5022, 'minimum': 5022, 'adb': 3166}], ['control 1', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 31, 'events': [[4, 5000], [24, -20000], [10, 10000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 5129, 'balance': 1000129, 'minimum': 15079, 'adb': 1006451}], ['control 2', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[3, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 1447, 'balance': 151447, 'minimum': 10000, 'adb': 146666}], ['control 3', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 30, 'events': [[6, -80000], [30, -80000], [3, 10000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 10, 'balance': -149990, 'minimum': 0, 'adb': 1000}], ['control 4', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [], 'min_bp': 150, 'min_floor': 2500}, {'interest': 0, 'balance': 0, 'minimum': 0, 'adb': 0}], ['control 5', {'rate_bp': 850, 'basis': 365, 'start_balance': 30000, 'cycle_days': 28, 'events': [[27, 10000], [8, 50000], [10, -80000], [12, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 289, 'balance': 60289, 'minimum': 10000, 'adb': 44285}], ['control 6', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[9, 10000], [16, 10000], [22, -80000], [9, 10000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 105, 'balance': -49895, 'minimum': 0, 'adb': 11428}]], [['regression: minimum payment cap', {'rate_bp': 1200, 'basis': 365, 'start_balance': 30000, 'cycle_days': 31, 'events': [[30, -80000], [4, 50000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 713, 'balance': 713, 'minimum': 713, 'adb': 70000}], ['control 1', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 28, 'events': [[1, 50000], [6, 5000], [24, 10000], [18, -80000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 1146, 'balance': 86146, 'minimum': 2500, 'adb': 124464}], ['control 2', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 31, 'events': [[25, 10000], [7, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 5313, 'balance': 1065313, 'minimum': 15913, 'adb': 1042580}], ['control 3', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 30, 'events': [[25, 10000], [30, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 12, 'balance': -9988, 'minimum': 0, 'adb': 1666}], ['control 4', {'rate_bp': 1200, 'basis': 365, 'start_balance': 30000, 'cycle_days': 28, 'events': [[18, 10000], [3, -80000], [4, 5000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 20, 'balance': -34980, 'minimum': 0, 'adb': 2142}], ['control 5', {'rate_bp': 850, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[6, 50000], [1, -80000], [24, 50000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 540, 'balance': 120540, 'minimum': 10000, 'adb': 74838}], ['control 6', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 28, 'events': [[24, 50000], [22, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 957, 'balance': 130957, 'minimum': 10000, 'adb': 103928}]], [['regression: minimum payment cap', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[3, 10000], [9, -80000], [6, 50000], [1, -80000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 61, 'balance': 61, 'minimum': 61, 'adb': 12333}], ['control 1', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[8, 5000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 4620, 'balance': 1009620, 'minimum': 14670, 'adb': 1003750}], ['control 2', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[3, 5000], [20, 5000], [25, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 44, 'balance': -9956, 'minimum': 0, 'adb': 4821}], ['control 3', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[20, 5000], [17, 10000], [26, -20000], [10, -20000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 440, 'balance': 75440, 'minimum': 2500, 'adb': 89166}], ['control 4', {'rate_bp': 850, 'basis': 365, 'start_balance': 30000, 'cycle_days': 30, 'events': [[22, -80000], [1, -80000], [8, -20000], [6, -80000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 0, 'balance': -230000, 'minimum': 0, 'adb': 0}], ['control 5', {'rate_bp': 1200, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 30, 'events': [[29, 5000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 9866, 'balance': 1014866, 'minimum': 24941, 'adb': 1000333}], ['control 6', {'rate_bp': 850, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[5, -80000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 0, 'balance': -80000, 'minimum': 0, 'adb': 0}]], [['regression: minimum payment