FA-58816 / Loan amortization schedules / Open access

Graduated payment schedule: step compounding base · case 01

Later-year payments grow linearly instead of compounding.

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

ROOT CAUSE

Each step adds a simple percentage of the initial payment.

THE FAILURE

Each step adds a simple percentage of the initial payment.

Unsuccessful approach: Compounding the unrounded initial payment differs from compounding the rounded yearly payments.

Case contract

x = {'principal', 'rate_bp', 'months', 'initial_payment', 'step_bp', 'steps'}. Month m (1-based) is in year t = (m-1)//12. For t < steps+1 the year payment starts at initial_payment and each new year multiplies the previous year payment by (10000+step_bp)/10000, rounded half-up. At the start of year steps+1 (if the loan runs that long) the payment is re-leveled on the balance over the remaining months (exact annuity, half-up) and stays fixed. Interest round_half_up(balance*bp/120000); balance += interest - payment (it may grow). Return {'year_payments', 'peak_balance', 'end_balance'}.

Why this case matters

Amortization engines drive borrower statements, payoff quotes and investor remittances; a misplaced rounding step, boundary or ordering rule compounds across hundreds of periods.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    def rnd(n, d):
        q, r = divmod(n, d)
        return q + (1 if 2 * r >= d else 0)
    def level(P, n):
        if n <= 0 or P <= 0:
            return 0
        if bp == 0:
            exact = Fraction(P, n)
        else:
            r = Fraction(bp, 120000)
            exact = P * r / (1 - (1 + r) ** -n)
        return math.floor(exact + Fraction(1, 2))
    bp = x['rate_bp']
    n = x['months']
    bal = x['principal']
    pay = x['initial_payment']
    years = [pay]
    peak = bal
    for m in range(1, n + 1):
        t = (m - 1) // 12
        if m > 1 and (m - 1) % 12 == 0:
            if t <= x['steps']:
                pay = rnd(x['initial_payment'] * (10000 + x['step_bp'] * t), 10000)
            elif t == x['steps'] + 1:
                pay = level(bal, n - m + 1)
            years.append(pay)
        interest = rnd(bal * bp, 120000)
        bal += interest - pay
        peak = max(peak, bal)
    return {'year_payments': years, 'peak_balance': peak, 'end_balance': bal}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: step compounding base', {'principal': 1000000, 'rate_bp': 600, 'months': 36, 'initial_payment': 20000, 'step_bp': 750, 'steps': 2}, {'year_payments': [20000, 21500, 23113], 'peak_balance': 1000000, 'end_balance': 351915}], ['regression: step compounding base, partial-repair probe', {'principal': 100000, 'rate_bp': 900, 'months': 36, 'initial_payment': 500, 'step_bp': 250, 'steps': 2}, {'year_payments': [500, 513, 526], 'peak_balance': 109781, 'end_balance': 109781}], ['control 1', {'principal': 250000, 'rate_bp': 600, 'months': 24, 'initial_payment': 3000, 'step_bp': 250, 'steps': 3}, {'year_payments': [3000, 3075], 'peak_balance': 250000, 'end_balance': 204568}], ['control 2', {'principal': 250000, 'rate_bp': 900, 'months': 36, 'initial_payment': 8000, 'step_bp': 250, 'steps': 0}, {'year_payments': [8000, 7921, 7921], 'peak_balance': 250000, 'end_balance': 9}], ['control 3', {'principal': 100000, 'rate_bp': 600, 'months': 24, 'initial_payment': 500, 'step_bp': 250, 'steps': 0}, {'year_payments': [500, 8607], 'peak_balance': 100000, 'end_balance': -4}], ['control 4', {'principal': 250000, 'rate_bp': 900, 'months': 60, 'initial_payment': 8000, 'step_bp': 250, 'steps': 1}, {'year_payments': [8000, 8200, 2770, 2770, 2770], 'peak_balance': 250000, 'end_balance': -23}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 60, 'initial_payment': 20000, 'step_bp': 250, 