FA-58431 / Loan amortization schedules / Open access

Interest-only period with funding stub: amortization term · case 01

The amortizing payment is too small and a large final payment remains.

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ROOT CAUSE

The payment is leveled over the whole loan term including the interest-only months.

THE FAILURE

The payment is leveled over the whole loan term including the interest-only months.

Unsuccessful approach: Reducing principal by interest-only payments treats interest as if it repaid principal.

Case contract

x = {'principal', 'rate_bp', 'io_months' >= 1, 'amort_months' >= 1, 'fund_day' 1..30}. IO month m pays interest round_half_up(P*bp*days/(120000*30)) with days = 31 - fund_day for the first IO month and 30 otherwise. Then the level payment on the full principal over amort_months (exact annuity, half-up) amortizes with monthly interest round_half_up(balance*bp/120000); the last month pays balance + interest. Return {'io_bills': list of IO payments, 'payment', 'final_payment', 'total_interest'}.

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']
    P = x['principal']
    io_bills = []
    total_int = 0
    for m in range(x['io_months']):
        days = 31 - x['fund_day'] if m == 0 else 30
        interest = rnd(P * bp * days, 120000 * 30)
        io_bills.append(interest)
        total_int += interest
    pay = level(P, x['io_months'] + x['amort_months'])
    bal = P
    final = 0
    for k in range(1, x['amort_months'] + 1):
        interest = rnd(bal * bp, 120000)
        total_int += interest
        if k == x['amort_months']:
            final = bal + interest
        else:
            bal -= pay - interest
    return {'io_bills': io_bills, 'payment': pay, 'final_payment': final, 'total_interest': total_int}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: amortization term', {'principal': 3000000, 'rate_bp': 500, 'io_months': 3, 'amort_months': 60, 'fund_day': 1}, {'io_bills': [12500, 12500, 12500], 'payment': 56614, 'final_payment': 56596, 'total_interest': 434322}], ['sample 1', {'principal': 12345, 'rate_bp': 725, 'io_months': 12, 'amort_months': 12, 'fund_day': 15}, {'io_bills': [40, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75], 'payment': 1070, 'final_payment': 1065, 'total_interest': 1355}], ['sample 2', {'principal': 250000, 'rate_bp': 725, 'io_months': 3, 'amort_months': 12, 'fund_day': 29}, {'io_bills': [101, 1510, 1510], 'payment': 21661, 'final_payment': 21655, 'total_interest': 13047}], ['sample 3', {'principal': 250000, 'rate_bp': 1200, 'io_months': 3, 'amort_months': 24, 'fund_day': 29}, {'io_bills': [167, 2500, 2500], 'payment': 11768, 'final_payment': 11778, 'total_interest': 37609}], ['sample 4', {'principal': 3000000, 'rate_bp': 1200, 'io_months': 3, 'amort_months': 1, 'fund_day': 2}, {'io_bills': [29000, 30000, 30000], 'payment': 3030000, 'final_payment': 3030000, 'total_interest': 119000}], ['sample 5', {'principal': 12345, 'rate_bp': 0, 'io_months': 1, 'amort_months': 24, 'fund_day': 2}, {'io_bills': [0], 'payment': 514, 'final_payment': 523, 'total_interest': 0}], ['sample 6', {'principal': 12345, 'rate_bp': 500, 'io_months': 3, 'amort_months': 12, 'fund_day': 15}, {'io_bills': [27, 51, 51], 'payment': 1057, 'final_payment': 1054, 'total_interest': 465}]], [['regression: amortization term', {'principal': 12345, 'rate_bp': 0, 'io_months': 3, 'amort_months': 12, 'fund_day': 1}, {'io_bills': [0, 0, 0], 'payment': 1029, 'final_payment': 1026, 'total_interest': 0}], ['regression: amortization term, partial-repair probe', {'principal': 100000, 'rate_bp': 