FAILURE MAP
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FA-58581 / Loan amortization schedules / Open access

Balloon maturity payment: balloon payment composition · case 01

The balloon payment is inflated by a full regular payment.

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

ROOT CAUSE

The balloon adds the regular payment to the remaining balance.

THE FAILURE

The balloon adds the regular payment to the remaining balance.

Unsuccessful approach: Taking the larger of balance and payment omits interest.

Case contract

x = {'principal', 'rate_bp', 'amort_months', 'term_months'}. The level payment amortizes over amort_months (exact annuity, half-up). Payments run to the earlier of term and amortization end; the last one pays balance + interest (the balloon). Monthly interest is round_half_up(balance*bp/120000). Return {'payment', 'final_payment', 'balloon_excess': 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']
    pay = level(P, x['amort_months'])
    last_k = min(x['term_months'], x['amort_months'])
    bal = P
    total = 0
    final = 0
    for k in range(1, last_k + 1):
        interest = rnd(bal * bp, 120000)
        total += interest
        if k == last_k:
            final = bal + pay
        else:
            bal -= pay - interest
    return {'payment': pay, 'final_payment': final, 'balloon_excess': final - pay, 'total_interest': total}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: balloon payment composition', {'principal': 100000, 'rate_bp': 0, 'amort_months': 5, 'term_months': 3}, {'payment': 20000, 'final_payment': 60000, 'balloon_excess': 40000, 'total_interest': 0}], ['regression: balloon payment composition, partial-repair probe', {'principal': 55555, 'rate_bp': 600, 'amort_months': 12, 'term_months': 84}, {'payment': 4781, 'final_payment': 4786, 'balloon_excess': 5, 'total_interest': 1822}], ['sample 1', {'principal': 1000000, 'rate_bp': 600, 'amort_months': 360, 'term_months': 60}, {'payment': 5996, 'final_payment': 936506, 'balloon_excess': 930510, 'total_interest': 290270}], ['sample 2', {'principal': 1000000, 'rate_bp': 600, 'amort_months': 12, 'term_months': 84}, {'payment': 86066, 'final_payment': 86070, 'balloon_excess': 4, 'total_interest': 32796}], ['sample 3', {'principal': 3000000, 'rate_bp': 600, 'amort_months': 5, 'term_months': 84}, {'payment': 609030, 'final_payment': 609030, 'balloon_excess': 0, 'total_interest': 45150}], ['sample 4', {'principal': 55555, 'rate_bp': 725, 'amort_months': 60, 'term_months': 84}, {'payment': 1107, 'final_payment': 1081, 'balloon_excess': -26, 'total_interest': 10839}], ['sample 5', {'principal': 55555, 'rate_bp': 0, 'amort_months': 360, 'term_months': 5}, {'payment': 154, 'final_payment': 54939, 'balloon_excess': 54785, 'total_interest': 0}]], [['regression: balloon payment composition', {'principal': 100000, 'rate_bp': 0, 'amort_months': 12, 'term_months': 5}, {'payment': 8333, 'final_payment': 66668, 'balloon_excess': 58335, 'total_interest': 0}], ['regression: balloon payment composition, partial-repair probe', {'principal': 100000, 'rate_bp': 725, 'amort_months': 360, 'term_months': 5}, {'payment': 682, 'final_payment': 100288, 'balloon_excess': 99606, 