FA-58716 / Loan amortization schedules / Open access

Forbearance capitalization or deferral: forbearance accrual compounding · case 01

Forbearance interest compounds monthly.

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ROOT CAUSE

Accrued interest is included in the balance that accrues further interest.

VERIFIED REPAIR

Accrue simple interest on the unchanged balance, rounded each month.

Unsuccessful approach: Cumulative rounding spreads cents differently than rounding each month.

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 + acc) * bp, 120000)
    remaining = n - (start - 1)
    if x['mode'] == 'capitalize':
        bal += acc
        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: forbearance accrual compounding', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'capitalize'}, {'balance': 102071, 'deferred': 0, 'payment': 4990}], ['regression: forbearance accrual compounding, partial-repair probe', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 230288, 'deferred': 13818, 'payment': 22212}], ['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': 100000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 92115, 'deferred': 921, 'payment': 8885}], ['control 5', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'capitalize'}, {'balance': 20837, 'deferred': 0, 'payment': 20837}]], [['regression: forbearance accrual compounding', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 801419, 'deferred': 24042, 'payment': 44321}], ['control 1', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 2', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 21406, 'deferred': 107, 'payment': 21517}], ['control 3', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 91665, 'deferred': 0, 'payment': 1667}], ['control 4', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 231905, 'deferred': 1160, 'payment': 4833}], ['control 5', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 1000000, 'deferred': 5000, 'payment': 19333}], ['control 6', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 20837, 'deferred': 0, 'payment': 20833}]], [['regression: forbearance accrual compounding', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 975088, 'deferred': 0, 'payment': 44985}], ['control 1', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [1, 1], 'mode': 'capitalize'}, {'balance': 101000, 'deferred': 0, 'payment': 2247}], ['control 2', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 3', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 801419, 'deferred': 4007, 'payment': 44321}], ['control 4', {'principal': 250000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 3], 'mode': 'defer'}, {'balance': 239583, 'deferred': 0, 'payment': 10417}], ['control 5', {'principal': 1000000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 1], 'mode': 'capitalize'}, {'balance': 958333, 'deferred': 0, 'payment': 41667}], ['control 6', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 85843, 'deferred': 858, 'payment': 2224}]], [['regression: forbearance accrual compounding', {'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': 100000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 8337, 'deferred': 0, 'payment': 8333}], ['control 5', {'principal': 100000, 'rate_bp': 600, 'months': 24, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 55929, 'deferred': 0, 'payment': 4454}], ['control 6', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 927614, 'deferred': 4638, 'payment': 19333}]], [['regression: forbearance accrual compounding', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}], ['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': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 918934, 'deferred': 4595, 'payment': 86066}], ['control 4', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 8560, 'deferred': 43, 'payment': 8607}], ['control 5', {'principal': 1000000, 'rate_bp': 0, 'months': 24, 'forbear': [12, 3], 'mode': 'capitalize'}, {'balance': 541663, 'deferred': 0, 'payment': 41666}], ['control 6', {'principal': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 86070, 'deferred': 0, 'payment': 86500}]]]
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: forbearance accrual compounding	`{'balance': 102217, 'deferred': 0, 'payment': 4997}`	`{'balance': 102071, 'deferred': 0, 'payment': 4990}`	Failed
regression: forbearance accrual compounding, partial-repair probe	`{'balance': 230288, 'deferred': 14167, 'payment': 22212}`	`{'balance': 230288, 'deferred': 13818, 'payment': 22212}`	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': 92115, 'deferred': 921, 'payment': 8885}`	`{'balance': 92115, 'deferred': 921, 'payment': 8885}`	Passed
control 5	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	Passed