725, 'io_months': 2, 'amort_months': 60, 'fund_day': 1}, {'io_bills': [604, 604], 'payment': 1992, 'final_payment': 1987, 'total_interest': 20723}], ['sample 1', {'principal': 250000, 'rate_bp': 500, 'io_months': 2, 'amort_months': 60, 'fund_day': 30}, {'io_bills': [35, 1042], 'payment': 4718, 'final_payment': 4703, 'total_interest': 34142}], ['sample 2', {'principal': 3000000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 60, 'fund_day': 2}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 50000, 'final_payment': 50000, 'total_interest': 0}], ['sample 3', {'principal': 100000, 'rate_bp': 1200, 'io_months': 3, 'amort_months': 24, 'fund_day': 30}, {'io_bills': [33, 1000, 1000], 'payment': 4707, 'final_payment': 4718, 'total_interest': 15012}], ['sample 4', {'principal': 12345, 'rate_bp': 725, 'io_months': 3, 'amort_months': 60, 'fund_day': 15}, {'io_bills': [40, 75, 75], 'payment': 246, 'final_payment': 239, 'total_interest': 2598}], ['sample 5', {'principal': 3000000, 'rate_bp': 500, 'io_months': 3, 'amort_months': 12, 'fund_day': 1}, {'io_bills': [12500, 12500, 12500], 'payment': 256822, 'final_payment': 256827, 'total_interest': 119369}]], [['regression: amortization term', {'principal': 3000000, 'rate_bp': 500, 'io_months': 2, 'amort_months': 24, 'fund_day': 29}, {'io_bills': [833, 12500], 'payment': 131614, 'final_payment': 131618, 'total_interest': 172073}], ['sample 1', {'principal': 3000000, 'rate_bp': 500, 'io_months': 3, 'amort_months': 24, 'fund_day': 1}, {'io_bills': [12500, 12500, 12500], 'payment': 131614, 'final_payment': 131618, 'total_interest': 196240}], ['sample 2', {'principal': 12345, 'rate_bp': 500, 'io_months': 2, 'amort_months': 12, 'fund_day': 15}, {'io_bills': [27, 51], 'payment': 1057, 'final_payment': 1054, 'total_interest': 414}], ['sample 3', {'principal': 100000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 24, 'fund_day': 29}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 4167, 'final_payment': 4159, 'total_interest': 0}], ['sample 4', {'principal': 100000, 'rate_bp': 500, 'io_months': 12, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [222, 417, 417, 417, 417, 417, 417, 417, 417, 417, 417, 417], 'payment': 4387, 'final_payment': 4389, 'total_interest': 10099}], ['sample 5', {'principal': 100000, 'rate_bp': 500, 'io_months': 12, 'amort_months': 12, 'fund_day': 29}, {'io_bills': [28, 417, 417, 417, 417, 417, 417, 417, 417, 417, 417, 417], 'payment': 8561, 'final_payment': 8559, 'total_interest': 7345}], ['sample 6', {'principal': 12345, 'rate_bp': 0, 'io_months': 2, 'amort_months': 24, 'fund_day': 30}, {'io_bills': [0, 0], 'payment': 514, 'final_payment': 523, 'total_interest': 0}]], [['regression: amortization term', {'principal': 250000, 'rate_bp': 500, 'io_months': 12, 'amort_months': 60, 'fund_day': 15}, {'io_bills': [556, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1042], 'payment': 4718, 'final_payment': 4703, 'total_interest': 45083}], ['sample 1', {'principal': 100000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 60, 'fund_day': 29}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 1667, 'final_payment': 1647, 'total_interest': 0}], ['sample 2', {'principal': 250000, 'rate_bp': 0, 'io_months': 3, 'amort_months': 1, 'fund_day': 2}, {'io_bills': [0, 0, 0], 'payment': 250000, 'final_payment': 250000, 'total_interest': 0}], ['sample 3', {'principal': 250000, 'rate_bp': 1200, 'io_months': 12, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [1333, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500], 'payment': 11768, 'final_payment': 11778, 'total_interest': 