FA-58351 / Loan amortization schedules / Open access

Level payment with final adjustment: zero-rate payment · case 01

Interest-free loans leave a large catch-up final payment when rounding up.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The zero-rate payment is truncated to whole cents before the rounding rule runs.

VERIFIED REPAIR

Keep P/n exact and let the configured rounding apply.

Unsuccessful approach: Floating division with banker rounding ignores the round-up mode and rounds halves to even.

Case contract

x = {'principal', 'rate_bp' (annual, monthly rate = bp/120000), 'months', 'round': 'nearest'|'up'}. The exact annuity payment P*r/(1-(1+r)^-n) (P/n at zero rate) is rounded half-up ('nearest') or up to the cent. Monthly interest is round_half_up(balance*bp/120000); months 1..n-1 pay the level payment and month n pays balance + interest. Return {'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):
    P = x['principal']
    n = x['months']
    bp = x['rate_bp']
    if bp == 0:
        exact = Fraction(P // n)
    else:
        r = Fraction(bp, 120000)
        exact = P * r / (1 - (1 + r) ** -n)
    if x['round'] == 'up':
        pay = math.ceil(exact)
    else:
        pay = math.floor(exact + Fraction(1, 2))
    bal = P
    total_int = 0
    last = 0
    for k in range(1, n + 1):
        q, rem = divmod(bal * bp, 120000)
        interest = q + (1 if 2 * rem >= 120000 else 0)
        total_int += interest
        if k == n:
            last = bal + interest
        else:
            bal = bal + interest - pay
    return {'payment': pay, 'final_payment': last, 'total_interest': total_int}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: zero-rate payment', {'principal': 999999, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 16667, 'final_payment': 16646, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 30000000, 'rate_bp': 0, 'months': 36, 'round': 'up'}, {'payment': 833334, 'final_payment': 833310, 'total_interest': 0}], ['control 1', {'principal': 7, 'rate_bp': 725, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -1123, 'total_interest': -771}], ['control 2', {'principal': 1000000, 'rate_bp': 13, 'months': 36, 'round': 'up'}, {'payment': 27834, 'final_payment': 27808, 'total_interest': 1998}], ['control 3', {'principal': 12345, 'rate_bp': 1200, 'months': 1, 'round': 'nearest'}, {'payment': 12468, 'final_payment': 12468, 'total_interest': 123}], ['control 4', {'principal': 1000000, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333334, 'total_interest': 0}], ['control 5', {'principal': 1000000, 'rate_bp': 1200, 'months': 360, 'round': 'nearest'}, {'payment': 10286, 'final_payment': 10743, 'total_interest': 2703417}]], [['regression: zero-rate payment', {'principal': 999999, 'rate_bp': 0, 'months': 36, 'round': 'nearest'}, {'payment': 27778, 'final_payment': 27769, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 2500000, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 208334, 'final_payment': 208326, 'total_interest': 0}], ['control 1', {'principal': 500, 'rate_bp': 13, 'months': 3, 'round': 'up'}, {'payment': 167, 'final_payment': 166, 'total_interest': 0}], ['control 2', {'principal': 2500000, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 861250, 'final_payment': 861251, 'total_interest': 83751}], ['control 3', {'principal': 999999, 'rate_bp': 725, 'months': 360, 'round': 'nearest'}, {'payment': 6822, 'final_payment': 6503, 'total_interest': 1455602}], ['control 4', {'principal': 7, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 0, 'final_payment': 7, 'total_interest': 0}], ['control 5', {'principal': 999999, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333333, 'total_interest': 0}]], [['regression: zero-rate payment', {'principal': 12345, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 