FA-58731 / Loan amortization schedules / Open access

Forbearance capitalization or deferral: capitalization · case 01

Capitalized forbearance interest never reaches the principal balance.

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ROOT CAUSE

The capitalize branch does not add the accrued interest to the balance.

THE FAILURE

The capitalize branch does not add the accrued interest to the balance.

Unsuccessful approach: Also reporting the interest as deferred double-counts it.

Case contract

x = {'principal', 'rate_bp', 'months' n, 'forbear': [start_month, count], 'mode': 'capitalize'|'defer'}. Months before start_month are paid with the level payment (exact annuity, half-up, interest round_half_up(balance*bp/120000)). During the count forbearance months interest accrues on the unchanged balance, rounded monthly, without compounding. The remaining payment count n - (start - 1) is preserved (term extended). capitalize: accrued interest is added to the balance and the payment re-leveled over the remaining count; defer: accrued interest goes to a non-interest bucket and the payment is unchanged. Return {'balance', 'deferred', 'payment'}.

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']
    P = x['principal']
    pay = level(P, n)
    bal = P
    start, count = x['forbear']
    for k in range(1, start):
        interest = rnd(bal * bp, 120000)
        bal -= pay - interest
    acc = 0
    for k in range(count):
        acc += rnd(bal * bp, 120000)
    remaining = n - (start - 1)
    if x['mode'] == 'capitalize':
        new_pay = level(bal, remaining)
        deferred = 0
    else:
        deferred = acc
        new_pay = pay
    return {'balance': bal, 'deferred': deferred, 'payment': new_pay}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: capitalization', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'capitalize'}, {'balance': 102071, 'deferred': 0, 'payment': 4990}], ['control 1', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'forbear': [1, 3], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 4167}], ['control 2', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 3], 'mode': 'capitalize'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['control 3', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 54163, 'deferred': 0, 'payment': 4166}], ['control 4', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 230288, 'deferred': 13818, 'payment': 22212}], ['control 5', {'principal': 100000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 92115, 'deferred': 921, 'payment': 8885}], ['control 6', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'capitalize'}, {'balance': 20837, 'deferred': 0, 'payment': 20837}]], [['regression: capitalization', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [12, 6], 'mode': 'capitalize'}, {'balance': 23316, 'deferred': 0, 'payment': 23549}], ['control 1', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 801419, 'deferred': 24042, 'payment': 44321}], ['control 2', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 3', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 21406, 'deferred': 107, 'payment': 21517}], ['control 4', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 91665, 'deferred': 0, 'payment': 1667}], ['control 5', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 231905, 'deferred': 1160, 'payment': 4833}], ['control 6', {'principal': 250000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'defer'}, {'balance': 240170, 'deferred': 3603, 'payment': 11080}]], [['regression: capitalization', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 975088, 'deferred': 0, 'payment': 44985}], ['control 1', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 2', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 142798, 'deferred': 4284, 'payment': 11768}], ['control 3', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 801419, 'deferred': 4007, 'payment': 44321}], ['control 4', {'principal': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 85642, 'deferred': 1284, 'payment': 86066}], ['control 5', {'principal': 250000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 3], 'mode': 'defer'}, {'balance': 239583, 'deferred': 0, 'payment': 10417}], ['control 6', {'principal': 1000000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 1], 'mode': 'capitalize'}, {'balance': 958333, 'deferred': 0, 'payment': 41667}]], [['regression: capitalization', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 3], 'mode': 'capitalize'}, {'balance': 235385, 'deferred': 0, 'payment': 4906}], ['control 1', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 20837, 'deferred': 0, 'payment': 20837}], ['control 2', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 250000, 'deferred': 1250, 'payment': 21517}], ['control 3', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'capitalize'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['control 4', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 962927, 'deferred': 57774, 'payment': 47073}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 8337, 'deferred': 0, 'payment': 8333}], ['control 6', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}]], [['regression: capitalization', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 991814, 'deferred': 0, 'payment': 48486}], ['control 1', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 98333, 'deferred': 0, 'payment': 1667}], ['control 2', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['control 3', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}], ['control 4', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [6, 3], 'mode': 'defer'}, {'balance': 59058, 'deferred': 885, 'payment': 8607}], ['control 5', {'principal': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 918934, 'deferred': 4595, 'payment': 86066}], ['control 6', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 8560, 'deferred': 43, 'payment': 8607}]]]
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: capitalization	`{'balance': 96293, 'deferred': 0, 'payment': 4707}`	`{'balance': 102071, 'deferred': 0, 'payment': 4990}`	Failed
control 1	`{'balance': 100000, 'deferred': 0, 'payment': 4167}`	`{'balance': 100000, 'deferred': 0, 'payment': 4167}`	Passed
control 2	`{'balance': 1000000, 'deferred': 0, 'payment': 16667}`	`{'balance': 1000000, 'deferred': 0, 'payment': 16667}`	Passed
control 3	`{'balance': 54163, 'deferred': 0, 'payment': 4166}`	`{'balance': 54163, 'deferred': 0, 'payment': 4166}`	Passed
control 4	`{'balance': 230288, 'deferred': 13818, 'payment': 22212}`	`{'balance': 230288, 'deferred': 13818, 'payment': 22212}`	Passed
control 5	`{'balance': 92115, 'deferred': 921, 'payment': 8885}`	`{'balance': 92115, 'deferred': 921, 'payment': 8885}`	Passed
control 6	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	Passed