61275}], ['sample 4', {'principal': 100000, 'rate_bp': 725, 'io_months': 12, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [322, 604, 604, 604, 604, 604, 604, 604, 604, 604, 604, 604], 'payment': 4489, 'final_payment': 4477, 'total_interest': 14690}], ['sample 5', {'principal': 12345, 'rate_bp': 1200, 'io_months': 2, 'amort_months': 24, 'fund_day': 30}, {'io_bills': [4, 123], 'payment': 581, 'final_payment': 584, 'total_interest': 1729}], ['sample 6', {'principal': 100000, 'rate_bp': 500, 'io_months': 1, 'amort_months': 12, 'fund_day': 30}, {'io_bills': [14], 'payment': 8561, 'final_payment': 8559, 'total_interest': 2744}]], [['regression: amortization term', {'principal': 12345, 'rate_bp': 725, 'io_months': 1, 'amort_months': 12, 'fund_day': 2}, {'io_bills': [72], 'payment': 1070, 'final_payment': 1065, 'total_interest': 562}], ['sample 1', {'principal': 3000000, 'rate_bp': 725, 'io_months': 1, 'amort_months': 60, 'fund_day': 29}, {'io_bills': [1208], 'payment': 59758, 'final_payment': 59764, 'total_interest': 586694}], ['sample 2', {'principal': 100000, 'rate_bp': 500, 'io_months': 3, 'amort_months': 60, 'fund_day': 2}, {'io_bills': [403, 417, 417], 'payment': 1887, 'final_payment': 1894, 'total_interest': 14464}], ['sample 3', {'principal': 250000, 'rate_bp': 725, 'io_months': 1, 'amort_months': 60, 'fund_day': 15}, {'io_bills': [806], 'payment': 4980, 'final_payment': 4967, 'total_interest': 49593}], ['sample 4', {'principal': 100000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 24, 'fund_day': 30}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 4167, 'final_payment': 4159, 'total_interest': 0}], ['sample 5', {'principal': 12345, 'rate_bp': 725, 'io_months': 2, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [40, 75], 'payment': 554, 'final_payment': 559, 'total_interest': 1071}], ['sample 6', {'principal': 3000000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 125000, 'final_payment': 125000, 'total_interest': 0}]]]
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: amortization term	`{'final_payment': 215601, 'io_bills': [12500, 12500, 12500], 'payment': 54241, 'total_interest': 453320}`	`{'final_payment': 56596, 'io_bills': [12500, 12500, 12500], 'payment': 56614, 'total_interest': 434322}`	Failed
sample 1	`{'final_payment': 6953, 'io_bills': [40, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75], 'payment': 554, 'total_interest': 1567}`	`{'final_payment': 1065, 'io_bills': [40, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75], 'payment': 1070, 'total_interest': 1355}`	Failed
sample 2	`{'final_payment': 69303, 'io_bills': [101, 1510, 1510], 'payment': 17484, 'total_interest': 14748}`	`{'final_payment': 21655, 'io_bills': [101, 1510, 1510], 'payment': 21661, 'total_interest': 13047}`	Failed
sample 3	`{'final_payment': 41828, 'io_bills': [167, 2500, 2500], 'payment': 10611, 'total_interest': 41048}`	`{'final_payment': 11778, 'io_bills': [167, 2500, 2500], 'payment': 11768, 'total_interest': 37609}`	Failed
sample 4	`{'final_payment': 3030000, 'io_bills': [29000, 30000, 30000], 'payment': 768843, 'total_interest': 119000}`	`{'final_payment': 3030000, 'io_bills': [29000, 30000, 30000], 'payment': 3030000, 'total_interest': 119000}`	Failed
sample 5	`{'final_payment': 983, 'io_bills': [0], 'payment': 494, 'total_interest': 0}`	`{'final_payment': 523, 'io_bills': [0], 'payment': 514, 'total_interest': 0}`	Failed
sample 6	`{'final_payment': 3377, 'io_bills': [27, 51, 51], 'payment': 851, 'total_interest': 522}`	`{'final_payment': 1054, 'io_bills': [27, 51, 51], 'payment': 1057, 'total_interest': 465}`	Failed

