{"abstract":"An oversized prepayment drives the balance negative and the loan never reports a payoff payment.","category":"Loan amortization schedules","checks":7,"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}.","evaluation_group":"w2-loan-amortization-schedules-curtailment-recast-or-shorten","failed_approach":"Capping at balance plus interest still overshoots, since interest was already paid.","family":"w2-loan-amortization-schedules-curtailment-recast-or-shorten-extra-principal-cap","id":"FA-58401","implementations":{"attempt":{"sha256":"dbabe261f99a59e9e60048d9d2854f61609050fd1708effcd9525a1bb3c2c9e5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    def rnd(n, d):\n        q, r = divmod(n, d)\n        return q + (1 if 2 * r >= d else 0)\n    def level(P, n):\n        if n <= 0 or P <= 0:\n            return 0\n        if bp == 0:\n            exact = Fraction(P, n)\n        else:\n            r = Fraction(bp, 120000)\n            exact = P * r / (1 - (1 + r) ** -n)\n        return math.floor(exact + Fraction(1, 2))\n    bp = x['rate_bp']\n    n = x['months']\n    bal = x['principal']\n    pay = level(bal, n)\n    history = [pay]\n    total = 0\n    k = 0\n    final = 0\n    while bal > 0 and k < n:\n        k += 1\n        interest = rnd(bal * bp, 120000)\n        total += interest\n        if bal + interest <= pay or k == n:\n            final = bal + interest\n            bal = 0\n            break\n        bal -= pay - interest\n        extra = min(x['prepay'].get(str(k), 0), bal + interest)\n        if extra:\n            bal -= extra\n            if x['mode'] == 'recast' and bal > 0:\n                pay = level(bal, n - k)\n                history.append(pay)\n            if bal == 0:\n                final = pay + extra\n    return {'months_paid': k, 'total_interest': total, 'final_payment': final, 'payments': history}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['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]}]]]\nfor label, args, expected in fixtures[N-1]:\n    try:\n        actual = solve(args)\n    except Exception as exc:\n        actual = 'raised ' + type(exc).__name__\n    check(label, actual, expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"f1904d6a7a6a071f5d6e0e9220eb63b8828c54126577665e602f54a36ef4db8a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    def rnd(n, d):\n        q, r = divmod(n, d)\n        return q + (1 if 2 * r >= d else 0)\n    def level(P, n):\n        if n <= 0 or P <= 0:\n            return 0\n        if bp == 0:\n            exact = Fraction(P, n)\n        else:\n            r = Fraction(bp, 120000)\n            exact = P * r / (1 - (1 + r) ** -n)\n        return math.floor(exact + Fraction(1, 2))\n    bp = x['rate_bp']\n    n = x['months']\n    bal = x['principal']\n    pay = level(bal, n)\n    history = [pay]\n    total = 0\n    k = 0\n    final = 0\n    while bal > 0 and k < n:\n        k += 1\n        interest = rnd(bal * bp, 120000)\n        total += interest\n        if bal + interest <= pay or k == n:\n            final = bal + interest\n            bal = 0\n            break\n        bal -= pay - interest\n        extra = x['prepay'].get(str(k), 0)\n        if extra:\n            bal -= extra\n            if x['mode'] == 'recast' and bal > 0:\n                pay = level(bal, n - k)\n                history.append(pay)\n            if bal == 0:\n                final = pay + extra\n    return {'months_paid': k, 'total_interest': total, 'final_payment': final, 'payments': history}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['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]}]]]\nfor label, args, expected in fixtures[N-1]:\n    try:\n        actual = solve(args)\n    except Exception as exc:\n        actual = 'raised ' + type(exc).