1029, 'final_payment': 1026, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 999999, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 83334, 'final_payment': 83325, 'total_interest': 0}], ['control 1', {'principal': 2500000, 'rate_bp': 13, 'months': 1, 'round': 'nearest'}, {'payment': 2500271, 'final_payment': 2500271, 'total_interest': 271}], ['control 2', {'principal': 100000, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 34450, 'final_payment': 34450, 'total_interest': 3350}], ['control 3', {'principal': 999999, 'rate_bp': 0, 'months': 12, 'round': 'nearest'}, {'payment': 83333, 'final_payment': 83336, 'total_interest': 0}], ['control 4', {'principal': 999999, 'rate_bp': 1999, 'months': 3, 'round': 'up'}, {'payment': 344500, 'final_payment': 344499, 'total_interest': 33500}], ['control 5', {'principal': 500, 'rate_bp': 1200, 'months': 3, 'round': 'nearest'}, {'payment': 170, 'final_payment': 170, 'total_interest': 10}]], [['regression: zero-rate payment', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'round': 'up'}, {'payment': 16667, 'final_payment': 16647, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 999999, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 83334, 'final_payment': 83325, 'total_interest': 0}], ['control 1', {'principal': 7, 'rate_bp': 13, 'months': 12, 'round': 'up'}, {'payment': 1, 'final_payment': -4, 'total_interest': 0}], ['control 2', {'principal': 1000000, 'rate_bp': 13, 'months': 60, 'round': 'up'}, {'payment': 16722, 'final_payment': 16710, 'total_interest': 3308}], ['control 3', {'principal': 500, 'rate_bp': 725, 'months': 7, 'round': 'up'}, {'payment': 74, 'final_payment': 68, 'total_interest': 12}], ['control 4', {'principal': 7, 'rate_bp': 725, 'months': 7, 'round': 'up'}, {'payment': 2, 'final_payment': -5, 'total_interest': 0}], ['control 5', {'principal': 100000, 'rate_bp': 1999, 'months': 60, 'round': 'up'}, {'payment': 2649, 'final_payment': 2626, 'total_interest': 58917}]], [['regression: zero-rate payment', {'principal': 500, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 42, 'final_payment': 38, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 8334, 'final_payment': 8326, 'total_interest': 0}], ['control 1', {'principal': 30000000, 'rate_bp': 499, 'months': 2, 'round': 'nearest'}, {'payment': 15093627, 'final_payment': 15093627, 'total_interest': 187254}], ['control 2', {'principal': 999999, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333333, 'total_interest': 0}], ['control 3', {'principal': 500, 'rate_bp': 0, 'months': 2, 'round': 'up'}, {'payment': 250, 'final_payment': 250, 'total_interest': 0}], ['control 4', {'principal': 7, 'rate_bp': 600, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -876, 'total_interest': -524}], ['control 5', {'principal': 100000, 'rate_bp': 499, 'months': 60, 'round': 'up'}, {'payment': 1887, 'final_payment': 1866, 'total_interest': 13199}]]]
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: zero-rate payment	`{'final_payment': 16705, 'payment': 16666, 'total_interest': 0}`	`{'final_payment': 16646, 'payment': 16667, 'total_interest': 0}`	Failed
regression: zero-rate payment, partial-repair probe	`{'final_payment': 833345, 'payment': 833333, 'total_interest': 0}`	`{'final_payment': 833310, 'payment': 833334, 'total_interest': 0}`	Failed
control 1	`{'final_payment': -1123, 'payment': 1, 'total_interest': -771}`	`{'final_payment': -1123, 'payment': 1, 'total_interest': -771}`	Passed
control 2	`{'final_payment': 27808, 'payment': 27834, 'total_interest': 1998}`	`{'final_payment': 27808, 'payment': 27834, 'total_interest': 1998}`	Passed
control 3	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	Passed
control 4	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	Passed
control 5	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	Passed

