FA-58356 / Loan amortization schedules / Open access

Level payment with final adjustment: round-up mode · case 01

Loans configured to round the payment up get a payment rounded down.

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

ROOT CAUSE

The up mode floors the exact payment.

THE FAILURE

The up mode floors the exact payment.

Unsuccessful approach: Rounding to nearest still rounds down whenever the fraction is below half a cent.

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.floor(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: round-up mode', {'principal': 7, 'rate_bp': 725, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -1123, 'total_interest': -771}], ['control 1', {'principal': 12345, 'rate_bp': 1200, 'months': 1, 'round': 'nearest'}, {'payment': 12468, 'final_payment': 12468, 'total_interest': 123}], ['control 2', {'principal': 999999, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 16667, 'final_payment': 16646, 'total_interest': 0}], ['control 3', {'principal': 1000000, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333334, 'total_interest': 0}], ['control 4', {'principal': 1000000, 'rate_bp': 1200, 'months': 360, 'round': 'nearest'}, {'payment': 10286, 'final_payment': 10743, 'total_interest': 2703417}], ['control 5', {'principal': 100000, 'rate_bp': 725, 'months': 360, 'round': 'nearest'}, {'payment': 682, 'final_payment': 923, 'total_interest': 145761}], ['control 6', {'principal': 100000, 'rate_bp': 725, 'months': 36, 'round': 'nearest'}, {'payment': 3099, 'final_payment': 3106, 'total_interest': 11571}]], [['regression: round-up mode', {'principal': 500, 'rate_bp': 13, 'months': 3, 'round': 'up'}, {'payment': 167, 'final_payment': 166, 'total_interest': 0}], ['regression: round-up mode, partial-repair probe', {'principal': 100000, 'rate_bp': 499, 'months': 2, 'round': 'up'}, {'payment': 50313, 'final_payment': 50311, 'total_interest': 624}], ['control 1', {'principal': 2500000, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 861250, 'final_payment': 861251, 'total_interest': 83751}], ['control 2', {'principal': 999999, 'rate_bp': 725, 'months': 360, 'round': 'nearest'}, {'payment': 6822, 'final_payment': 6503, 'total_interest': 1455602}], ['control 3', {'principal': 7, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 0, 'final_payment': 7, 'total_interest': 0}], ['control 4', {'principal': 999999, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333333, 'total_interest': 0}], ['control 5', {'principal': 999999, 'rate_bp': 0, 'months': 36, 'round': 'nearest'}, {'payment': 27778, 'final_payment': 27769, 'total_interest': 0}]], [['regression: round-up mode', {'principal': 12345, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 1029, 'final_payment': 1026, 'total_interest': 0}], ['regression: round-up mode, partial-repair probe', {'principal': 2500000, 'rate_bp': 13, 'months': 360, 'round': 'up'}, {'payment': 7082, 'final_payment': 6755, 'total_interest': 49193}], ['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': 500, 'rate_bp': 1200, 'months': 3, 'round': 'nearest'}, {'payment': 170, 'final_payment': 170, 'total_interest': 10}], ['control 5', {'principal': 1000000, 'rate_bp': 1200, 'months': 7, 'round': 'nearest'}, {'payment': 148628, 'final_payment': 148631, 'total_interest': 40399}]], [['regression: round-up mode', {'principal': 7, 'rate_bp': 13, 'months': 12, 'round': 'up'}, {'payment': 1, 'final_payment': -4, 'total_interest': 0}], ['regression: round-up mode, partial-repair probe', {'principal': 500, 'rate_bp': 725, 'months': 7, 'round': 'up'}, {'payment': 74, 'final_payment': 68, 'total_interest': 12}], ['control 1', {'principal': 500, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 172, 'final_payment': 173, 'total_interest': 17}], ['control 2', {'principal': 7, 'rate_bp': 1999, 'months': 7, 'round': 'nearest'}, {'payment': 1, 'final_payment': 1, 'total_interest': 0}], ['control 3', {'principal': 30000000, 'rate_bp': 0, 'months': 360, 'round': 'nearest'}, {'payment': 83333, 'final_payment': 83453, 'total_interest': 0}], ['control 4', {'principal': 999999, 'rate_bp': 13, 'months': 2, 'round': 'nearest'}, {'payment': 500081, 'final_payment': 500080, 'total_interest': 162}], ['control 5', {'principal': 999999, 'rate_bp': 1200, 'months': 7, 'round': 'nearest'}, {'payment': 148628, 'final_payment': 148630, 'total_interest': 40399}]], [['regression: round-up mode', {'principal': 7, 'rate_bp': 600, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -876, 'total_interest': -524}], ['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': 2500000, 'rate_bp': 499, 'months': 1, 'round': 'nearest'}, {'payment': 2510396, 'final_payment': 2510396, 'total_interest': 10396}], ['control 5', {'principal': 2500000, 'rate_bp': 13, 'months': 360, 'round': 'nearest'}, {'payment': 7081, 'final_payment': 7125, 'total_interest': 49204}], ['control 6', {'principal': 999999, 'rate_bp': 725, 'months': 12, 'round': 'nearest'}, {'payment': 86642, 'final_payment': 86643, 'total_interest': 39706}]]]
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: round-up mode	`{'final_payment': 7, 'payment': 0, 'total_interest': 0}`	`{'final_payment': -1123, 'payment': 1, 'total_interest': -771}`	Failed
control 1	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	Passed
control 2	`{'final_payment': 16646, 'payment': 16667, 'total_interest': 0}`	`{'final_payment': 16646, 'payment': 16667, 'total_interest': 0}`	Passed
control 3	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	Passed
control 4	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	Passed
control 5	`{'final_payment': 923, 'payment': 682, 'total_interest': 145761}`	`{'final_payment': 923, 'payment': 682, 'total_interest': 145761}`	Passed
control 6	`{'final_payment': 3106, 'payment': 3099, 'total_interest': 11571}`	`{'final_payment': 3106, 'payment': 3099, 'total_interest': 11571}`	Passed