'steps': 1}, {'year_payments': [20000, 20500, 0, 0, 0], 'peak_balance': 250000, 'end_balance': -326758}]], [['regression: step compounding base', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'initial_payment': 500, 'step_bp': 250, 'steps': 2}, {'year_payments': [500, 513, 526, 52144, 52144], 'peak_balance': 1176523, 'end_balance': 4}], ['control 1', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'initial_payment': 3000, 'step_bp': 250, 'steps': 2}, {'year_payments': [3000, 3075], 'peak_balance': 250000, 'end_balance': 235565}], ['control 2', {'principal': 250000, 'rate_bp': 600, 'months': 24, 'initial_payment': 3000, 'step_bp': 1000, 'steps': 1}, {'year_payments': [3000, 3300], 'peak_balance': 250000, 'end_balance': 201795}], ['control 3', {'principal': 100000, 'rate_bp': 900, 'months': 24, 'initial_payment': 500, 'step_bp': 1000, 'steps': 3}, {'year_payments': [500, 550], 'peak_balance': 105921, 'end_balance': 105921}], ['control 4', {'principal': 250000, 'rate_bp': 900, 'months': 60, 'initial_payment': 500, 'step_bp': 250, 'steps': 1}, {'year_payments': [500, 513, 9090, 9090, 9090], 'peak_balance': 285848, 'end_balance': -7}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 36, 'initial_payment': 8000, 'step_bp': 250, 'steps': 0}, {'year_payments': [8000, 8485, 8485], 'peak_balance': 250000, 'end_balance': -6}], ['control 6', {'principal': 100000, 'rate_bp': 1200, 'months': 36, 'initial_payment': 500, 'step_bp': 250, 'steps': 0}, {'year_payments': [500, 5006, 5006], 'peak_balance': 106341, 'end_balance': -5}]], [['regression: step compounding base', {'principal': 1000000, 'rate_bp': 1200, 'months': 60, 'initial_payment': 8000, 'step_bp': 250, 'steps': 2}, {'year_payments': [8000, 8200, 8405, 50753, 50753], 'peak_balance': 1078159, 'end_balance': -8}], ['regression: step compounding base, partial-repair probe', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'initial_payment': 500, 'step_bp': 250, 'steps': 3}, {'year_payments': [500, 513, 526, 539, 8520], 'peak_balance': 100000, 'end_balance': 6}], ['control 1', {'principal': 1000000, 'rate_bp': 900, 'months': 36, 'initial_payment': 3000, 'step_bp': 750, 'steps': 1}, {'year_payments': [3000, 3225, 97511], 'peak_balance': 1115035, 'end_balance': 6}], ['control 2', {'principal': 250000, 'rate_bp': 900, 'months': 24, 'initial_payment': 3000, 'step_bp': 750, 'steps': 1}, {'year_payments': [3000, 3225], 'peak_balance': 250000, 'end_balance': 217726}], ['control 3', {'principal': 1000000, 'rate_bp': 900, 'months': 36, 'initial_payment': 20000, 'step_bp': 1000, 'steps': 1}, {'year_payments': [20000, 22000, 56636], 'peak_balance': 1000000, 'end_balance': 0}], ['control 4', {'principal': 100000, 'rate_bp': 900, 'months': 24, 'initial_payment': 3000, 'step_bp': 750, 'steps': 0}, {'year_payments': [3000, 6284], 'peak_balance': 100000, 'end_balance': -2}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 60, 'initial_payment': 20000, 'step_bp': 250, 'steps': 0}, {'year_payments': [20000, 739, 739, 739, 739], 'peak_balance': 250000, 'end_balance': -10}]], [['regression: step compounding base', {'principal': 100000, 'rate_bp': 1200, 'months': 36, 'initial_payment': 3000, 'step_bp': 1000, 'steps': 2}, {'year_payments': [3000, 3300, 3630], 'peak_balance': 100000, 'end_balance': 1568}], ['regression: step compounding base, partial-repair probe', {'principal': 250000, 'rate_bp': 600, 'months': 36, 'initial_payment': 500, 'step_bp': 250, 'steps': 3}, {'year_payments': [500, 513, 526], 'peak_balance': 279010, 'end_balance': 279010}], ['control 1', {'principal': 100000, 'rate_bp': 900, 'months': 24, 'initial_payment': 20000, 'step_bp': 750, 'steps': 3}, {'year_payments': [20000, 21500], 'peak_balance': 100000, 'end_balance': -422889}], ['control 2', {'principal': 1000000, 