FA-58401 / Loan amortization schedules / Open access
Principal curtailment with recast or term shortening: extra principal cap · case 01
An oversized prepayment drives the balance negative and the loan never reports a payoff payment.
ROOT CAUSE
The extra principal is not capped at the remaining balance.
VERIFIED REPAIR
Cap the extra at the balance remaining after the scheduled payment.
Unsuccessful approach: Capping at balance plus interest still overshoots, since interest was already paid.
Case contract
x = {'principal', 'rate_bp', 'months', 'prepay': {'k': extra cents after payment k}, 'mode': 'shorten'|'recast'}. The level payment is the exact annuity rounded half-up. Each month: interest = round_half_up(balance*bp/120000); if balance + interest <= payment or it is month n, pay balance + interest and stop. Otherwise reduce the balance by payment - interest, then apply the extra (capped at the balance). In recast mode a nonzero extra that leaves a balance re-levels the payment over the n - k remaining months. An extra that clears the balance ends the loan with final payment = payment + extra. Return {'months_paid', 'total_interest', 'final_payment', 'payments': payment history}.
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
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
def rnd(n, d):
q, r = divmod(n, d)
return q + (1 if 2 * r >= d else 0)
def level(P, n):
if n <= 0 or P <= 0:
return 0
if bp == 0:
exact = Fraction(P, n)
else:
r = Fraction(bp, 120000)
exact = P * r / (1 - (1 + r) ** -n)
return math.floor(exact + Fraction(1, 2))
bp = x['rate_bp']
n = x['months']
bal = x['principal']
pay = level(bal, n)
history = [pay]
total = 0
k = 0
final = 0
while bal > 0 and k < n:
k += 1
interest = rnd(bal * bp, 120000)
total += interest
if bal + interest <= pay or k == n:
final = bal + interest
bal = 0
break
bal -= pay - interest
extra = x['prepay'].get(str(k), 0)
if extra:
bal -= extra
if x['mode'] == 'recast' and bal > 0:
pay = level(bal, n - k)
history.append(pay)
if bal == 0:
final = pay + extra
return {'months_paid': k, 'total_interest': total, 'final_payment': final, 'payments': history}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: extra principal cap', {'principal': 60000, 'rate_bp': 0, 'months': 36, 'prepay': {'21': 5000, '12': 200000, '35': 2000000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 41663, 'payments': [1667]}], ['regression: extra principal cap, partial-repair probe', {'principal': 60000, 'rate_bp': 600, 'months': 12, 'prepay': {'8': 200000, '7': 20000}, 'mode': 'recast'}, {'months_paid': 8, 'total_interest': 1612, 'final_payment': 5464, 'payments': [5164, 1104]}], ['control 1', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'prepay': {'10': 1000, '6': 5000, '7': 5000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 18501, 'payments': [20833, 20000, 19000, 18501]}], ['control 2', {'principal': 60000, 'rate_bp': 1200, 'months': 24, 'prepay': {'16': 5000, '9': 1000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 7480, 'final_payment': 2100, 'payments': [2824, 2753, 2099]}], ['control 3', {'principal': 100000, 'rate_bp': 1200, 'months': 6, 'prepay': {'5': 5000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 3478, 'final_payment': 12203, 'payments': [17255, 12203]}], ['control 4', {'principal': 60000, 'rate_bp': 0, 'months': 12, 'prepay': {'9': 5000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 3334, 'payments': [5000, 3333]}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 32442, 'final_payment': 11778, 'payments': [11768]}]], [['regression: extra principal cap', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'prepay': {'19': 200000, '18': 20000, '24': 5000}, 'mode': 'recast'}, {'months_paid': 19, 'total_interest': 0, 'final_payment': 4994, 'payments': [4167, 832]}], ['regression: extra principal cap, partial-repair probe', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {'19': 20000, '1': 2000000, '3': 2000000}, 'mode': 'shorten'}, {'months_paid': 1, 'total_interest': 2500, 'final_payment': 252500, 'payments': [11768]}], ['control 1', {'principal': 250000, 'rate_bp': 0, 'months': 24, 'prepay': {'24': 200000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 0, 'final_payment': 10409, 