SHA-256 / 14b9be44edc953e418c142d2fe9ea90f4fac62175c76c97447f2431c869f4911

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 * (k + 1), 120000) - rnd(bal * bp * k, 120000)
    remaining = n - (start - 1)
    if x['mode'] == 'capitalize':
        bal += acc
        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: forbearance accrual compounding', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'capitalize'}, {'balance': 102071, 'deferred': 0, 'payment': 4990}], ['regression: forbearance accrual compounding, partial-repair probe', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 230288, 'deferred': 13818, 'payment': 22212}], ['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': 100000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 92115, 'deferred': 921, 'payment': 8885}], ['control 5', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'capitalize'}, {'balance': 20837, 'deferred': 0, 'payment': 20837}]], [['regression: forbearance accrual compounding', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 801419, 'deferred': 24042, 'payment': 44321}], ['control 1', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 2', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 21406, 'deferred': 107, 'payment': 21517}], ['control 3', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 91665, 'deferred': 0, 'payment': 1667}], ['control 4', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 231905, 'deferred': 1160, 'payment': 4833}], ['control 5', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 1000000, 'deferred': 5000, 'payment': 19333}], ['control 6', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 20837, 'deferred': 0, 'payment': 20833}]], [['regression: forbearance accrual compounding', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 975088, 'deferred': 0, 'payment': 44985}], ['control 1', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [1, 1], 'mode': 'capitalize'}, {'balance': 101000, 'deferred': 0, 'payment': 2247}], ['control 2', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 3', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 801419, 'deferred': 4007, 'payment': 44321}], ['control 4', {'principal': 250000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 3], 'mode': 'defer'}, {'balance': 239583, 'deferred': 0, 'payment': 10417}], ['control 5', {'principal': 1000000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 1], 'mode': 'capitalize'}, {'balance': 958333, 'deferred': 0, 'payment': 41667}], ['control 6', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 85843, 'deferred': 858, 'payment': 2224}]], [['regression: forbearance accrual compounding', {'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': 100000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 8337, 'deferred': 0, 'payment': 8333}], ['control 5', {'principal': 100000, 'rate_bp': 600, 'months': 24, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 55929, 'deferred': 0, 'payment': 4454}], ['control 6', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 927614, 'deferred': 4638, 'payment': 19333}]], [['regression: forbearance accrual compounding', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}], ['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': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 918934, 'deferred': 4595, 'payment': 86066}], ['control 4', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 8560, 'deferred': 43, 'payment': 8607}], ['control 5', {'principal': 1000000, 'rate_bp': 0, 'months': 24, 'forbear': [12, 3], 'mode': 'capitalize'}, {'balance': 541663, 'deferred': 0, 'payment': 41666}], ['control 6', {'principal': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 86070, 'deferred': 0, 'payment': 86500}]]]
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: forbearance accrual compounding	`{'balance': 102071, 'deferred': 0, 'payment': 4990}`	`{'balance': 102071, 'deferred': 0, 'payment': 4990}`	Passed
regression: forbearance accrual compounding, partial-repair probe	`{'balance': 230288, 'deferred': 13817, 'payment': 22212}`	`{'balance': 230288, 'deferred': 13818, 'payment': 22212}`	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': 92115, 'deferred': 921, 'payment': 8885}`	`{'balance': 92115, 'deferred': 921, 'payment': 8885}`	Passed
control 5	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	Passed

SHA-256 / f52daf5cc89a9a6242fef1fb52dcac05865580668c308cc73a22252583b98142

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):
    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 = 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: forbearance accrual compounding', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'capitalize'}, {'balance': 102071, 'deferred': 0, 'payment': 4990}], ['regression: forbearance accrual compounding, partial-repair probe', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 230288, 'deferred': 13818, 'payment': 22212}], ['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': 100000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 92115, 'deferred': 921, 'payment': 8885}], ['control 5', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'capitalize'}, {'balance': 20837, 'deferred': 0, 'payment': 20837}]], [['regression: forbearance accrual compounding', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 801419, 'deferred': 24042, 'payment': 44321}], ['control 1', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 2', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 21406, 'deferred': 107, 'payment': 21517}], ['control 3', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 91665, 'deferred': 0, 'payment': 1667}], ['control 4', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 231905, 'deferred': 1160, 'payment': 4833}], ['control 5', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 1000000, 'deferred': 5000, 'payment': 19333}], ['control 6', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 20837, 'deferred': 0, 'payment': 20833}]], [['regression: forbearance accrual compounding', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 975088, 'deferred': 0, 'payment': 44985}], ['control 1', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [1, 1], 'mode': 'capitalize'}, {'balance': 101000, 'deferred': 0, 'payment': 2247}], ['control 2', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['control 3', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 801419, 'deferred': 4007, 'payment': 44321}], ['control 4', {'principal': 250000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 3], 'mode': 'defer'}, {'balance': 239583, 'deferred': 0, 'payment': 10417}], ['control 5', {'principal': 1000000, 'rate_bp': 0, 'months': 24, 'forbear': [2, 1], 'mode': 'capitalize'}, {'balance': 958333, 'deferred': 0, 'payment': 41667}], ['control 6', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 85843, 'deferred': 858, 'payment': 2224}]], [['regression: forbearance accrual compounding', {'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': 100000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 8337, 'deferred': 0, 'payment': 8333}], ['control 5', {'principal': 100000, 'rate_bp': 600, 'months': 24, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 55929, 'deferred': 0, 'payment': 4454}], ['control 6', {'principal': 1000000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 927614, 'deferred': 4638, 'payment': 19333}]], [['regression: forbearance accrual compounding', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}], ['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': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 918934, 'deferred': 4595, 'payment': 86066}], ['control 4', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 8560, 'deferred': 43, 'payment': 8607}], ['control 5', {'principal': 1000000, 'rate_bp': 0, 'months': 24, 'forbear': [12, 3], 'mode': 'capitalize'}, {'balance': 541663, 'deferred': 0, 'payment': 41666}], ['control 6', {'principal': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 86070, 'deferred': 0, 'payment': 86500}]]]
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: forbearance accrual compounding	`{'balance': 102071, 'deferred': 0, 'payment': 4990}`	`{'balance': 102071, 'deferred': 0, 'payment': 4990}`	Passed
regression: forbearance accrual compounding, partial-repair probe	`{'balance': 230288, 'deferred': 13818, 'payment': 22212}`	`{'balance': 230288, 'deferred': 13818, 'payment': 22212}`	Passed
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': 92115, 'deferred': 921, 'payment': 8885}`	`{'balance': 92115, 'deferred': 921, 'payment': 8885}`	Passed
control 5	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	`{'balance': 20837, 'deferred': 0, 'payment': 20837}`	Passed

SHA-256 / 2a5cb16e83ff37e2d2103aa5bd590951259aec9f1e0000fcf176d80744a62255

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 2026-09-29T14:46:29.382607+00:00.

Case digest / 6d88144115551f15993306109389a8132484a28a5f87378e766cb68ada4dc38b