'rate_bp': 900, 'months': 36, 'initial_payment': 8000, 'step_bp': 250, 'steps': 1}, {'year_payments': [8000, 8200, 86087], 'peak_balance': 1000000, 'end_balance': 5}], ['control 3', {'principal': 1000000, 'rate_bp': 900, 'months': 60, 'initial_payment': 500, 'step_bp': 250, 'steps': 0}, {'year_payments': [500, 27064, 27064, 27064, 27064], 'peak_balance': 1087553, 'end_balance': -13}], ['control 4', {'principal': 250000, 'rate_bp': 900, 'months': 36, 'initial_payment': 20000, 'step_bp': 750, 'steps': 1}, {'year_payments': [20000, 21500, 0], 'peak_balance': 250000, 'end_balance': -266261}], ['control 5', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'initial_payment': 8000, 'step_bp': 1000, 'steps': 0}, {'year_payments': [8000, 22616, 22616, 22616, 22616], 'peak_balance': 1000000, 'end_balance': 0}]], [['regression: step compounding base', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'initial_payment': 500, 'step_bp': 1000, 'steps': 3}, {'year_payments': [500, 550, 605, 666, 8252], 'peak_balance': 100000, 'end_balance': 1}], ['regression: step compounding base, partial-repair probe', {'principal': 100000, 'rate_bp': 1200, 'months': 36, 'initial_payment': 500, 'step_bp': 250, 'steps': 2}, {'year_payments': [500, 513, 526], 'peak_balance': 121021, 'end_balance': 121021}], ['control 1', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'initial_payment': 20000, 'step_bp': 750, 'steps': 1}, {'year_payments': [20000, 21500, 18254, 18254, 18254], 'peak_balance': 1000000, 'end_balance': -11}], ['control 2', {'principal': 1000000, 'rate_bp': 900, 'months': 60, 'initial_payment': 3000, 'step_bp': 1000, 'steps': 1}, {'year_payments': [3000, 3300, 35428, 35428, 35428], 'peak_balance': 1114096, 'end_balance': -5}], ['control 3', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'initial_payment': 3000, 'step_bp': 250, 'steps': 1}, {'year_payments': [3000, 3075], 'peak_balance': 250000, 'end_balance': 235565}], ['control 4', {'principal': 1000000, 'rate_bp': 600, 'months': 36, 'initial_payment': 3000, 'step_bp': 1000, 'steps': 1}, {'year_payments': [3000, 3300, 90126], 'peak_balance': 1047163, 'end_balance': -6}], ['control 5', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'initial_payment': 500, 'step_bp': 250, 'steps': 0}, {'year_payments': [500, 9448], 'peak_balance': 106341, 'end_balance': 5}]]]
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: step compounding base	`{'end_balance': 353310, 'peak_balance': 1000000, 'year_payments': [20000, 21500, 23000]}`	`{'end_balance': 351915, 'peak_balance': 1000000, 'year_payments': [20000, 21500, 23113]}`	Failed
regression: step compounding base, partial-repair probe	`{'end_balance': 109794, 'peak_balance': 109794, 'year_payments': [500, 513, 525]}`	`{'end_balance': 109781, 'peak_balance': 109781, 'year_payments': [500, 513, 526]}`	Failed
control 1	`{'end_balance': 204568, 'peak_balance': 250000, 'year_payments': [3000, 3075]}`	`{'end_balance': 204568, 'peak_balance': 250000, 'year_payments': [3000, 3075]}`	Passed
control 2	`{'end_balance': 9, 'peak_balance': 250000, 'year_payments': [8000, 7921, 7921]}`	`{'end_balance': 9, 'peak_balance': 250000, 'year_payments': [8000, 7921, 7921]}`	Passed
control 3	`{'end_balance': -4, 'peak_balance': 100000, 'year_payments': [500, 8607]}`	`{'end_balance': -4, 'peak_balance': 100000, 'year_payments': [500, 8607]}`	Passed
control 4	`{'end_balance': -23, 'peak_balance': 250000, 'year_payments': [8000, 8200, 2770, 2770, 2770]}`	`{'end_balance': -23, 'peak_balance': 250000, 'year_payments': [8000, 8200, 2770, 2770, 2770]}`	Passed
control 5	`{'end_balance': -326758, 'peak_balance': 250000, 'year_payments': [20000, 20500, 0, 0, 0]}`	`{'end_balance': -326758, 'peak_balance': 250000, 'year_payments': [20000, 20500, 0, 0, 0]}`	Passed