'payments': [10417]}], ['control 2', {'principal': 250000, 'rate_bp': 0, 'months': 6, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 41665, 'payments': [41667]}], ['control 3', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'prepay': {'10': 5000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 12595, 'final_payment': 4326, 'payments': [4707, 4323]}], ['control 4', {'principal': 60000, 'rate_bp': 0, 'months': 12, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 5000, 'payments': [5000]}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 0, 'final_payment': 4159, 'payments': [4167]}]], [['regression: extra principal cap', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'prepay': {'12': 5000, '20': 20000, '4': 1000}, 'mode': 'shorten'}, {'months_paid': 20, 'total_interest': 11928, 'final_payment': 16495, 'payments': [4707]}], ['control 1', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'prepay': {'10': 1000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 3272, 'final_payment': 8101, 'payments': [8607, 8101]}], ['control 2', {'principal': 100000, 'rate_bp': 600, 'months': 6, 'prepay': {'5': 1000, '3': 20000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 1552, 'final_payment': 9220, 'payments': [16960, 10226, 9220]}], ['control 3', {'principal': 60000, 'rate_bp': 600, 'months': 24, 'prepay': {'15': 20000, '5': 1000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 3267, 'final_payment': 324, 'payments': [2659, 2604, 326]}], ['control 4', {'principal': 250000, 'rate_bp': 600, 'months': 36, 'prepay': {'10': 20000, '11': 1000}, 'mode': 'shorten'}, {'months_paid': 33, 'total_interest': 21026, 'final_payment': 6666, 'payments': [7605]}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 8337, 'payments': [8333]}], ['control 6', {'principal': 60000, 'rate_bp': 600, 'months': 6, 'prepay': {}, 'mode': 'shorten'}, {'months_paid': 6, 'total_interest': 1055, 'final_payment': 10175, 'payments': [10176]}]], [['regression: extra principal cap', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'prepay': {'7': 200000, '3': 5000}, 'mode': 'shorten'}, {'months_paid': 7, 'total_interest': 0, 'final_payment': 120002, 'payments': [20833]}], ['regression: extra principal cap, partial-repair probe', {'principal': 60000, 'rate_bp': 600, 'months': 36, 'prepay': {'24': 2000000, '33': 1000, '12': 2000000}, 'mode': 'shorten'}, {'months_paid': 12, 'total_interest': 3088, 'final_payment': 43013, 'payments': [1825]}], ['control 1', {'principal': 100000, 'rate_bp': 600, 'months': 36, 'prepay': {}, 'mode': 'shorten'}, {'months_paid': 36, 'total_interest': 9520, 'final_payment': 3050, 'payments': [3042]}], ['control 2', {'principal': 60000, 'rate_bp': 0, 'months': 24, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 0, 'final_payment': 2500, 'payments': [2500]}], ['control 3', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'prepay': {'1': 200000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 4349, 'final_payment': 2927, 'payments': [22212, 2921]}], ['control 4', {'principal': 60000, 'rate_bp': 600, 'months': 12, 'prepay': {'8': 5000}, 'mode': 'shorten'}, {'months_paid': 12, 'total_interest': 1867, 'final_payment': 63, 'payments': [5164]}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 6, 'prepay': {'1': 5000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 15665, 'payments': [16667, 15667]}]], [['regression: extra principal cap', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'prepay': {'8': 200000}, 'mode': 'shorten'}, {'months_paid': 8, 'total_interest': 7134, 'final_payment': 106515, 'payments': [21517]}], ['control 1', {'principal': 60000, 'rate_bp': 0, 'months': 6, 'prepay': {'4': 1000}, 'mode': 'shorten'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 9000, 'payments': [10000]}], ['control 2', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {}, 'mode': 'shorten'}, {'months_paid': 24, 'total_interest': 32442, 'final_payment': 11778, 'payments': [11768]}], ['control 3', {'principal': 100000, 'rate_bp': 0, 'months': 6, 'prepay': {'3': 1000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 16333, 'payments': [16667, 16333]}], ['control 4', {'principal': 60000, 'rate_bp': 0, 'months': 12, 'prepay': {'10': 5000}, 'mode': 'shorten'}, {'months_paid': 11, 'total_interest': 0, 'final_payment': 5000, 'payments': [5000]}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {'4': 1000, '9': 20000}, 'mode': 'shorten'}, {'months_paid': 22, 'total_interest': 29136, 'final_payment': 11008, 'payments': [11768]}], ['control 6', {'principal': 100000, 'rate_bp': 600, 'months': 36, 'prepay': {'22': 5000}, 'mode': 'shorten'}, {'months_paid': 35, 'total_interest': 9173, 'final_payment': 745, 'payments': [3042]}]]]