SHA-256 / 8185ecd6c7c76f0a0395ecb4d1c8e4d721516e53f7baaaa487f630d2332c9808

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']
    P = x['principal']
    io_bills = []
    total_int = 0
    for m in range(x['io_months']):
        days = 31 - x['fund_day'] if m == 0 else 30
        interest = rnd(P * bp * days, 120000 * 30)
        io_bills.append(interest)
        total_int += interest
    pay = level(P - sum(io_bills), x['amort_months'])
    bal = P
    final = 0
    for k in range(1, x['amort_months'] + 1):
        interest = rnd(bal * bp, 120000)
        total_int += interest
        if k == x['amort_months']:
            final = bal + interest
        else:
            bal -= pay - interest
    return {'io_bills': io_bills, 'payment': pay, 'final_payment': final, 'total_interest': total_int}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: amortization term', {'principal': 3000000, 'rate_bp': 500, 'io_months': 3, 'amort_months': 60, 'fund_day': 1}, {'io_bills': [12500, 12500, 12500], 'payment': 56614, 'final_payment': 56596, 'total_interest': 434322}], ['sample 1', {'principal': 12345, 'rate_bp': 725, 'io_months': 12, 'amort_months': 12, 'fund_day': 15}, {'io_bills': [40, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75], 'payment': 1070, 'final_payment': 1065, 'total_interest': 1355}], ['sample 2', {'principal': 250000, 'rate_bp': 725, 'io_months': 3, 'amort_months': 12, 'fund_day': 29}, {'io_bills': [101, 1510, 1510], 'payment': 21661, 'final_payment': 21655, 'total_interest': 13047}], ['sample 3', {'principal': 250000, 'rate_bp': 1200, 'io_months': 3, 'amort_months': 24, 'fund_day': 29}, {'io_bills': [167, 2500, 2500], 'payment': 11768, 'final_payment': 11778, 'total_interest': 37609}], ['sample 4', {'principal': 3000000, 'rate_bp': 1200, 'io_months': 3, 'amort_months': 1, 'fund_day': 2}, {'io_bills': [29000, 30000, 30000], 'payment': 3030000, 'final_payment': 3030000, 'total_interest': 119000}], ['sample 5', {'principal': 12345, 'rate_bp': 0, 'io_months': 1, 'amort_months': 24, 'fund_day': 2}, {'io_bills': [0], 'payment': 514, 'final_payment': 523, 'total_interest': 0}], ['sample 6', {'principal': 12345, 'rate_bp': 500, 'io_months': 3, 'amort_months': 12, 'fund_day': 15}, {'io_bills': [27, 51, 51], 'payment': 1057, 'final_payment': 1054, 'total_interest': 465}]], [['regression: amortization term', {'principal': 12345, 'rate_bp': 0, 'io_months': 3, 'amort_months': 12, 'fund_day': 1}, {'io_bills': [0, 0, 0], 'payment': 1029, 'final_payment': 1026, 'total_interest': 0}], ['regression: amortization term, partial-repair probe', {'principal': 100000, 'rate_bp': 725, 'io_months': 2, 'amort_months': 60, 'fund_day': 1}, {'io_bills': [604, 604], 'payment': 1992, 'final_payment': 1987, 'total_interest': 20723}], ['sample 1', {'principal': 250000, 'rate_bp': 500, 'io_months': 2, 'amort_months': 60, 'fund_day': 30}, {'io_bills': [35, 1042], 'payment': 4718, 'final_payment': 4703, 'total_interest': 34142}], ['sample 2', {'principal': 3000000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 60, 'fund_day': 2}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 50000, 'final_payment': 50000, 'total_interest': 0}], ['sample 3', {'principal': 100000, 'rate_bp': 1200, 'io_months': 3, 'amort_months': 24, 'fund_day': 30}, {'io_bills': [33, 1000, 1000], 'payment': 4707, 'final_payment': 4718, 'total_interest': 15012}], ['sample 4', {'principal': 