__name__\n    check(label, actual, expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"fixed":{"sha256":"63290b65df606561e59c0e54391a6ac9323d2081599155f74814be11c08c7760","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    def rnd(n, d):\n        q, r = divmod(n, d)\n        return q + (1 if 2 * r >= d else 0)\n    def level(P, n):\n        if n <= 0 or P <= 0:\n            return 0\n        if bp == 0:\n            exact = Fraction(P, n)\n        else:\n            r = Fraction(bp, 120000)\n            exact = P * r / (1 - (1 + r) ** -n)\n        return math.floor(exact + Fraction(1, 2))\n    bp = x['rate_bp']\n    n = x['months']\n    bal = x['principal']\n    pay = level(bal, n)\n    history = [pay]\n    total = 0\n    k = 0\n    final = 0\n    while bal > 0 and k < n:\n        k += 1\n        interest = rnd(bal * bp, 120000)\n        total += interest\n        if bal + interest <= pay or k == n:\n            final = bal + interest\n            bal = 0\n            break\n        bal -= pay - interest\n        extra = min(x['prepay'].get(str(k), 0), bal)\n        if extra:\n            bal -= extra\n            if x['mode'] == 'recast' and bal > 0:\n                pay = level(bal, n - k)\n                history.append(pay)\n            if bal == 0:\n                final = pay + extra\n    return {'months_paid': k, 'total_interest': total, 'final_payment': final, 'payments': history}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['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]}]]]\nfor label, args, expected in fixtures[N-1]:\n    try:\n        actual = solve(args)\n    except Exception as exc:\n        actual = 'raised ' + type(exc).__name__\n    check(label, actual, expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-loan-amortization-schedules-curtailment-recast-or-shorten-extra-principal-cap","generated_at":"2026-09-29T14:46:26.283872+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Amortization engines drive borrower statements, payoff quotes and investor remittances; a misplaced rounding step, boundary or ordering rule compounds across hundreds of periods.","repair":"Cap the extra at the balance remaining after the scheduled payment.","root_cause":"The extra principal is not capped at the remaining balance.","sha256":"4ecd2856cbd6a9a2d839405432cc52847f3ed21f1ed8ba40bdb65453c4a334b7","title":"Principal curtailment with recast or term shortening: extra principal cap · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.457,"exit_code":1,"observations":[{"actual":{"final_payment":41663,"months_paid":12,"payments":[1667],"total_interest":0},"check":"regression: extra principal cap","expected":{"final_payment":41663,"months_paid":12,"payments":[1667],"total_interest":0},"passed":true},{"actual":{"final_payment":0,"months_paid":8,"payments":[5164,1104],"total_interest":1612},"check":"regression: extra principal cap, partial-repair probe","expected":{"final_payment":5464,"months_paid":8,"payments":[5164,1104],"total_interest":1612},"passed":false},{"actual":{"final_payment":18501,"months_paid":12,"payments":[20833,20000,19000,18501],"total_interest":0},"check":"control 1","expected":{"final_payment":18501,"months_paid":12,"payments":[20833,20000,19000,18501],"total_interest":0},"passed":true},{"actual":{"final_payment":2100,"months_paid":24,"payments":[2824,2753,2099],"total_interest":7480},"check":"control 2","expected":{"final_payment":2100,"months_paid":24,"payments":[2824,2753,2099],"total_interest":7480},"passed":true},{"actual":{"final_payment":12203,"months_paid":6,"payments":[17255,12203],"total_interest":3478},"check":"control 3","expected":{"final_payment":12203,"months_paid":6,"payments":[17255,12203],"total_interest":3478},"passed":true},{"actual":{"final_payment":3334,"months_paid":12,"payments":[5000,3333],"total_interest":0},"check":"control 4","expected":{"final_payment":3334,"months_paid":12,"payments":[5000,3333],"total_interest":0},"passed":true},{"actual":{"final_payment":11778,"months_paid":24,"payments":[11768],"total_interest":32442},"check":"control 5","expected":{"final_payment":11778,"months_paid":24,"payments":[11768],"total_interest":32442},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: extra principal cap\", \"actual\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 41663, \"payments\": [1667]}, \"expected\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 41663, \"payments\": [1667]}, \"passed\": true}, {\"check\": \"regression: extra principal cap, partial-repair probe\", \"actual\": {\"months_paid\": 8, \"total_interest\": 1612, \"final_payment\": 0, \"payments\": [5164, 1104]}, \"expected\": {\"months_paid\": 8, \"total_interest\": 1612, \"final_payment\": 5464, \"payments\": [5164, 1104]}, \"passed\": false}, {\"check\": \"control 1\", \"actual\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 