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: extra principal cap | {'final_payment': 0, 'months_paid': 12, 'payments': [1667], 'total_interest': 0} | {'final_payment': 41663, 'months_paid': 12, 'payments': [1667], 'total_interest': 0} | Failed |
| regression: extra principal cap, partial-repair probe | {'final_payment': 0, 'months_paid': 8, 'payments': [5164, 1104], 'total_interest': 1612} | {'final_payment': 5464, 'months_paid': 8, 'payments': [5164, 1104], 'total_interest': 1612} | Failed |
| control 1 | {'final_payment': 18501, 'months_paid': 12, 'payments': [20833, 20000, 19000, 18501], 'total_interest': 0} | {'final_payment': 18501, 'months_paid': 12, 'payments': [20833, 20000, 19000, 18501], 'total_interest': 0} | Passed |
| control 2 | {'final_payment': 2100, 'months_paid': 24, 'payments': [2824, 2753, 2099], 'total_interest': 7480} | {'final_payment': 2100, 'months_paid': 24, 'payments': [2824, 2753, 2099], 'total_interest': 7480} | Passed |
| control 3 | {'final_payment': 12203, 'months_paid': 6, 'payments': [17255, 12203], 'total_interest': 3478} | {'final_payment': 12203, 'months_paid': 6, 'payments': [17255, 12203], 'total_interest': 3478} | Passed |
| control 4 | {'final_payment': 3334, 'months_paid': 12, 'payments': [5000, 3333], 'total_interest': 0} | {'final_payment': 3334, 'months_paid': 12, 'payments': [5000, 3333], 'total_interest': 0} | Passed |
| control 5 | {'final_payment': 11778, 'months_paid': 24, 'payments': [11768], 'total_interest': 32442} | {'final_payment': 11778, 'months_paid': 24, 'payments': [11768], 'total_interest': 32442} | Passed |
SHA-256 / f1904d6a7a6a071f5d6e0e9220eb63b8828c54126577665e602f54a36ef4db8a
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
def rnd(n, d):
q, r = divmod(n, d)
return q + (1 if 2 * r >= d else 0)
def level(P, n):
if n <= 0 or P <= 0:
return 0
if bp == 0:
exact = Fraction(P, n)
else:
r = Fraction(bp, 120000)
exact = P * r / (1 - (1 + r) ** -n)
return math.floor(exact + Fraction(1, 2))
bp = x['rate_bp']
n = x['months']
bal = x['principal']
pay = level(bal, n)
history = [pay]
total = 0
k = 0
final = 0
while bal > 0 and k < n:
k += 1
interest = rnd(bal * bp, 120000)
total += interest
if bal + interest <= pay or k == n:
final = bal + interest
bal = 0
break
bal -= pay - interest
extra = min(x['prepay'].get(str(k), 0), bal + interest)
if extra:
bal -= extra
if x['mode'] == 'recast' and bal > 0:
pay = level(bal, n - k)
history.append(pay)
if bal == 0:
final = pay + extra
return {'months_paid': k, 'total_interest': total, 'final_payment': final, 'payments': history}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: extra principal cap', {'principal': 60000, 'rate_bp': 0, 'months': 36, 'prepay': {'21': 5000, '12': 200000, '35': 2000000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 41663, 'payments': [1667]}], ['regression: extra principal cap, partial-repair probe', {'principal': 60000, 'rate_bp': 600, 'months': 12, 'prepay': {'8': 200000, '7': 20000}, 'mode': 'recast'}, {'months_paid': 8, 'total_interest': 1612, 'final_payment': 5464, 'payments': [5164, 1104]}], ['control 1', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'prepay': {'10': 1000, '6': 5000, '7': 5000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 18501, 'payments': [20833, 20000, 19000, 18501]}], ['control 2', {'principal': 60000, 'rate_bp': 1200, 'months': 24, 'prepay': {'16': 5000, '9': 1000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 7480, 'final_payment': 2100, 'payments': [2824, 2753, 2099]}], ['control 3', {'principal': 100000, 'rate_bp': 1200, 'months': 6, 'prepay': {'5': 5000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 3478, 'final_payment': 12203, 'payments': [17255, 12203]}], ['control 4', {'principal': 60000, 'rate_bp': 