SHA-256 / ee81a35a83b980853a08d651929ce206c0e4c0a322be9e649366d8dcdbd3f313

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']
    P = x['principal']
    pay = level(P, n)
    bal = P
    start, count = x['forbear']
    for k in range(1, start):
        interest = rnd(bal * bp, 120000)
        bal -= pay - interest
    acc = 0
    for k in range(count):
        acc += rnd(bal * bp, 120000)
    remaining = n - (start - 1)
    if x['mode'] == 'capitalize':
        bal += acc
        new_pay = level(bal, remaining)
        deferred = acc
    else:
        deferred = acc
        new_pay = pay
    return {'balance': bal, 'deferred': deferred, 'payment': new_pay}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: capitalization', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'capitalize'}, {'balance': 102071, 'deferred': 0, 'payment': 4990}], ['control 1', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'forbear': [1, 3], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 4167}], ['control 2', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 3], 'mode': 'capitalize'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['control 3', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 54163, 'deferred': 0, 'payment': 4166}], ['control 4', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 230288, 'deferred': 13818, 'payment': 22212}], ['control 5', {'principal': 100000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 92115, 'deferred': 921, 'payment': 8885}], ['control 6', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'capitalize'}, {'balance': 20837, 'deferred': 0, 'payment': 20837}]], [['regression: capitalization', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [12, 6], 'mode': 'capitalize'}, {'balance': 23316, 'deferred': 0, 'payment': 23549}], ['control 1', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 801419, 'deferred': 24042, 'payment': 44321}], ['control 2', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 3', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 21406, 'deferred': 107, 'payment': 21517}], ['control 4', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 91665, 'deferred': 0, 'payment': 1667}], ['control 5', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 231905, 'deferred': 1160, 'payment': 4833}], ['control 6', {'principal': 250000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'defer'}, {'balance': 240170, 'deferred': 3603, 'payment': 11080}]], [['regression: capitalization', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 975088, 'deferred': 0, 'payment': 44985}], ['control 1', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 2', {'principal': 250000, 'rate_bp': 1200, 'months': 24, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 142798, 'deferred': 4284, 'payment': 11768}], ['control 3', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 801419, 'deferred': 4007, 'payment': 44321}], ['control 4', {'principal': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 85642, 'deferred': 1284, 'payment': 86066}], ['control 5', {'principal': 250000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 3], 'mode': 'defer'}, {'balance': 239583, 'deferred': 0, 'payment': 10417}], ['control 6', {'principal': 1000000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 1], 'mode': 'capitalize'}, {'balance': 958333, 'deferred': 0, 'payment': 41667}]], [['regression: capitalization', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 3], 'mode': 'capitalize'}, {'balance': 235385, 'deferred': 0, 'payment': 4906}], ['control 1', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 20837, 'deferred': 0, 'payment': 20837}], ['control 2', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 250000, 'deferred': 1250, 'payment': 21517}], ['control 3', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'capitalize'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['control 4', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 962927, 'deferred': 57774, 'payment': 47073}], ['control 5', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 8337, 'deferred': 0, 'payment': 8333}], ['control 6', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}]], [['regression: capitalization', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 991814, 'deferred': 0, 'payment': 48486}], ['control 1', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 98333, 'deferred': 0, 'payment': 1667}], ['control 2', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['control 3', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}], ['control 4', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [6, 3], 'mode': 'defer'}, {'balance': 59058, 'deferred': 885, 'payment': 8607}], ['control 5', {'principal': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 918934, 'deferred': 4595, 'payment': 86066}], ['control 6', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 8560, 'deferred': 43, 'payment': 8607}]]]
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: capitalization	`{'balance': 102071, 'deferred': 5778, 'payment': 4990}`	`{'balance': 102071, 'deferred': 0, 'payment': 4990}`	Failed
control 1	`{'balance': 100000, 'deferred': 0, 'payment': 4167}`	`{'balance': 100000, 'deferred': 0, 'payment': 4167}`	Passed
control 2	`{'balance': 1000000, 'deferred': 0, 'payment': 16667}`	`{'balance': 1000000, 'deferred': 0, 'payment': 16667}`	Passed
control 3	`{'balance': 54163, 'deferred': 0, 'payment': 4166}`	`{'balance': 54163, 'deferred': 0, 'payment': 4166}`	Passed
control 4	`{'balance': 230288, 'deferred': 13818, 'payment': 22212}`	`{'balance': 230288, 'deferred': 13818, 'payment': 22212}`	Passed
control 5	`{'balance': 92115, 'deferred': 921, 'payment': 8885}`	`{'balance': 92115, 'deferred': 921, 'payment': 8885}`	Passed
control 6	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	Passed

SHA-256 / 719bc31a78a6f2114be52675f8bc81938130190f66ba312cfe2d458ca8517ccf

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 2026-09-29T14:46:29.503352+00:00.

Case digest / 25dbdd3b4fb28cd038ad353c6d127d9791003f7f4d030767d56e3e58d134a816