18501, \"payments\": [20833, 20000, 19000, 18501]}, \"expected\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 18501, \"payments\": [20833, 20000, 19000, 18501]}, \"passed\": true}, {\"check\": \"control 2\", \"actual\": {\"months_paid\": 24, \"total_interest\": 7480, \"final_payment\": 2100, \"payments\": [2824, 2753, 2099]}, \"expected\": {\"months_paid\": 24, \"total_interest\": 7480, \"final_payment\": 2100, \"payments\": [2824, 2753, 2099]}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": {\"months_paid\": 6, \"total_interest\": 3478, \"final_payment\": 12203, \"payments\": [17255, 12203]}, \"expected\": {\"months_paid\": 6, \"total_interest\": 3478, \"final_payment\": 12203, \"payments\": [17255, 12203]}, \"passed\": true}, {\"check\": \"control 4\", \"actual\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 3334, \"payments\": [5000, 3333]}, \"expected\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 3334, \"payments\": [5000, 3333]}, \"passed\": true}, {\"check\": \"control 5\", \"actual\": {\"months_paid\": 24, \"total_interest\": 32442, \"final_payment\": 11778, \"payments\": [11768]}, \"expected\": {\"months_paid\": 24, \"total_interest\": 32442, \"final_payment\": 11778, \"payments\": [11768]}, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.82,"exit_code":1,"observations":[{"actual":{"final_payment":0,"months_paid":12,"payments":[1667],"total_interest":0},"check":"regression: extra principal cap","expected":{"final_payment":41663,"months_paid":12,"payments":[1667],"total_interest":0},"passed":false},{"actual":{"final_payment":0,"months_paid":8,"payments":[5164,1104],"total_interest":1612},"check":"regression: extra principal cap, partial-repair probe","expected":{"final_payment":5464,"months_paid":8,"payments":[5164,1104],"total_interest":1612},"passed":false},{"actual":{"final_payment":18501,"months_paid":12,"payments":[20833,20000,19000,18501],"total_interest":0},"check":"control 1","expected":{"final_payment":18501,"months_paid":12,"payments":[20833,20000,19000,18501],"total_interest":0},"passed":true},{"actual":{"final_payment":2100,"months_paid":24,"payments":[2824,2753,2099],"total_interest":7480},"check":"control 2","expected":{"final_payment":2100,"months_paid":24,"payments":[2824,2753,2099],"total_interest":7480},"passed":true},{"actual":{"final_payment":12203,"months_paid":6,"payments":[17255,12203],"total_interest":3478},"check":"control 3","expected":{"final_payment":12203,"months_paid":6,"payments":[17255,12203],"total_interest":3478},"passed":true},{"actual":{"final_payment":3334,"months_paid":12,"payments":[5000,3333],"total_interest":0},"check":"control 4","expected":{"final_payment":3334,"months_paid":12,"payments":[5000,3333],"total_interest":0},"passed":true},{"actual":{"final_payment":11778,"months_paid":24,"payments":[11768],"total_interest":32442},"check":"control 5","expected":{"final_payment":11778,"months_paid":24,"payments":[11768],"total_interest":32442},"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: extra principal cap\", \"actual\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 0, \"payments\": [1667]}, \"expected\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 41663, \"payments\": [1667]}, \"passed\": false}, {\"check\": \"regression: extra principal cap, partial-repair probe\", \"actual\": {\"months_paid\": 8, \"total_interest\": 1612, \"final_payment\": 0, \"payments\": [5164, 1104]}, \"expected\": {\"months_paid\": 8, \"total_interest\": 1612, \"final_payment\": 5464, \"payments\": [5164, 1104]}, \"passed\": false}, {\"check\": \"control 1\", \"actual\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 18501, \"payments\": [20833, 20000, 19000, 18501]}, \"expected\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 18501, \"payments\": [20833, 20000, 19000, 18501]}, \"passed\": true}, {\"check\": \"control 2\", \"actual\": {\"months_paid\": 24, \"total_interest\": 7480, \"final_payment\": 2100, \"payments\": [2824, 2753, 2099]}, \"expected\": {\"months_paid\": 24, \"total_interest\": 7480, \"final_payment\": 2100, \"payments\": [2824, 2753, 2099]}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": {\"months_paid\": 6, \"total_interest\": 3478, \"final_payment\": 12203, \"payments\": [17255, 12203]}, \"expected\": {\"months_paid\": 6, \"total_interest\": 