'total_interest': 3016}], ['sample 1', {'principal': 100000, 'rate_bp': 600, 'amort_months': 5, 'term_months': 5}, {'payment': 20301, 'final_payment': 20300, 'balloon_excess': -1, 'total_interest': 1504}], ['sample 2', {'principal': 100000, 'rate_bp': 1200, 'amort_months': 60, 'term_months': 60}, {'payment': 2224, 'final_payment': 2262, 'balloon_excess': 38, 'total_interest': 33478}], ['sample 3', {'principal': 3000000, 'rate_bp': 1200, 'amort_months': 360, 'term_months': 84}, {'payment': 30858, 'final_payment': 2918745, 'balloon_excess': 2887887, 'total_interest': 2479959}], ['sample 4', {'principal': 3000000, 'rate_bp': 0, 'amort_months': 60, 'term_months': 12}, {'payment': 50000, 'final_payment': 2450000, 'balloon_excess': 2400000, 'total_interest': 0}], ['sample 5', {'principal': 100000, 'rate_bp': 1200, 'amort_months': 60, 'term_months': 5}, {'payment': 2224, 'final_payment': 95980, 'balloon_excess': 93756, 'total_interest': 4876}]], [['regression: balloon payment composition', {'principal': 100000, 'rate_bp': 0, 'amort_months': 5, 'term_months': 3}, {'payment': 20000, 'final_payment': 60000, 'balloon_excess': 40000, 'total_interest': 0}], ['regression: balloon payment composition, partial-repair probe', {'principal': 55555, 'rate_bp': 600, 'amort_months': 5, 'term_months': 3}, {'payment': 11278, 'final_payment': 33668, 'balloon_excess': 22390, 'total_interest': 669}], ['sample 1', {'principal': 1000000, 'rate_bp': 1200, 'amort_months': 5, 'term_months': 60}, {'payment': 206040, 'final_payment': 206040, 'balloon_excess': 0, 'total_interest': 30200}], ['sample 2', {'principal': 100000, 'rate_bp': 0, 'amort_months': 60, 'term_months': 5}, {'payment': 1667, 'final_payment': 93332, 'balloon_excess': 91665, 'total_interest': 0}], ['sample 3', {'principal': 55555, 'rate_bp': 600, 'amort_months': 60, 'term_months': 84}, {'payment': 1074, 'final_payment': 1074, 'balloon_excess': 0, 'total_interest': 8885}], ['sample 4', {'principal': 100000, 'rate_bp': 600, 'amort_months': 12, 'term_months': 3}, {'payment': 8607, 'final_payment': 84164, 'balloon_excess': 75557, 'total_interest': 1378}], ['sample 5', {'principal': 100000, 'rate_bp': 1200, 'amort_months': 12, 'term_months': 12}, {'payment': 8885, 'final_payment': 8884, 'balloon_excess': -1, 'total_interest': 6619}]], [['regression: balloon payment composition', {'principal': 1000000, 'rate_bp': 725, 'amort_months': 360, 'term_months': 12}, {'payment': 6822, 'final_payment': 997140, 'balloon_excess': 990318, 'total_interest': 72182}], ['sample 1', {'principal': 1000000, 'rate_bp': 1200, 'amort_months': 360, 'term_months': 12}, {'payment': 10286, 'final_payment': 1006656, 'balloon_excess': 996370, 'total_interest': 119802}], ['sample 2', {'principal': 55555, 'rate_bp': 0, 'amort_months': 5, 'term_months': 84}, {'payment': 11111, 'final_payment': 11111, 'balloon_excess': 0, 'total_interest': 0}], ['sample 3', {'principal': 55555, 'rate_bp': 725, 'amort_months': 360, 'term_months': 5}, {'payment': 379, 'final_payment': 55715, 'balloon_excess': 55336, 'total_interest': 1676}], ['sample 4', {'principal': 1000000, 'rate_bp': 0, 'amort_months': 60, 'term_months': 3}, {'payment': 16667, 'final_payment': 966666, 'balloon_excess': 949999, 