SHA-256 / 4147b39fba38b31707b138b9a8dc9956db3ec1b9984aae879098b8af4d40d59b

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(P, n)
    else:
        r = Fraction(bp, 120000)
        exact = P * r / (1 - (1 + r) ** -n)
    if x['round'] == 'up':
        pay = round(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: round-up mode', {'principal': 7, 'rate_bp': 725, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -1123, 'total_interest': -771}], ['control 1', {'principal': 12345, 'rate_bp': 1200, 'months': 1, 'round': 'nearest'}, {'payment': 12468, 'final_payment': 12468, 'total_interest': 123}], ['control 2', {'principal': 999999, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 16667, 'final_payment': 16646, 'total_interest': 0}], ['control 3', {'principal': 1000000, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333334, 'total_interest': 0}], ['control 4', {'principal': 1000000, 'rate_bp': 1200, 'months': 360, 'round': 'nearest'}, {'payment': 10286, 'final_payment': 10743, 'total_interest': 2703417}], ['control 5', {'principal': 100000, 'rate_bp': 725, 'months': 360, 'round': 'nearest'}, {'payment': 682, 'final_payment': 923, 'total_interest': 145761}], ['control 6', {'principal': 100000, 'rate_bp': 725, 'months': 36, 'round': 'nearest'}, {'payment': 3099, 'final_payment': 3106, 'total_interest': 11571}]], [['regression: round-up mode', {'principal': 500, 'rate_bp': 13, 'months': 3, 'round': 'up'}, {'payment': 167, 'final_payment': 166, 'total_interest': 0}], ['regression: round-up mode, partial-repair probe', {'principal': 100000, 'rate_bp': 499, 'months': 2, 'round': 'up'}, {'payment': 50313, 'final_payment': 50311, 'total_interest': 624}], ['control 1', {'principal': 2500000, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 861250, 'final_payment': 861251, 'total_interest': 83751}], ['control 2', {'principal': 999999, 'rate_bp': 725, 'months': 360, 'round': 'nearest'}, {'payment': 6822, 'final_payment': 6503, 'total_interest': 1455602}], ['control 3', {'principal': 7, 'rate_bp': 0, 'months': 60, 'round': 'nearest'}, {'payment': 0, 'final_payment': 7, 'total_interest': 0}], ['control 4', {'principal': 999999, 'rate_bp': 0, 'months': 3, 'round': 'nearest'}, {'payment': 333333, 'final_payment': 333333, 'total_interest': 0}], ['control 5', {'principal': 999999, 'rate_bp': 0, 'months': 36, 'round': 'nearest'}, {'payment': 27778, 'final_payment': 27769, 'total_interest': 0}]], [['regression: round-up mode', {'principal': 12345, 'rate_bp': 0, 'months': 12, 'round': 'up'}, {'payment': 1029, 'final_payment': 1026, 'total_interest': 0}], ['regression: round-up mode, partial-repair probe', {'principal': 2500000, 'rate_bp': 13, 'months': 360, 'round': 'up'}, {'payment': 7082, 'final_payment': 6755, 'total_interest': 49193}], ['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': 500, 'rate_bp': 1200, 'months': 3, 'round': 'nearest'}, {'payment': 170, 'final_payment': 170, 'total_interest': 10}], ['control 5', {'principal': 1000000, 'rate_bp': 1200, 'months': 7, 'round': 'nearest'}, {'payment': 148628, 'final_payment': 148631, 'total_interest': 40399}]], [['regression: round-up mode', {'principal': 