SHA-256 / a3e6acc373903cfcaf2b9cee26b224e755a3e112f94c97c1cc8e5db129f2c29c

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(x):
    def rnd(n, d):
        q, r = divmod(n, d)
        return q + (1 if 2 * r >= d else 0)
    def level(P, n):
        if n <= 0 or P <= 0:
            return 0
        if bp == 0:
            exact = Fraction(P, n)
        else:
            r = Fraction(bp, 120000)
            exact = P * r / (1 - (1 + r) ** -n)
        return math.floor(exact + Fraction(1, 2))
    bp = x['rate_bp']
    n = x['months']
    bal = x['principal']
    pay = x['initial_payment']
    years = [pay]
    peak = bal
    for m in range(1, n + 1):
        t = (m - 1) // 12
        if m > 1 and (m - 1) % 12 == 0:
            if t <= x['steps']:
                pay = rnd(x['initial_payment'] * (10000 + x['step_bp']) ** t, 10000 ** t)
            elif t == x['steps'] + 1:
                pay = level(bal, n - m + 1)
            years.append(pay)
        interest = rnd(bal * bp, 120000)
        bal += interest - pay
        peak = max(peak, bal)
    return {'year_payments': years, 'peak_balance': peak, 'end_balance': bal}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: step compounding base', {'principal': 1000000, 'rate_bp': 600, 'months': 36, 'initial_payment': 20000, 'step_bp': 750, 'steps': 2}, {'year_payments': [20000, 21500, 23113], 'peak_balance': 1000000, 'end_balance': 351915}], ['regression: step compounding base, partial-repair probe', {'principal': 100000, 'rate_bp': 900, 'months': 36, 'initial_payment': 500, 'step_bp': 250, 'steps': 2}, {'year_payments': [500, 513, 526], 'peak_balance': 109781, 'end_balance': 109781}], ['control 1', {'principal': 250000, 'rate_bp': 600, 'months': 24, 'initial_payment': 3000, 'step_bp': 250, 'steps': 3}, {'year_payments': [3000, 3075], 'peak_balance': 250000, 'end_balance': 204568}], ['control 2', {'principal': 250000, 'rate_bp': 900, 'months': 36, 'initial_payment': 8000, 'step_bp': 250, 'steps': 0}, {'year_payments': [8000, 7921, 7921], 'peak_balance': 250000, 'end_balance': 9}], ['control 3', {'principal': 100000, 'rate_bp': 600, 'months': 24, 'initial_payment': 500, 'step_bp': 250, 'steps': 0}, {'year_payments': [500, 8607], 'peak_balance': 100000, 'end_balance': -4}], ['control 4', {'principal': 250000, 'rate_bp': 900, 'months': 60, 'initial_payment': 8000, 'step_bp': 250, 'steps': 1}, {'year_payments': [8000, 8200, 2770, 2770, 2770], 'peak_balance': 250000, 'end_balance': -23}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 60, 'initial_payment': 20000, 'step_bp': 250, 'steps': 1}, {'year_payments': [20000, 20500, 0, 0, 0], 'peak_balance': 250000, 'end_balance': -326758}]], [['regression: step compounding base', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'initial_payment': 500, 'step_bp': 250, 'steps': 2}, {'year_payments': [500, 513, 526, 52144, 52144], 'peak_balance': 1176523, 'end_balance': 4}], ['control 1', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'initial_payment': 3000, 'step_bp': 250, 'steps': 2}, {'year_payments': [3000, 3075], 'peak_balance': 250000, 'end_balance': 235565}], ['control 2', {'principal': 250000, 'rate_bp': 600, 'months': 24, 'initial_payment': 3000, 'step_bp': 1000, 'steps': 1}, {'year_payments': [3000, 3300], 'peak_balance': 250000, 'end_balance': 201795}], ['control 3', {'principal': 100000, 'rate_bp': 900, 'months': 24, 'initial_payment': 500, 'step_bp': 1000, 'steps': 3}, {'year_payments': [500, 550], 'peak_balance': 105921, 'end_balance': 105921}], ['control 4', {'principal': 250000, 'rate_bp': 900, 'months': 60, 'initial_payment': 