SHA-256 / 30891c6581668244a55dd18173a78213830bc5aae4f9c06ba012c3340194074a

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):
    P = x['principal']
    n = x['months']
    bp = x['rate_bp']
    if bp == 0:
        exact = Fraction(round(P / n))
    else:
        r = Fraction(bp, 120000)
        exact = P * r / (1 - (1 + r) ** -n)
    if x['round'] == 'up':
        pay = math.ceil(exact)
    else:
        pay = math.floor(exact + Fraction(1, 2))
    bal = P
    total_int = 0
    last = 0
    for k in range(1, n + 1):
        q, rem = divmod(bal * bp, 120000)
        interest = q + (1 if 2 * rem >= 120000 else 0)
        total_int += interest
        if k == n:
            last = bal + interest
        else:
            bal = bal + interest - pay
    return {'payment': pay, 'final_payment': last, 'total_interest': total_int}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: zero-rate payment', {'principal': 999999, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 16667, 'final_payment': 16646, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 30000000, 'rate_bp': 0, 'months': 36, 'round': 'up'}, {'payment': 833334, 'final_payment': 833310, 'total_interest': 0}], ['control 1', {'principal': 7, 'rate_bp': 725, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -1123, 'total_interest': -771}], ['control 2', {'principal': 1000000, 'rate_bp': 13, 'months': 36, 'round': 'up'}, {'payment': 27834, 'final_payment': 27808, 'total_interest': 1998}], ['control 3', {'principal': 12345, 'rate_bp': 1200, 'months': 1, 'round': 'nearest'}, {'payment': 12468, 'final_payment': 12468, 'total_interest': 123}], ['control 4', {'principal': 1000000, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333334, 'total_interest': 0}], ['control 5', {'principal': 1000000, 'rate_bp': 1200, 'months': 360, 'round': 'nearest'}, {'payment': 10286, 'final_payment': 10743, 'total_interest': 2703417}]], [['regression: zero-rate payment', {'principal': 999999, 'rate_bp': 0, 'months': 36, 'round': 'nearest'}, {'payment': 27778, 'final_payment': 27769, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 2500000, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 208334, 'final_payment': 208326, 'total_interest': 0}], ['control 1', {'principal': 500, 'rate_bp': 13, 'months': 3, 'round': 'up'}, {'payment': 167, 'final_payment': 166, 'total_interest': 0}], ['control 2', {'principal': 2500000, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 861250, 'final_payment': 861251, 'total_interest': 83751}], ['control 3', {'principal': 999999, 'rate_bp': 725, 'months': 360, 'round': 'nearest'}, {'payment': 6822, 'final_payment': 6503, 'total_interest': 1455602}], ['control 4', {'principal': 7, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 0, 'final_payment': 7, 'total_interest': 0}], ['control 5', {'principal': 999999, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333333, 'total_interest': 0}]], [['regression: zero-rate payment', {'principal': 12345, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 1029, 'final_payment': 1026, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 999999, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 83334, 'final_payment': 83325, 'total_interest': 0}], ['control 1', {'principal': 2500000, 'rate_bp': 13, 'months': 1, 'round': 'nearest'}, {'payment': 2500271, 'final_payment': 2500271, 'total_interest': 271}], ['control 2', {'principal': 100000, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 34450, 'final_payment': 34450, 'total_interest': 3350}], ['control 3', {'principal': 999999, 'rate_bp': 0, 'months': 12, 'round': 'nearest'}, {'payment': 83333, 'final_payment': 83336, 'total_interest': 0}], ['control 4', {'principal': 999999, 'rate_bp': 1999, 'months': 3, 'round': 'up'}, {'payment': 344500, 'final_payment': 344499, 'total_interest': 33500}], ['control 5', {'principal': 500, 'rate_bp': 1200, 'months': 3, 'round': 'nearest'}, {'payment': 170, 'final_payment': 170, 'total_interest': 10}]], [['regression: zero-rate payment', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'round': 'up'}, {'payment': 16667, 'final_payment': 16647, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 999999, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 83334, 'final_payment': 83325, 'total_interest': 0}], ['control 1', {'principal': 7, 'rate_bp': 13, 'months': 12, 'round': 'up'}, {'payment': 1, 'final_payment': -4, 'total_interest': 0}], ['control 2', {'principal': 1000000, 'rate_bp': 13, 'months': 60, 'round': 'up'}, {'payment': 16722, 'final_payment': 16710, 'total_interest': 3308}], ['control 3', {'principal': 500, 'rate_bp': 725, 'months': 7, 'round': 'up'}, {'payment': 74, 'final_payment': 68, 'total_interest': 12}], ['control 4', {'principal': 7, 'rate_bp': 725, 'months': 7, 'round': 'up'}, {'payment': 2, 'final_payment': -5, 'total_interest': 0}], ['control 5', {'principal': 100000, 'rate_bp': 1999, 'months': 60, 'round': 'up'}, {'payment': 2649, 'final_payment': 2626, 'total_interest': 58917}]], [['regression: zero-rate payment', {'principal': 500, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 42, 'final_payment': 38, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 8334, 'final_payment': 8326, 'total_interest': 0}], ['control 1', {'principal': 30000000, 'rate_bp': 499, 'months': 2, 'round': 'nearest'}, {'payment': 15093627, 'final_payment': 15093627, 'total_interest': 187254}], ['control 2', {'principal': 999999, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333333, 'total_interest': 0}], ['control 3', {'principal': 500, 'rate_bp': 0, 'months': 2, 'round': 'up'}, {'payment': 250, 'final_payment': 250, 'total_interest': 0}], ['control 4', {'principal': 7, 'rate_bp': 600, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -876, 'total_interest': -524}], ['control 5', {'principal': 100000, 'rate_bp': 499, 'months': 60, 'round': 'up'}, {'payment': 1887, 'final_payment': 1866, 'total_interest': 13199}]]]
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: zero-rate payment	`{'final_payment': 16646, 'payment': 16667, 'total_interest': 0}`	`{'final_payment': 16646, 'payment': 16667, 'total_interest': 0}`	Passed
regression: zero-rate payment, partial-repair probe	`{'final_payment': 833345, 'payment': 833333, 'total_interest': 0}`	`{'final_payment': 833310, 'payment': 833334, 'total_interest': 0}`	Failed
control 1	`{'final_payment': -1123, 'payment': 1, 'total_interest': -771}`	`{'final_payment': -1123, 'payment': 1, 'total_interest': -771}`	Passed
control 2	`{'final_payment': 27808, 'payment': 27834, 'total_interest': 1998}`	`{'final_payment': 27808, 'payment': 27834, 'total_interest': 1998}`	Passed
control 3	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	Passed
control 4	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	Passed
control 5	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	Passed