0, 'months': 12, 'prepay': {'9': 5000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 3334, 'payments': [5000, 3333]}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 32442, 'final_payment': 11778, 'payments': [11768]}]], [['regression: extra principal cap', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'prepay': {'19': 200000, '18': 20000, '24': 5000}, 'mode': 'recast'}, {'months_paid': 19, 'total_interest': 0, 'final_payment': 4994, 'payments': [4167, 832]}], ['regression: extra principal cap, partial-repair probe', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {'19': 20000, '1': 2000000, '3': 2000000}, 'mode': 'shorten'}, {'months_paid': 1, 'total_interest': 2500, 'final_payment': 252500, 'payments': [11768]}], ['control 1', {'principal': 250000, 'rate_bp': 0, 'months': 24, 'prepay': {'24': 200000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 0, 'final_payment': 10409, 'payments': [10417]}], ['control 2', {'principal': 250000, 'rate_bp': 0, 'months': 6, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 41665, 'payments': [41667]}], ['control 3', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'prepay': {'10': 5000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 12595, 'final_payment': 4326, 'payments': [4707, 4323]}], ['control 4', {'principal': 60000, 'rate_bp': 0, 'months': 12, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 5000, 'payments': [5000]}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 0, 'final_payment': 4159, 'payments': [4167]}]], [['regression: extra principal cap', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'prepay': {'12': 5000, '20': 20000, '4': 1000}, 'mode': 'shorten'}, {'months_paid': 20, 'total_interest': 11928, 'final_payment': 16495, 'payments': [4707]}], ['control 1', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'prepay': {'10': 1000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 3272, 'final_payment': 8101, 'payments': [8607, 8101]}], ['control 2', {'principal': 100000, 'rate_bp': 600, 'months': 6, 'prepay': {'5': 1000, '3': 20000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 1552, 'final_payment': 9220, 'payments': [16960, 10226, 9220]}], ['control 3', {'principal': 60000, 'rate_bp': 600, 'months': 24, 'prepay': {'15': 20000, '5': 1000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 3267, 'final_payment': 324, 'payments': [2659, 2604, 326]}], ['control 4', {'principal': 250000, 'rate_bp': 600, 'months': 36, 'prepay': {'10': 20000, '11': 1000}, 'mode': 'shorten'}, {'months_paid': 33, 'total_interest': 21026, 'final_payment': 6666, 'payments': [7605]}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 8337, 'payments': [8333]}], ['control 6', {'principal': 60000, 'rate_bp': 600, 'months': 6, 'prepay': {}, 'mode': 'shorten'}, {'months_paid': 6, 'total_interest': 1055, 'final_payment': 10175, 'payments': [10176]}]], [['regression: extra principal cap', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'prepay': {'7': 200000, '3': 5000}, 'mode': 'shorten'}, {'months_paid': 7, 'total_interest': 0, 'final_payment': 120002, 'payments': [20833]}], ['regression: extra principal cap, partial-repair probe', {'principal': 60000, 'rate_bp': 600, 'months': 36, 'prepay': {'24': 2000000, '33': 1000, '12': 2000000}, 'mode': 'shorten'}, {'months_paid': 12, 'total_interest': 3088, 'final_payment': 43013, 'payments': [1825]}], ['control 1', {'principal': 100000, 'rate_bp': 600, 'months': 36, 'prepay': {}, 'mode': 'shorten'}, {'months_paid': 36, 'total_interest': 9520, 'final_payment': 3050, 'payments': [3042]}], ['control 2', {'principal': 60000, 'rate_bp': 0, 'months': 24, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 0, 'final_payment': 2500, 'payments': [2500]}], ['control 3', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'prepay': {'1': 200000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 4349, 'final_payment': 2927, 'payments': [22212, 2921]}], ['control 4', {'principal': 60000, 'rate_bp': 600, 'months': 12, 'prepay': {'8': 5000}, 'mode': 'shorten'}, {'months_paid': 12, 'total_interest': 1867, 'final_payment': 63, 'payments': [5164]}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 6, 'prepay': {'1': 5000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 