cap', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[22, -80000], [2, -20000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 279, 'balance': 279, 'minimum': 279, 'adb': 56666}], ['control 1', {'rate_bp': 850, 'basis': 365, 'start_balance': 100000, 'cycle_days': 30, 'events': [[20, 50000], [29, -80000], [30, -80000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 773, 'balance': -9227, 'minimum': 0, 'adb': 110666}], ['control 2', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[23, 50000], [7, 10000], [8, 10000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 4723, 'balance': 1074723, 'minimum': 20773, 'adb': 1026071}], ['control 3', {'rate_bp': 600, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[22, 5000], [2, 50000], [3, -80000], [3, 10000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 431, 'balance': 85431, 'minimum': 2500, 'adb': 84516}], ['control 4', {'rate_bp': 600, 'basis': 365, 'start_balance': 30000, 'cycle_days': 28, 'events': [], 'min_bp': 150, 'min_floor': 2500}, {'interest': 138, 'balance': 30138, 'minimum': 2500, 'adb': 30000}], ['control 5', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[6, -20000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 4527, 'balance': 984527, 'minimum': 19227, 'adb': 983571}], ['control 6', {'rate_bp': 1200, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 31, 'events': [], 'min_bp': 100, 'min_floor': 10000}, {'interest': 10192, 'balance': 1010192, 'minimum': 20192, 'adb': 1000000}]], [['regression: minimum payment cap', {'rate_bp': 1200, 'basis': 365, 'start_balance': 30000, 'cycle_days': 31, 'events': [[26, -20000], [20, -20000], [31, 10000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 207, 'balance': 207, 'minimum': 207, 'adb': 20322}], ['control 1', {'rate_bp': 600, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 28, 'events': [[21, 10000], [25, -80000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 4563, 'balance': 934563, 'minimum': 13863, 'adb': 991428}], ['control 2', {'rate_bp': 600, 'basis': 365, 'start_balance': 0, 'cycle_days': 31, 'events': [[15, 50000], [8, -80000], [21, 5000], [31, -20000]], 'min_bp': 150, 'min_floor': 10000}, {'interest': 0, 'balance': -45000, 'minimum': 0, 'adb': 0}], ['control 3', {'rate_bp': 1200, 'basis': 365, 'start_balance': 1000000, 'cycle_days': 30, 'events': [[28, 50000]], 'min_bp': 150, 'min_floor': 2500}, {'interest': 9912, 'balance': 1059912, 'minimum': 25662, 'adb': 1005000}], ['control 4', {'rate_bp': 1200, 'basis': 365, 'start_balance': 0, 'cycle_days': 28, 'events': [[5, -80000], [22, 5000]], 'min_bp': 100, 'min_floor': 10000}, {'interest': 0, 'balance': -75000, 'minimum': 0, 'adb': 0}], ['control 5', {'rate_bp': 1200, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[31, -20000], [27, -20000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 980, 'balance': 60980, 'minimum': 2500, 'adb': 96129}], ['control 6', {'rate_bp': 850, 'basis': 365, 'start_balance': 100000, 'cycle_days': 31, 'events': [[15, 10000], [15, -80000], [4, 10000], [10, -20000]], 'min_bp': 100, 'min_floor': 2500}, {'interest': 408, 'balance': 20408, 'minimum': 2500, 'adb': 56451}]]]
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: minimum payment cap | {'adb': 3166, 'balance': 5022, 'interest': 22, 'minimum': 5022} | {'adb': 3166, 'balance': 5022, 'interest': 22, 'minimum': 5022} | Passed |
| control 1 | {'adb': 1006451, 'balance': 1000129, 'interest': 5129, 'minimum': 15079} | {'adb': 1006451, 'balance': 1000129, 'interest': 5129, 'minimum': 15079} | Passed |
| control 2 | {'adb': 146666, 'balance': 151447, 'interest': 1447, 'minimum': 10000} | {'adb': 146666, 'balance': 151447, 'interest': 1447, 'minimum': 10000} | Passed |
| control 3 | {'adb': 1000, 'balance': -149990, 'interest': 10, 'minimum': 0} | {'adb': 1000, 'balance': -149990, 'interest': 10, 'minimum': 0} | Passed |
| control 4 | {'adb': 0, 'balance': 0, 'interest': 0, 'minimum': 0} | {'adb': 0, 'balance': 0, 'interest': 0, 'minimum': 0} | Passed |
| control 5 | {'adb': 44285, 'balance': 60289, 'interest': 289, 'minimum': 10000} | {'adb': 44285, 'balance': 60289, 'interest': 289, 'minimum': 10000} | Passed |
| control 6 | {'adb': 11428, 'balance': -49895, 'interest': 105, 'minimum': 0} | {'adb': 11428, 'balance': -49895, 'interest': 105, 'minimum': 0} | Passed |
SHA-256 / 3961b05e27a6102c69d09f24cd92b8a4a07b27490169dc2189d26ad7d07b4c73
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 2026-09-29T14:46:30.177926+00:00.
Case digest / e9262916afc9021f1fdd569d1ddec6b63b9e0c571022b260231ba48d90d71fad