'total_interest': 0}], ['sample 5', {'principal': 3000000, 'rate_bp': 0, 'amort_months': 60, 'term_months': 84}, {'payment': 50000, 'final_payment': 50000, 'balloon_excess': 0, 'total_interest': 0}], ['sample 6', {'principal': 1000000, 'rate_bp': 600, 'amort_months': 5, 'term_months': 5}, {'payment': 203010, 'final_payment': 203010, 'balloon_excess': 0, 'total_interest': 15050}]], [['regression: balloon payment composition', {'principal': 3000000, 'rate_bp': 1200, 'amort_months': 60, 'term_months': 12}, {'payment': 66733, 'final_payment': 2600867, 'balloon_excess': 2534134, 'total_interest': 334930}], ['sample 1', {'principal': 55555, 'rate_bp': 725, 'amort_months': 12, 'term_months': 3}, {'payment': 4813, 'final_payment': 46855, 'balloon_excess': 42042, 'total_interest': 926}], ['sample 2', {'principal': 100000, 'rate_bp': 600, 'amort_months': 60, 'term_months': 60}, {'payment': 1933, 'final_payment': 1952, 'balloon_excess': 19, 'total_interest': 15999}], ['sample 3', {'principal': 55555, 'rate_bp': 1200, 'amort_months': 12, 'term_months': 60}, {'payment': 4936, 'final_payment': 4938, 'balloon_excess': 2, 'total_interest': 3679}], ['sample 4', {'principal': 55555, 'rate_bp': 0, 'amort_months': 60, 'term_months': 60}, {'payment': 926, 'final_payment': 921, 'balloon_excess': -5, 'total_interest': 0}], ['sample 5', {'principal': 1000000, 'rate_bp': 725, 'amort_months': 360, 'term_months': 60}, {'payment': 6822, 'final_payment': 950593, 'balloon_excess': 943771, 'total_interest': 353091}], ['sample 6', {'principal': 100000, 'rate_bp': 1200, 'amort_months': 12, 'term_months': 12}, {'payment': 8885, 'final_payment': 8884, 'balloon_excess': -1, 'total_interest': 6619}]]]
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 fixtureActualExpectedOutcome
regression: balloon payment composition{'balloon_excess': 60000, 'final_payment': 80000, 'payment': 20000, 'total_interest': 0}{'balloon_excess': 40000, 'final_payment': 60000, 'payment': 20000, 'total_interest': 0}Failed
regression: balloon payment composition, partial-repair probe{'balloon_excess': 4762, 'final_payment': 9543, 'payment': 4781, 'total_interest': 1822}{'balloon_excess': 5, 'final_payment': 4786, 'payment': 4781, 'total_interest': 1822}Failed
sample 1{'balloon_excess': 931847, 'final_payment': 937843, 'payment': 5996, 'total_interest': 290270}{'balloon_excess': 930510, 'final_payment': 936506, 'payment': 5996, 'total_interest': 290270}Failed
sample 2{'balloon_excess': 85642, 'final_payment': 171708, 'payment': 86066, 'total_interest': 32796}{'balloon_excess': 4, 'final_payment': 86070, 'payment': 86066, 'total_interest': 32796}Failed
sample 3{'balloon_excess': 606000, 'final_payment': 1215030, 'payment': 609030, 'total_interest': 45150}{'balloon_excess': 0, 'final_payment': 609030, 'payment': 609030, 'total_interest': 45150}Failed
sample 4{'balloon_excess': 1075, 'final_payment': 2182, 'payment': 1107, 'total_interest': 10839}{'balloon_excess': -26, 'final_payment': 1081, 'payment': 1107, 'total_interest': 10839}Failed
sample 5{'balloon_excess': 54939, 'final_payment': 55093, 'payment': 154, 'total_interest': 0}{'balloon_excess': 54785, 'final_payment': 54939, 'payment': 154, 'total_interest': 0}Failed