3478, \"final_payment\": 12203, \"payments\": [17255, 12203]}, \"passed\": true}, {\"check\": \"control 4\", \"actual\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 3334, \"payments\": [5000, 3333]}, \"expected\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 3334, \"payments\": [5000, 3333]}, \"passed\": true}, {\"check\": \"control 5\", \"actual\": {\"months_paid\": 24, \"total_interest\": 32442, \"final_payment\": 11778, \"payments\": [11768]}, \"expected\": {\"months_paid\": 24, \"total_interest\": 32442, \"final_payment\": 11778, \"payments\": [11768]}, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":47.669,"exit_code":0,"observations":[{"actual":{"final_payment":41663,"months_paid":12,"payments":[1667],"total_interest":0},"check":"regression: extra principal cap","expected":{"final_payment":41663,"months_paid":12,"payments":[1667],"total_interest":0},"passed":true},{"actual":{"final_payment":5464,"months_paid":8,"payments":[5164,1104],"total_interest":1612},"check":"regression: extra principal cap, partial-repair probe","expected":{"final_payment":5464,"months_paid":8,"payments":[5164,1104],"total_interest":1612},"passed":true},{"actual":{"final_payment":18501,"months_paid":12,"payments":[20833,20000,19000,18501],"total_interest":0},"check":"control 1","expected":{"final_payment":18501,"months_paid":12,"payments":[20833,20000,19000,18501],"total_interest":0},"passed":true},{"actual":{"final_payment":2100,"months_paid":24,"payments":[2824,2753,2099],"total_interest":7480},"check":"control 2","expected":{"final_payment":2100,"months_paid":24,"payments":[2824,2753,2099],"total_interest":7480},"passed":true},{"actual":{"final_payment":12203,"months_paid":6,"payments":[17255,12203],"total_interest":3478},"check":"control 3","expected":{"final_payment":12203,"months_paid":6,"payments":[17255,12203],"total_interest":3478},"passed":true},{"actual":{"final_payment":3334,"months_paid":12,"payments":[5000,3333],"total_interest":0},"check":"control 4","expected":{"final_payment":3334,"months_paid":12,"payments":[5000,3333],"total_interest":0},"passed":true},{"actual":{"final_payment":11778,"months_paid":24,"payments":[11768],"total_interest":32442},"check":"control 5","expected":{"final_payment":11778,"months_paid":24,"payments":[11768],"total_interest":32442},"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: extra principal cap\", \"actual\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 41663, \"payments\": [1667]}, \"expected\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 41663, \"payments\": [1667]}, \"passed\": true}, {\"check\": \"regression: extra principal cap, partial-repair probe\", \"actual\": {\"months_paid\": 8, \"total_interest\": 1612, \"final_payment\": 5464, \"payments\": [5164, 1104]}, \"expected\": {\"months_paid\": 8, \"total_interest\": 1612, \"final_payment\": 5464, \"payments\": [5164, 1104]}, \"passed\": true}, {\"check\": \"control 1\", \"actual\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 18501, \"payments\": [20833, 20000, 19000, 18501]}, \"expected\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 18501, \"payments\": [20833, 20000, 19000, 18501]}, \"passed\": true}, {\"check\": \"control 2\", \"actual\": {\"months_paid\": 24, \"total_interest\": 7480, \"final_payment\": 2100, \"payments\": [2824, 2753, 2099]}, \"expected\": {\"months_paid\": 24, \"total_interest\": 7480, \"final_payment\": 2100, \"payments\": [2824, 2753, 2099]}, \"passed\": true}, {\"check\": \"control 3\", \"actual\": {\"months_paid\": 6, \"total_interest\": 3478, \"final_payment\": 12203, \"payments\": [17255, 12203]}, \"expected\": {\"months_paid\": 6, \"total_interest\": 3478, \"final_payment\": 12203, \"payments\": [17255, 12203]}, \"passed\": true}, {\"check\": \"control 4\", \"actual\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 3334, \"payments\": [5000, 3333]}, \"expected\": {\"months_paid\": 12, \"total_interest\": 0, \"final_payment\": 3334, \"payments\": [5000, 3333]}, \"passed\": true}, {\"check\": \"control 5\", \"actual\": {\"months_paid\": 24, \"total_interest\": 32442, \"final_payment\": 11778, \"payments\": [11768]}, \"expected\": {\"months_paid\": 24, \"total_interest\": 32442, \"final_payment\": 11778, \"payments\": [11768]}, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}