SHA-256 / ce57997ebcec7bc5e795356b121327d2a59a6f921da4ebfcf5c2fb476073f006

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):
    P = x['principal']
    n = x['months']
    bp = x['rate_bp']
    if bp == 0:
        exact = Fraction(P, n)
    else:
        r = Fraction(bp, 120000)
        exact = P * r / (1 - (1 + r) ** -n)
    if x['round'] == 'up':
        pay = math.ceil(exact)
    else:
        pay = math.floor(exact + Fraction(1, 2))
    bal = P
    total_int = 0
    last = 0
    for k in range(1, n + 1):
        q, rem = divmod(bal * bp, 120000)
        interest = q + (1 if 2 * rem >= 120000 else 0)
        total_int += interest
        if k == n:
            last = bal + interest
        else:
            bal = bal + interest - pay
    return {'payment': pay, 'final_payment': last, 'total_interest': total_int}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: zero-rate payment', {'principal': 999999, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 16667, 'final_payment': 16646, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 30000000, 'rate_bp': 0, 'months': 36, 'round': 'up'}, {'payment': 833334, 'final_payment': 833310, 'total_interest': 0}], ['control 1', {'principal': 7, 'rate_bp': 725, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -1123, 'total_interest': -771}], ['control 2', {'principal': 1000000, 'rate_bp': 13, 'months': 36, 'round': 'up'}, {'payment': 27834, 'final_payment': 27808, 'total_interest': 1998}], ['control 3', {'principal': 12345, 'rate_bp': 1200, 'months': 1, 'round': 'nearest'}, {'payment': 12468, 'final_payment': 12468, 'total_interest': 123}], ['control 4', {'principal': 1000000, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333334, 'total_interest': 0}], ['control 5', {'principal': 1000000, 'rate_bp': 1200, 'months': 360, 'round': 'nearest'}, {'payment': 10286, 'final_payment': 10743, 'total_interest': 2703417}]], [['regression: zero-rate payment', {'principal': 999999, 'rate_bp': 0, 'months': 36, 'round': 'nearest'}, {'payment': 27778, 'final_payment': 27769, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 2500000, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 208334, 'final_payment': 208326, 'total_interest': 0}], ['control 1', {'principal': 500, 'rate_bp': 13, 'months': 3, 'round': 'up'}, {'payment': 167, 'final_payment': 166, 'total_interest': 0}], ['control 2', {'principal': 2500000, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 861250, 'final_payment': 861251, 'total_interest': 83751}], ['control 3', {'principal': 999999, 'rate_bp': 725, 'months': 360, 'round': 'nearest'}, {'payment': 6822, 'final_payment': 6503, 'total_interest': 1455602}], ['control 4', {'principal': 7, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 0, 'final_payment': 7, 'total_interest': 0}], ['control 5', {'principal': 999999, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333333, 'total_interest': 0}]], [['regression: zero-rate payment', {'principal': 12345, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 1029, 'final_payment': 1026, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 999999, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 83334, 'final_payment': 83325, 'total_interest': 0}], ['control 1', {'principal': 2500000, 'rate_bp': 13, 'months': 1, 'round': 'nearest'}, {'payment': 2500271, 'final_payment': 2500271, 'total_interest': 271}], ['control 2', {'principal': 100000, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 34450, 'final_payment': 34450, 'total_interest': 3350}], ['control 3', {'principal': 999999, 'rate_bp': 0, 'months': 12, 