15665, 'payments': [16667, 15667]}]], [['regression: extra principal cap', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'prepay': {'8': 200000}, 'mode': 'shorten'}, {'months_paid': 8, 'total_interest': 7134, 'final_payment': 106515, 'payments': [21517]}], ['control 1', {'principal': 60000, 'rate_bp': 0, 'months': 6, 'prepay': {'4': 1000}, 'mode': 'shorten'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 9000, 'payments': [10000]}], ['control 2', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {}, 'mode': 'shorten'}, {'months_paid': 24, 'total_interest': 32442, 'final_payment': 11778, 'payments': [11768]}], ['control 3', {'principal': 100000, 'rate_bp': 0, 'months': 6, 'prepay': {'3': 1000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 16333, 'payments': [16667, 16333]}], ['control 4', {'principal': 60000, 'rate_bp': 0, 'months': 12, 'prepay': {'10': 5000}, 'mode': 'shorten'}, {'months_paid': 11, 'total_interest': 0, 'final_payment': 5000, 'payments': [5000]}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {'4': 1000, '9': 20000}, 'mode': 'shorten'}, {'months_paid': 22, 'total_interest': 29136, 'final_payment': 11008, 'payments': [11768]}], ['control 6', {'principal': 100000, 'rate_bp': 600, 'months': 36, 'prepay': {'22': 5000}, 'mode': 'shorten'}, {'months_paid': 35, 'total_interest': 9173, 'final_payment': 745, 'payments': [3042]}]]]
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: extra principal cap | {'final_payment': 41663, 'months_paid': 12, 'payments': [1667], 'total_interest': 0} | {'final_payment': 41663, 'months_paid': 12, 'payments': [1667], 'total_interest': 0} | Passed |
| regression: extra principal cap, partial-repair probe | {'final_payment': 0, 'months_paid': 8, 'payments': [5164, 1104], 'total_interest': 1612} | {'final_payment': 5464, 'months_paid': 8, 'payments': [5164, 1104], 'total_interest': 1612} | Failed |
| control 1 | {'final_payment': 18501, 'months_paid': 12, 'payments': [20833, 20000, 19000, 18501], 'total_interest': 0} | {'final_payment': 18501, 'months_paid': 12, 'payments': [20833, 20000, 19000, 18501], 'total_interest': 0} | Passed |
| control 2 | {'final_payment': 2100, 'months_paid': 24, 'payments': [2824, 2753, 2099], 'total_interest': 7480} | {'final_payment': 2100, 'months_paid': 24, 'payments': [2824, 2753, 2099], 'total_interest': 7480} | Passed |
| control 3 | {'final_payment': 12203, 'months_paid': 6, 'payments': [17255, 12203], 'total_interest': 3478} | {'final_payment': 12203, 'months_paid': 6, 'payments': [17255, 12203], 'total_interest': 3478} | Passed |
| control 4 | {'final_payment': 3334, 'months_paid': 12, 'payments': [5000, 3333], 'total_interest': 0} | {'final_payment': 3334, 'months_paid': 12, 'payments': [5000, 3333], 'total_interest': 0} | Passed |
| control 5 | {'final_payment': 11778, 'months_paid': 24, 'payments': [11768], 'total_interest': 32442} | {'final_payment': 11778, 'months_paid': 24, 'payments': [11768], 'total_interest': 32442} | Passed |
SHA-256 / dbabe261f99a59e9e60048d9d2854f61609050fd1708effcd9525a1bb3c2c9e5
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
def rnd(n, d):
q, r = divmod(n, d)
return q + (1 if 2 * r >= d else 0)
def level(P, n):
if n <= 0 or P <= 0:
return 0
if bp == 0:
exact = Fraction(P, n)
else:
r = Fraction(bp, 120000)
exact = P * r / (1 - (1 + r) ** -n)
return math.floor(exact + Fraction(1, 2))
bp = x['rate_bp']
n = x['months']
bal = x['principal']
pay = level(bal, n)
history = [pay]
total = 0
k = 0
final = 0
while bal > 0 and k < n:
k += 1
interest = rnd(bal * bp, 120000)
total += interest
if bal + interest <= pay or k == n:
final = bal + interest
bal = 0
break
bal -= pay - interest
extra = min(x['prepay'].get(str(k), 0), bal)
if extra:
bal -= extra
if x['mode'] == 'recast' and bal > 0:
pay = level(bal, n - k)
history.append(pay)
if bal == 0:
final = pay + extra