SHA-256 / 1d1df2b619da1f5d848bbec3344a60c70e09b6673945f8fb5cd5041e055ad7bf

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']
    pay = level(P, x['amort_months'])
    last_k = min(x['term_months'], x['amort_months'])
    bal = P
    total = 0
    final = 0
    for k in range(1, last_k + 1):
        interest = rnd(bal * bp, 120000)
        total += interest
        if k == last_k:
            final = max(bal, pay)
        else:
            bal -= pay - interest
    return {'payment': pay, 'final_payment': final, 'balloon_excess': final - pay, 'total_interest': total}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: balloon payment composition', {'principal': 100000, 'rate_bp': 0, 'amort_months': 5, 'term_months': 3}, {'payment': 20000, 'final_payment': 60000, 'balloon_excess': 40000, 'total_interest': 0}], ['regression: balloon payment composition, partial-repair probe', {'principal': 55555, 'rate_bp': 600, 'amort_months': 12, 'term_months': 84}, {'payment': 4781, 'final_payment': 4786, 'balloon_excess': 5, 'total_interest': 1822}], ['sample 1', {'principal': 1000000, 'rate_bp': 600, 'amort_months': 360, 'term_months': 60}, {'payment': 5996, 'final_payment': 936506, 'balloon_excess': 930510, 'total_interest': 290270}], ['sample 2', {'principal': 1000000, 'rate_bp': 600, 'amort_months': 12, 'term_months': 84}, {'payment': 86066, 'final_payment': 86070, 'balloon_excess': 4, 'total_interest': 32796}], ['sample 3', {'principal': 3000000, 'rate_bp': 600, 'amort_months': 5, 'term_months': 84}, {'payment': 609030, 'final_payment': 609030, 'balloon_excess': 0, 'total_interest': 45150}], ['sample 4', {'principal': 55555, 'rate_bp': 725, 'amort_months': 60, 'term_months': 84}, {'payment': 1107, 'final_payment': 1081, 'balloon_excess': -26, 'total_interest': 10839}], ['sample 5', {'principal': 55555, 'rate_bp': 0, 'amort_months': 360, 'term_months': 5}, {'payment': 154, 'final_payment': 54939, 'balloon_excess': 54785, 'total_interest': 0}]], [['regression: balloon payment composition', {'principal': 100000, 'rate_bp': 0, 'amort_months': 12, 'term_months': 5}, {'payment': 8333, 'final_payment': 66668, 'balloon_excess': 58335, 'total_interest': 0}], ['regression: balloon payment composition, partial-repair probe', {'principal': 100000, 'rate_bp': 725, 'amort_months': 360, 'term_months': 5}, {'payment': 682, 'final_payment': 100288, 'balloon_excess': 99606, 'total_interest': 3016}], ['sample 1', {'principal': 100000, 'rate_bp': 600, 'amort_months': 5, 'term_months': 5}, {'payment': 20301, 'final_payment': 20300, 'balloon_excess': -1, 'total_interest': 1504}], ['sample 2', {'principal': 100000, 'rate_bp': 1200, 'amort_months': 60, 'term_months': 60}, {'payment': 2224, 'final_payment': 2262, 'balloon_excess': 38, 'total_interest': 33478}], ['sample 3', {'principal': 3000000, 'rate_bp': 1200, 'amort_months': 360, 'term_months': 84}, {'payment': 30858, 'final_payment': 2918745, 'balloon_excess': 2887887, 'total_interest': 2479959}], ['sample 4', {'principal': 3000000, 'rate_bp': 0, 'amort_months': 60, 'term_months': 12}, {'payment': 50000, 'final_payment': 2450000, 'balloon_excess': 2400000, 'total_interest': 0}], ['sample 5', {'principal': 100000, 'rate_bp': 1200, 'amort_months': 60, 'term_months': 5}, {'payment': 2224, 'final_payment': 95980, 'balloon_excess': 93756, 'total_interest': 4876}]], [['regression: balloon payment composition', {'principal': 100000, 'rate_bp': 0, 'amort_months': 5, 'term_months': 3}, {'payment': 20000, 'final_payment': 60000, 'balloon_excess': 40000, 'total_interest': 0}], ['regression: balloon payment composition, partial-repair probe', {'principal': 55555, 'rate_bp': 600, 'amort_months': 5, 'term_months': 3}, {'payment': 11278, 'final_payment': 33668, 'balloon_excess': 22390, 'total_interest': 669}], ['sample 1', {'principal': 1000000, 'rate_bp': 1200, 'amort_months': 5, 'term_months': 60}, {'payment': 206040, 'final_payment': 206040, 'balloon_excess': 0, 'total_interest': 30200}], ['sample 2', {'principal': 100000, 'rate_bp': 0, 'amort_months': 60, 'term_months': 5}, {'payment': 1667, 'final_payment': 93332, 'balloon_excess': 91665, 'total_interest': 0}], ['sample 3', {'principal': 55555, 'rate_bp': 600, 'amort_months': 60, 'term_months': 84}, {'payment': 1074, 'final_payment': 1074, 'balloon_excess': 0, 'total_interest': 8885}], ['sample 4', {'principal': 100000, 'rate_bp': 600, 'amort_months': 12, 'term_months': 3}, {'payment': 8607, 'final_payment': 84164, 'balloon_excess': 75557, 'total_interest': 1378}], ['sample 5', {'principal': 100000, 'rate_bp': 1200, 'amort_months': 12, 'term_months': 12}, {'payment': 