'round': 'nearest'}, {'payment': 83333, 'final_payment': 83336, 'total_interest': 0}], ['control 4', {'principal': 999999, 'rate_bp': 1999, 'months': 3, 'round': 'up'}, {'payment': 344500, 'final_payment': 344499, 'total_interest': 33500}], ['control 5', {'principal': 500, 'rate_bp': 1200, 'months': 3, 'round': 'nearest'}, {'payment': 170, 'final_payment': 170, 'total_interest': 10}]], [['regression: zero-rate payment', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'round': 'up'}, {'payment': 16667, 'final_payment': 16647, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 999999, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 83334, 'final_payment': 83325, 'total_interest': 0}], ['control 1', {'principal': 7, 'rate_bp': 13, 'months': 12, 'round': 'up'}, {'payment': 1, 'final_payment': -4, 'total_interest': 0}], ['control 2', {'principal': 1000000, 'rate_bp': 13, 'months': 60, 'round': 'up'}, {'payment': 16722, 'final_payment': 16710, 'total_interest': 3308}], ['control 3', {'principal': 500, 'rate_bp': 725, 'months': 7, 'round': 'up'}, {'payment': 74, 'final_payment': 68, 'total_interest': 12}], ['control 4', {'principal': 7, 'rate_bp': 725, 'months': 7, 'round': 'up'}, {'payment': 2, 'final_payment': -5, 'total_interest': 0}], ['control 5', {'principal': 100000, 'rate_bp': 1999, 'months': 60, 'round': 'up'}, {'payment': 2649, 'final_payment': 2626, 'total_interest': 58917}]], [['regression: zero-rate payment', {'principal': 500, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 42, 'final_payment': 38, 'total_interest': 0}], ['regression: zero-rate payment, partial-repair probe', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 8334, 'final_payment': 8326, 'total_interest': 0}], ['control 1', {'principal': 30000000, 'rate_bp': 499, 'months': 2, 'round': 'nearest'}, {'payment': 15093627, 'final_payment': 15093627, 'total_interest': 187254}], ['control 2', {'principal': 999999, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333333, 'total_interest': 0}], ['control 3', {'principal': 500, 'rate_bp': 0, 'months': 2, 'round': 'up'}, {'payment': 250, 'final_payment': 250, 'total_interest': 0}], ['control 4', {'principal': 7, 'rate_bp': 600, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -876, 'total_interest': -524}], ['control 5', {'principal': 100000, 'rate_bp': 499, 'months': 60, 'round': 'up'}, {'payment': 1887, 'final_payment': 1866, 'total_interest': 13199}]]]
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: zero-rate payment	`{'final_payment': 16646, 'payment': 16667, 'total_interest': 0}`	`{'final_payment': 16646, 'payment': 16667, 'total_interest': 0}`	Passed
regression: zero-rate payment, partial-repair probe	`{'final_payment': 833310, 'payment': 833334, 'total_interest': 0}`	`{'final_payment': 833310, 'payment': 833334, 'total_interest': 0}`	Passed
control 1	`{'final_payment': -1123, 'payment': 1, 'total_interest': -771}`	`{'final_payment': -1123, 'payment': 1, 'total_interest': -771}`	Passed
control 2	`{'final_payment': 27808, 'payment': 27834, 'total_interest': 1998}`	`{'final_payment': 27808, 'payment': 27834, 'total_interest': 1998}`	Passed
control 3	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	Passed
control 4	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	Passed
control 5	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	Passed

SHA-256 / 03192658fec31b5fe2d9eea61872a469db46dd9bd12ca380bf7af8a44a8f98d8

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 2026-09-29T14:46:25.839107+00:00.

Case digest / 2ba8eb1eecab27cc142e0fe72a66c375b3d135e1883e9ec3a195c3fe672a694d