500, 'step_bp': 250, 'steps': 1}, {'year_payments': [500, 513, 9090, 9090, 9090], 'peak_balance': 285848, 'end_balance': -7}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 36, 'initial_payment': 8000, 'step_bp': 250, 'steps': 0}, {'year_payments': [8000, 8485, 8485], 'peak_balance': 250000, 'end_balance': -6}], ['control 6', {'principal': 100000, 'rate_bp': 1200, 'months': 36, 'initial_payment': 500, 'step_bp': 250, 'steps': 0}, {'year_payments': [500, 5006, 5006], 'peak_balance': 106341, 'end_balance': -5}]], [['regression: step compounding base', {'principal': 1000000, 'rate_bp': 1200, 'months': 60, 'initial_payment': 8000, 'step_bp': 250, 'steps': 2}, {'year_payments': [8000, 8200, 8405, 50753, 50753], 'peak_balance': 1078159, 'end_balance': -8}], ['regression: step compounding base, partial-repair probe', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'initial_payment': 500, 'step_bp': 250, 'steps': 3}, {'year_payments': [500, 513, 526, 539, 8520], 'peak_balance': 100000, 'end_balance': 6}], ['control 1', {'principal': 1000000, 'rate_bp': 900, 'months': 36, 'initial_payment': 3000, 'step_bp': 750, 'steps': 1}, {'year_payments': [3000, 3225, 97511], 'peak_balance': 1115035, 'end_balance': 6}], ['control 2', {'principal': 250000, 'rate_bp': 900, 'months': 24, 'initial_payment': 3000, 'step_bp': 750, 'steps': 1}, {'year_payments': [3000, 3225], 'peak_balance': 250000, 'end_balance': 217726}], ['control 3', {'principal': 1000000, 'rate_bp': 900, 'months': 36, 'initial_payment': 20000, 'step_bp': 1000, 'steps': 1}, {'year_payments': [20000, 22000, 56636], 'peak_balance': 1000000, 'end_balance': 0}], ['control 4', {'principal': 100000, 'rate_bp': 900, 'months': 24, 'initial_payment': 3000, 'step_bp': 750, 'steps': 0}, {'year_payments': [3000, 6284], 'peak_balance': 100000, 'end_balance': -2}], ['control 5', {'principal': 250000, 'rate_bp': 1200, 'months': 60, 'initial_payment': 20000, 'step_bp': 250, 'steps': 0}, {'year_payments': [20000, 739, 739, 739, 739], 'peak_balance': 250000, 'end_balance': -10}]], [['regression: step compounding base', {'principal': 100000, 'rate_bp': 1200, 'months': 36, 'initial_payment': 3000, 'step_bp': 1000, 'steps': 2}, {'year_payments': [3000, 3300, 3630], 'peak_balance': 100000, 'end_balance': 1568}], ['regression: step compounding base, partial-repair probe', {'principal': 250000, 'rate_bp': 600, 'months': 36, 'initial_payment': 500, 'step_bp': 250, 'steps': 3}, {'year_payments': [500, 513, 526], 'peak_balance': 279010, 'end_balance': 279010}], ['control 1', {'principal': 100000, 'rate_bp': 900, 'months': 24, 'initial_payment': 20000, 'step_bp': 750, 'steps': 3}, {'year_payments': [20000, 21500], 'peak_balance': 100000, 'end_balance': -422889}], ['control 2', {'principal': 1000000, 'rate_bp': 900, 'months': 36, 'initial_payment': 8000, 'step_bp': 250, 'steps': 1}, {'year_payments': [8000, 8200, 86087], 'peak_balance': 1000000, 'end_balance': 5}], ['control 3', {'principal': 1000000, 'rate_bp': 900, 'months': 60, 'initial_payment': 500, 'step_bp': 250, 'steps': 0}, {'year_payments': [500, 27064, 27064, 27064, 27064], 'peak_balance': 1087553, 'end_balance': -13}], ['control 4', {'principal': 250000, 'rate_bp': 900, 'months': 36, 'initial_payment': 20000, 'step_bp': 750, 'steps': 1}, {'year_payments': [20000, 21500, 0], 'peak_balance': 250000, 'end_balance': -266261}], ['control 5', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'initial_payment': 8000, 'step_bp': 1000, 'steps': 0}, {'year_payments': [8000, 22616, 22616, 22616, 22616], 'peak_balance': 1000000, 'end_balance': 0}]], [['regression: step compounding base', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'initial_payment': 500, 'step_bp': 1000, 'steps': 3}, {'year_payments': [500, 550, 605, 666, 8252], 'peak_balance': 100000, 'end_balance': 1}], ['regression: step compounding base, partial-repair probe', {'principal': 100000, 'rate_bp': 1200, 'months': 36, 'initial_payment': 500, 'step_bp': 250, 'steps': 2}, {'year_payments': [500, 513, 526], 'peak_balance': 121021, 'end_balance': 121021}], ['control 1', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'initial_payment': 20000, 'step_bp': 750, 'steps': 1}, {'year_payments': [20000, 21500, 18254, 18254, 18254], 'peak_balance': 1000000, 'end_balance': -11}], ['control 2', {'principal': 1000000, 'rate_bp': 900, 'months': 60, 'initial_payment': 3000, 'step_bp': 1000, 'steps': 1}, {'year_payments': [3000, 3300, 35428, 35428, 35428], 'peak_balance': 1114096, 'end_balance': -5}], ['control 3', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'initial_payment': 3000, 'step_bp': 250, 'steps': 1}, {'year_payments': [3000, 3075], 'peak_balance': 250000, 'end_balance': 235565}], ['control 4', {'principal': 1000000, 'rate_bp': 600, 'months': 36, 'initial_payment': 3000, 'step_bp': 1000, 'steps': 1}, {'year_payments': [3000, 3300, 90126], 'peak_balance': 1047163, 'end_balance': -6}], ['control 5', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'initial_payment': 500, 'step_bp': 250, 'steps': 0}, {'year_payments': [500, 9448], 'peak_balance': 106341, 'end_balance': 5}]]]
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: step compounding base	`{'end_balance': 351915, 'peak_balance': 1000000, 'year_payments': [20000, 21500, 23113]}`	`{'end_balance': 351915, 'peak_balance': 1000000, 'year_payments': [20000, 21500, 23113]}`	Passed
regression: step compounding base, partial-repair probe	`{'end_balance': 109794, 'peak_balance': 109794, 'year_payments': [500, 513, 525]}`	`{'end_balance': 109781, 'peak_balance': 109781, 'year_payments': [500, 513, 526]}`	Failed
control 1	`{'end_balance': 204568, 'peak_balance': 250000, 'year_payments': [3000, 3075]}`	`{'end_balance': 204568, 'peak_balance': 250000, 'year_payments': [3000, 3075]}`	Passed
control 2	`{'end_balance': 9, 'peak_balance': 250000, 'year_payments': [8000, 7921, 7921]}`	`{'end_balance': 9, 'peak_balance': 250000, 'year_payments': [8000, 7921, 7921]}`	Passed
control 3	`{'end_balance': -4, 'peak_balance': 100000, 'year_payments': [500, 8607]}`	`{'end_balance': -4, 'peak_balance': 100000, 'year_payments': [500, 8607]}`	Passed
control 4	`{'end_balance': -23, 'peak_balance': 250000, 'year_payments': [8000, 8200, 2770, 2770, 2770]}`	`{'end_balance': -23, 'peak_balance': 250000, 'year_payments': [8000, 8200, 2770, 2770, 2770]}`	Passed
control 5	`{'end_balance': -326758, 'peak_balance': 250000, 'year_payments': [20000, 20500, 0, 0, 0]}`	`{'end_balance': -326758, 'peak_balance': 250000, 'year_payments': [20000, 20500, 0, 0, 0]}`	Passed

SHA-256 / 9d2f0344fdac15d28756dc9708410c847d3a74a6aa90d455932efea89a624c98

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The verified repair and its recorded checks are member-only.

This mechanism has 7 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

A deterministic bounded teaching model with stipulated toy lending rules stated in the contract; money is integer cents and rates are basis points; it makes no claim of conformance to any regulation, servicing standard or product. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:46:30.235563+00:00.

Case digest / 40a97463be630543bd0017e60b1a2a246b087e21badea2adaeda7d41a274c2ec