8885, 'final_payment': 8884, 'balloon_excess': -1, 'total_interest': 6619}]], [['regression: balloon payment composition', {'principal': 1000000, 'rate_bp': 725, 'amort_months': 360, 'term_months': 12}, {'payment': 6822, 'final_payment': 997140, 'balloon_excess': 990318, 'total_interest': 72182}], ['sample 1', {'principal': 1000000, 'rate_bp': 1200, 'amort_months': 360, 'term_months': 12}, {'payment': 10286, 'final_payment': 1006656, 'balloon_excess': 996370, 'total_interest': 119802}], ['sample 2', {'principal': 55555, 'rate_bp': 0, 'amort_months': 5, 'term_months': 84}, {'payment': 11111, 'final_payment': 11111, 'balloon_excess': 0, 'total_interest': 0}], ['sample 3', {'principal': 55555, 'rate_bp': 725, 'amort_months': 360, 'term_months': 5}, {'payment': 379, 'final_payment': 55715, 'balloon_excess': 55336, 'total_interest': 1676}], ['sample 4', {'principal': 1000000, 'rate_bp': 0, 'amort_months': 60, 'term_months': 3}, {'payment': 16667, 'final_payment': 966666, 'balloon_excess': 949999, 'total_interest': 0}], ['sample 5', {'principal': 3000000, 'rate_bp': 0, 'amort_months': 60, 'term_months': 84}, {'payment': 50000, 'final_payment': 50000, 'balloon_excess': 0, 'total_interest': 0}], ['sample 6', {'principal': 1000000, 'rate_bp': 600, 'amort_months': 5, 'term_months': 5}, {'payment': 203010, 'final_payment': 203010, 'balloon_excess': 0, 'total_interest': 15050}]], [['regression: balloon payment composition', {'principal': 3000000, 'rate_bp': 1200, 'amort_months': 60, 'term_months': 12}, {'payment': 66733, 'final_payment': 2600867, 'balloon_excess': 2534134, 'total_interest': 334930}], ['sample 1', {'principal': 55555, 'rate_bp': 725, 'amort_months': 12, 'term_months': 3}, {'payment': 4813, 'final_payment': 46855, 'balloon_excess': 42042, 'total_interest': 926}], ['sample 2', {'principal': 100000, 'rate_bp': 600, 'amort_months': 60, 'term_months': 60}, {'payment': 1933, 'final_payment': 1952, 'balloon_excess': 19, 'total_interest': 15999}], ['sample 3', {'principal': 55555, 'rate_bp': 1200, 'amort_months': 12, 'term_months': 60}, {'payment': 4936, 'final_payment': 4938, 'balloon_excess': 2, 'total_interest': 3679}], ['sample 4', {'principal': 55555, 'rate_bp': 0, 'amort_months': 60, 'term_months': 60}, {'payment': 926, 'final_payment': 921, 'balloon_excess': -5, 'total_interest': 0}], ['sample 5', {'principal': 1000000, 'rate_bp': 725, 'amort_months': 360, 'term_months': 60}, {'payment': 6822, 'final_payment': 950593, 'balloon_excess': 943771, 'total_interest': 353091}], ['sample 6', {'principal': 100000, 'rate_bp': 1200, 'amort_months': 12, 'term_months': 12}, {'payment': 8885, 'final_payment': 8884, 'balloon_excess': -1, 'total_interest': 6619}]]]
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 fixtureActualExpectedOutcome
regression: balloon payment composition{'balloon_excess': 40000, 'final_payment': 60000, 'payment': 20000, 'total_interest': 0}{'balloon_excess': 40000, 'final_payment': 60000, 'payment': 20000, 'total_interest': 0}Passed
regression: balloon payment composition, partial-repair probe{'balloon_excess': 0, 'final_payment': 4781, 'payment': 4781, 'total_interest': 1822}{'balloon_excess': 5, 'final_payment': 4786, 'payment': 4781, 'total_interest': 1822}Failed
sample 1{'balloon_excess': 925851, 'final_payment': 931847, 'payment': 5996, 'total_interest': 290270}{'balloon_excess': 930510, 'final_payment': 936506, 'payment': 5996, 'total_interest': 290270}Failed
sample 2{'balloon_excess': 0, 'final_payment': 86066, 'payment': 86066, 'total_interest': 32796}{'balloon_excess': 4, 'final_payment': 86070, 'payment': 86066, 'total_interest': 32796}Failed
sample 3{'balloon_excess': 0, 'final_payment': 609030, 'payment': 609030, 'total_interest': 45150}{'balloon_excess': 0, 'final_payment': 609030, 'payment': 609030, 'total_interest': 45150}Passed
sample 4{'balloon_excess': 0, 'final_payment': 1107, 'payment': 1107, 'total_interest': 10839}{'balloon_excess': -26, 'final_payment': 1081, 'payment': 1107, 'total_interest': 10839}Failed
sample 5{'balloon_excess': 54785, 'final_payment': 54939, 'payment': 154, 'total_interest': 0}{'balloon_excess': 54785, 'final_payment': 54939, 'payment': 154, 'total_interest': 0}Passed

SHA-256 / 75b61a74f8953ff4fc4928d9ada18594fa54ea2239ae3fe0df91b3cb4aac35f5

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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.

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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 2026-09-29T14:46:28.067429+00:00.

Case digest / 2b5baa7f6c3706c4173dc854bd9547eff4a9c8da3bcc8dababfc2d74880c5933