12345, 'rate_bp': 725, 'io_months': 3, 'amort_months': 60, 'fund_day': 15}, {'io_bills': [40, 75, 75], 'payment': 246, 'final_payment': 239, 'total_interest': 2598}], ['sample 5', {'principal': 3000000, 'rate_bp': 500, 'io_months': 3, 'amort_months': 12, 'fund_day': 1}, {'io_bills': [12500, 12500, 12500], 'payment': 256822, 'final_payment': 256827, 'total_interest': 119369}]], [['regression: amortization term', {'principal': 3000000, 'rate_bp': 500, 'io_months': 2, 'amort_months': 24, 'fund_day': 29}, {'io_bills': [833, 12500], 'payment': 131614, 'final_payment': 131618, 'total_interest': 172073}], ['sample 1', {'principal': 3000000, 'rate_bp': 500, 'io_months': 3, 'amort_months': 24, 'fund_day': 1}, {'io_bills': [12500, 12500, 12500], 'payment': 131614, 'final_payment': 131618, 'total_interest': 196240}], ['sample 2', {'principal': 12345, 'rate_bp': 500, 'io_months': 2, 'amort_months': 12, 'fund_day': 15}, {'io_bills': [27, 51], 'payment': 1057, 'final_payment': 1054, 'total_interest': 414}], ['sample 3', {'principal': 100000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 24, 'fund_day': 29}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 4167, 'final_payment': 4159, 'total_interest': 0}], ['sample 4', {'principal': 100000, 'rate_bp': 500, 'io_months': 12, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [222, 417, 417, 417, 417, 417, 417, 417, 417, 417, 417, 417], 'payment': 4387, 'final_payment': 4389, 'total_interest': 10099}], ['sample 5', {'principal': 100000, 'rate_bp': 500, 'io_months': 12, 'amort_months': 12, 'fund_day': 29}, {'io_bills': [28, 417, 417, 417, 417, 417, 417, 417, 417, 417, 417, 417], 'payment': 8561, 'final_payment': 8559, 'total_interest': 7345}], ['sample 6', {'principal': 12345, 'rate_bp': 0, 'io_months': 2, 'amort_months': 24, 'fund_day': 30}, {'io_bills': [0, 0], 'payment': 514, 'final_payment': 523, 'total_interest': 0}]], [['regression: amortization term', {'principal': 250000, 'rate_bp': 500, 'io_months': 12, 'amort_months': 60, 'fund_day': 15}, {'io_bills': [556, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1042, 1042], 'payment': 4718, 'final_payment': 4703, 'total_interest': 45083}], ['sample 1', {'principal': 100000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 60, 'fund_day': 29}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 1667, 'final_payment': 1647, 'total_interest': 0}], ['sample 2', {'principal': 250000, 'rate_bp': 0, 'io_months': 3, 'amort_months': 1, 'fund_day': 2}, {'io_bills': [0, 0, 0], 'payment': 250000, 'final_payment': 250000, 'total_interest': 0}], ['sample 3', {'principal': 250000, 'rate_bp': 1200, 'io_months': 12, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [1333, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500], 'payment': 11768, 'final_payment': 11778, 'total_interest': 61275}], ['sample 4', {'principal': 100000, 'rate_bp': 725, 'io_months': 12, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [322, 604, 604, 604, 604, 604, 604, 604, 604, 604, 604, 604], 'payment': 4489, 'final_payment': 4477, 'total_interest': 14690}], ['sample 5', {'principal': 12345, 'rate_bp': 1200, 'io_months': 2, 'amort_months': 24, 'fund_day': 30}, {'io_bills': [4, 123], 'payment': 581, 'final_payment': 584, 'total_interest': 1729}], ['sample 6', {'principal': 100000, 'rate_bp': 500, 'io_months': 1, 'amort_months': 12, 'fund_day': 30}, {'io_bills': [14], 'payment': 8561, 