return {'months_paid': k, 'total_interest': total, 'final_payment': final, 'payments': history}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: extra principal cap', {'principal': 60000, 'rate_bp': 0, 'months': 36, 'prepay': {'21': 5000, '12': 200000, '35': 2000000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 41663, 'payments': [1667]}], ['regression: extra principal cap, partial-repair probe', {'principal': 60000, 'rate_bp': 600, 'months': 12, 'prepay': {'8': 200000, '7': 20000}, 'mode': 'recast'}, {'months_paid': 8, 'total_interest': 1612, 'final_payment': 5464, 'payments': [5164, 1104]}], ['control 1', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'prepay': {'10': 1000, '6': 5000, '7': 5000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 18501, 'payments': [20833, 20000, 19000, 18501]}], ['control 2', {'principal': 60000, 'rate_bp': 1200, 'months': 24, 'prepay': {'16': 5000, '9': 1000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 7480, 'final_payment': 2100, 'payments': [2824, 2753, 2099]}], ['control 3', {'principal': 100000, 'rate_bp': 1200, 'months': 6, 'prepay': {'5': 5000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 3478, 'final_payment': 12203, 'payments': [17255, 12203]}], ['control 4', {'principal': 60000, 'rate_bp': 0, 'months': 12, 'prepay': {'9': 5000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 3334, 'payments': [5000, 3333]}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 32442, 'final_payment': 11778, 'payments': [11768]}]], [['regression: extra principal cap', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'prepay': {'19': 200000, '18': 20000, '24': 5000}, 'mode': 'recast'}, {'months_paid': 19, 'total_interest': 0, 'final_payment': 4994, 'payments': [4167, 832]}], ['regression: extra principal cap, partial-repair probe', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {'19': 20000, '1': 2000000, '3': 2000000}, 'mode': 'shorten'}, {'months_paid': 1, 'total_interest': 2500, 'final_payment': 252500, 'payments': [11768]}], ['control 1', {'principal': 250000, 'rate_bp': 0, 'months': 24, 'prepay': {'24': 200000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 0, 'final_payment': 10409, 'payments': [10417]}], ['control 2', {'principal': 250000, 'rate_bp': 0, 'months': 6, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 41665, 'payments': [41667]}], ['control 3', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'prepay': {'10': 5000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 12595, 'final_payment': 4326, 'payments': [4707, 4323]}], ['control 4', {'principal': 60000, 'rate_bp': 0, 'months': 12, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 5000, 'payments': [5000]}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 0, 'final_payment': 4159, 'payments': [4167]}]], [['regression: extra principal cap', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'prepay': {'12': 5000, '20': 20000, '4': 1000}, 'mode': 'shorten'}, {'months_paid': 20, 'total_interest': 11928, 'final_payment': 16495, 'payments': [4707]}], ['control 1', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'prepay': {'10': 1000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 3272, 'final_payment': 8101, 'payments': [8607, 8101]}], ['control 2', {'principal': 100000, 'rate_bp': 600, 'months': 6, 'prepay': {'5': 1000, '3': 20000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 1552, 'final_payment': 9220, 'payments': [16960, 10226, 9220]}], ['control 3', {'principal': 60000, 'rate_bp': 600, 'months': 24, 'prepay': {'15': 20000, '5': 1000}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 3267, 'final_payment': 324, 'payments': [2659, 2604, 326]}], ['control 4', {'principal': 250000, 'rate_bp': 600, 'months': 36, 'prepay': {'10': 20000, '11': 1000}, 'mode': 'shorten'}, {'months_paid': 33, 'total_interest': 21026, 'final_payment': 6666, 'payments': [7605]}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 0, 'final_payment': 8337, 'payments': [8333]}], ['control 6', {'principal': 60000, 'rate_bp': 600, 'months': 6, 'prepay': {}, 'mode': 'shorten'}, {'months_paid': 6, 'total_interest': 1055, 'final_payment': 10175, 'payments': [10176]}]], [['regression: extra principal cap', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'prepay': {'7': 200000, '3': 5000}, 'mode': 'shorten'}, {'months_paid': 7, 'total_interest': 0, 'final_payment': 120002, 'payments': [20833]}], ['regression: extra principal cap, partial-repair probe', {'principal': 60000, 'rate_bp': 600, 'months': 36, 'prepay': {'24': 2000000, '33': 1000, '12': 2000000}, 'mode': 'shorten'}, {'months_paid': 