7, 'rate_bp': 13, 'months': 12, 'round': 'up'}, {'payment': 1, 'final_payment': -4, 'total_interest': 0}], ['regression: round-up mode, partial-repair probe', {'principal': 500, 'rate_bp': 725, 'months': 7, 'round': 'up'}, {'payment': 74, 'final_payment': 68, 'total_interest': 12}], ['control 1', {'principal': 500, 'rate_bp': 1999, 'months': 3, 'round': 'nearest'}, {'payment': 172, 'final_payment': 173, 'total_interest': 17}], ['control 2', {'principal': 7, 'rate_bp': 1999, 'months': 7, 'round': 'nearest'}, {'payment': 1, 'final_payment': 1, 'total_interest': 0}], ['control 3', {'principal': 30000000, 'rate_bp': 0, 'months': 360, 'round': 'nearest'}, {'payment': 83333, 'final_payment': 83453, 'total_interest': 0}], ['control 4', {'principal': 999999, 'rate_bp': 13, 'months': 2, 'round': 'nearest'}, {'payment': 500081, 'final_payment': 500080, 'total_interest': 162}], ['control 5', {'principal': 999999, 'rate_bp': 1200, 'months': 7, 'round': 'nearest'}, {'payment': 148628, 'final_payment': 148630, 'total_interest': 40399}]], [['regression: round-up mode', {'principal': 7, 'rate_bp': 600, 'months': 360, 'round': 'up'}, {'payment': 1, 'final_payment': -876, 'total_interest': -524}], ['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': 2500000, 'rate_bp': 499, 'months': 1, 'round': 'nearest'}, {'payment': 2510396, 'final_payment': 2510396, 'total_interest': 10396}], ['control 5', {'principal': 2500000, 'rate_bp': 13, 'months': 360, 'round': 'nearest'}, {'payment': 7081, 'final_payment': 7125, 'total_interest': 49204}], ['control 6', {'principal': 999999, 'rate_bp': 725, 'months': 12, 'round': 'nearest'}, {'payment': 86642, 'final_payment': 86643, 'total_interest': 39706}]]]
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: round-up mode	`{'final_payment': 7, 'payment': 0, 'total_interest': 0}`	`{'final_payment': -1123, 'payment': 1, 'total_interest': -771}`	Failed
control 1	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	`{'final_payment': 12468, 'payment': 12468, 'total_interest': 123}`	Passed
control 2	`{'final_payment': 16646, 'payment': 16667, 'total_interest': 0}`	`{'final_payment': 16646, 'payment': 16667, 'total_interest': 0}`	Passed
control 3	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	`{'final_payment': 333334, 'payment': 333333, 'total_interest': 0}`	Passed
control 4	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	`{'final_payment': 10743, 'payment': 10286, 'total_interest': 2703417}`	Passed
control 5	`{'final_payment': 923, 'payment': 682, 'total_interest': 145761}`	`{'final_payment': 923, 'payment': 682, 'total_interest': 145761}`	Passed
control 6	`{'final_payment': 3106, 'payment': 3099, 'total_interest': 11571}`	`{'final_payment': 3106, 'payment': 3099, 'total_interest': 11571}`	Passed

SHA-256 / a1455b4ba66796bb36cc4a89ef4dc69a919db6f6bc611f91f4e6b3cfcca75a5e

HELD IN THE MEMBER ARCHIVE

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.

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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 2026-09-29T14:46:25.966305+00:00.

Case digest / e56c7db563afb5683c3c30708a187ee00a44ed9d3823b60220ea03fbd680f4ae