'final_payment': 8559, 'total_interest': 2744}]], [['regression: amortization term', {'principal': 12345, 'rate_bp': 725, 'io_months': 1, 'amort_months': 12, 'fund_day': 2}, {'io_bills': [72], 'payment': 1070, 'final_payment': 1065, 'total_interest': 562}], ['sample 1', {'principal': 3000000, 'rate_bp': 725, 'io_months': 1, 'amort_months': 60, 'fund_day': 29}, {'io_bills': [1208], 'payment': 59758, 'final_payment': 59764, 'total_interest': 586694}], ['sample 2', {'principal': 100000, 'rate_bp': 500, 'io_months': 3, 'amort_months': 60, 'fund_day': 2}, {'io_bills': [403, 417, 417], 'payment': 1887, 'final_payment': 1894, 'total_interest': 14464}], ['sample 3', {'principal': 250000, 'rate_bp': 725, 'io_months': 1, 'amort_months': 60, 'fund_day': 15}, {'io_bills': [806], 'payment': 4980, 'final_payment': 4967, 'total_interest': 49593}], ['sample 4', {'principal': 100000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 24, 'fund_day': 30}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 4167, 'final_payment': 4159, 'total_interest': 0}], ['sample 5', {'principal': 12345, 'rate_bp': 725, 'io_months': 2, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [40, 75], 'payment': 554, 'final_payment': 559, 'total_interest': 1071}], ['sample 6', {'principal': 3000000, 'rate_bp': 0, 'io_months': 12, 'amort_months': 24, 'fund_day': 15}, {'io_bills': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'payment': 125000, 'final_payment': 125000, 'total_interest': 0}]]]
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: amortization term	`{'final_payment': 104035, 'io_bills': [12500, 12500, 12500], 'payment': 55906, 'total_interest': 439989}`	`{'final_payment': 56596, 'io_bills': [12500, 12500, 12500], 'payment': 56614, 'total_interest': 434322}`	Failed
sample 1	`{'final_payment': 1920, 'io_bills': [40, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75], 'payment': 995, 'total_interest': 1385}`	`{'final_payment': 1065, 'io_bills': [40, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75], 'payment': 1070, 'total_interest': 1355}`	Failed
sample 2	`{'final_payment': 24746, 'io_bills': [101, 1510, 1510], 'payment': 21390, 'total_interest': 13157}`	`{'final_payment': 21655, 'io_bills': [101, 1510, 1510], 'payment': 21661, 'total_interest': 13047}`	Failed
sample 3	`{'final_payment': 18093, 'io_bills': [167, 2500, 2500], 'payment': 11525, 'total_interest': 38335}`	`{'final_payment': 11778, 'io_bills': [167, 2500, 2500], 'payment': 11768, 'total_interest': 37609}`	Failed
sample 4	`{'final_payment': 3030000, 'io_bills': [29000, 30000, 30000], 'payment': 2940110, 'total_interest': 119000}`	`{'final_payment': 3030000, 'io_bills': [29000, 30000, 30000], 'payment': 3030000, 'total_interest': 119000}`	Failed
sample 5	`{'final_payment': 523, 'io_bills': [0], 'payment': 514, 'total_interest': 0}`	`{'final_payment': 523, 'io_bills': [0], 'payment': 514, 'total_interest': 0}`	Passed
sample 6	`{'final_payment': 1179, 'io_bills': [27, 51, 51], 'payment': 1046, 'total_interest': 469}`	`{'final_payment': 1054, 'io_bills': [27, 51, 51], 'payment': 1057, 'total_interest': 465}`	Failed

SHA-256 / 6735f3a0ef9eb60733396d62f8be8231aa7ce051a7c5e3654f7dd853038423aa

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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 2026-09-29T14:46:26.711159+00:00.

Case digest / 72005aed447f98b7243dfbeba5ce5bd5e6bfaa4dce4051f1913bc6b587d9238b