12, 'total_interest': 3088, 'final_payment': 43013, 'payments': [1825]}], ['control 1', {'principal': 100000, 'rate_bp': 600, 'months': 36, 'prepay': {}, 'mode': 'shorten'}, {'months_paid': 36, 'total_interest': 9520, 'final_payment': 3050, 'payments': [3042]}], ['control 2', {'principal': 60000, 'rate_bp': 0, 'months': 24, 'prepay': {}, 'mode': 'recast'}, {'months_paid': 24, 'total_interest': 0, 'final_payment': 2500, 'payments': [2500]}], ['control 3', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'prepay': {'1': 200000}, 'mode': 'recast'}, {'months_paid': 12, 'total_interest': 4349, 'final_payment': 2927, 'payments': [22212, 2921]}], ['control 4', {'principal': 60000, 'rate_bp': 600, 'months': 12, 'prepay': {'8': 5000}, 'mode': 'shorten'}, {'months_paid': 12, 'total_interest': 1867, 'final_payment': 63, 'payments': [5164]}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 6, 'prepay': {'1': 5000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 15665, 'payments': [16667, 15667]}]], [['regression: extra principal cap', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'prepay': {'8': 200000}, 'mode': 'shorten'}, {'months_paid': 8, 'total_interest': 7134, 'final_payment': 106515, 'payments': [21517]}], ['control 1', {'principal': 60000, 'rate_bp': 0, 'months': 6, 'prepay': {'4': 1000}, 'mode': 'shorten'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 9000, 'payments': [10000]}], ['control 2', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {}, 'mode': 'shorten'}, {'months_paid': 24, 'total_interest': 32442, 'final_payment': 11778, 'payments': [11768]}], ['control 3', {'principal': 100000, 'rate_bp': 0, 'months': 6, 'prepay': {'3': 1000}, 'mode': 'recast'}, {'months_paid': 6, 'total_interest': 0, 'final_payment': 16333, 'payments': [16667, 16333]}], ['control 4', {'principal': 60000, 'rate_bp': 0, 'months': 12, 'prepay': {'10': 5000}, 'mode': 'shorten'}, {'months_paid': 11, 'total_interest': 0, 'final_payment': 5000, 'payments': [5000]}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'prepay': {'4': 1000, '9': 20000}, 'mode': 'shorten'}, {'months_paid': 22, 'total_interest': 29136, 'final_payment': 11008, 'payments': [11768]}], ['control 6', {'principal': 100000, 'rate_bp': 600, 'months': 36, 'prepay': {'22': 5000}, 'mode': 'shorten'}, {'months_paid': 35, 'total_interest': 9173, 'final_payment': 745, 'payments': [3042]}]]]
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: extra principal cap | {'final_payment': 41663, 'months_paid': 12, 'payments': [1667], 'total_interest': 0} | {'final_payment': 41663, 'months_paid': 12, 'payments': [1667], 'total_interest': 0} | Passed |
| regression: extra principal cap, partial-repair probe | {'final_payment': 5464, 'months_paid': 8, 'payments': [5164, 1104], 'total_interest': 1612} | {'final_payment': 5464, 'months_paid': 8, 'payments': [5164, 1104], 'total_interest': 1612} | Passed |
| control 1 | {'final_payment': 18501, 'months_paid': 12, 'payments': [20833, 20000, 19000, 18501], 'total_interest': 0} | {'final_payment': 18501, 'months_paid': 12, 'payments': [20833, 20000, 19000, 18501], 'total_interest': 0} | Passed |
| control 2 | {'final_payment': 2100, 'months_paid': 24, 'payments': [2824, 2753, 2099], 'total_interest': 7480} | {'final_payment': 2100, 'months_paid': 24, 'payments': [2824, 2753, 2099], 'total_interest': 7480} | Passed |
| control 3 | {'final_payment': 12203, 'months_paid': 6, 'payments': [17255, 12203], 'total_interest': 3478} | {'final_payment': 12203, 'months_paid': 6, 'payments': [17255, 12203], 'total_interest': 3478} | Passed |
| control 4 | {'final_payment': 3334, 'months_paid': 12, 'payments': [5000, 3333], 'total_interest': 0} | {'final_payment': 3334, 'months_paid': 12, 'payments': [5000, 3333], 'total_interest': 0} | Passed |
| control 5 | {'final_payment': 11778, 'months_paid': 24, 'payments': [11768], 'total_interest': 32442} | {'final_payment': 11778, 'months_paid': 24, 'payments': [11768], 'total_interest': 32442} | Passed |
SHA-256 / 63290b65df606561e59c0e54391a6ac9323d2081599155f74814be11c08c7760
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 2026-09-29T14:46:26.283872+00:00.
Case digest / 4ecd2856cbd6a9a2d839405432cc52847f3ed21f1ed8ba40bdb65453c4a334b7