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FA-58711 / Loan amortization schedules / Open access

Forbearance capitalization or deferral: payments before forbearance · case 01

The balance entering forbearance reflects a payment the borrower never made.

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

ROOT CAUSE

The first forbearance month is treated as a paid month.

THE FAILURE

The first forbearance month is treated as a paid month.

Unsuccessful approach: Starting at month 2 skips a payment that was made.

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 + 1):
        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: payments before forbearance', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'forbear': [1, 3], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 4167}], ['regression: payments before forbearance, partial-repair probe', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'capitalize'}, {'balance': 102071, 'deferred': 0, 'payment': 4990}], ['sample 1', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 3], 'mode': 'capitalize'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['sample 2', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 54163, 'deferred': 0, 'payment': 4166}], ['sample 3', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 230288, 'deferred': 13818, 'payment': 22212}], ['sample 4', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [12, 3], 'mode': 'capitalize'}, {'balance': 88417, 'deferred': 0, 'payment': 2291}], ['sample 5', {'principal': 100000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 92115, 'deferred': 921, 'payment': 8885}]], [['regression: payments before forbearance', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 801419, 'deferred': 24042, 'payment': 44321}], ['sample 1', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['sample 2', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 21406, 'deferred': 107, 'payment': 21517}], ['sample 3', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 91665, 'deferred': 0, 'payment': 1667}], ['sample 4', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 231905, 'deferred': 1160, 'payment': 4833}], ['sample 5', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [12, 6], 'mode': 'capitalize'}, {'balance': 23316, 'deferred': 0, 'payment': 23549}], ['sample 6', {'principal': 250000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'defer'}, {'balance': 240170, 'deferred': 3603, 'payment': 11080}]], [['regression: payments before forbearance', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 975088, 'deferred': 0, 'payment': 44985}], ['sample 1', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [6, 6], 'mode': 'capitalize'}, {'balance': 859545, 'deferred': 0, 'payment': 49898}], ['sample 2', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [1, 1], 'mode': 'capitalize'}, {'balance': 101000, 'deferred': 0, 'payment': 2247}], ['sample 3', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['sample 4', {'principal': 100000, 'rate_bp': 1200, 'months': 12, 'forbear': [6, 6], 'mode': 'capitalize'}, {'balance': 63367, 'deferred': 0, 'payment': 9418}], ['sample 5', {'principal': 250000, 'rate_bp': 1200, 'months': 60, 'forbear': [6, 6], 'mode': 'capitalize'}, {'balance': 248449, 'deferred': 0, 'payment': 5895}], ['sample 6', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 6], 'mode': 'capitalize'}, {'balance': 238865, 'deferred': 0, 'payment': 4978}]], [['regression: payments before forbearance', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 3], 'mode': 'capitalize'}, {'balance': 235385, 'deferred': 0, 'payment': 4906}], ['sample 1', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 20837, 'deferred': 0, 'payment': 20837}], ['sample 2', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 250000, 'deferred': 1250, 'payment': 21517}], ['sample 3', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'capitalize'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['sample 4', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 962927, 'deferred': 57774, 'payment': 47073}], ['sample 5', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 8337, 'deferred': 0, 'payment': 8333}], ['sample 6', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}]], [['regression: payments before forbearance', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 98333, 'deferred': 0, 'payment': 1667}], ['sample 1', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['sample 2', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}], ['sample 3', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [6, 3], 'mode': 'defer'}, {'balance': 59058, 'deferred': 885, 'payment': 8607}], ['sample 4', {'principal': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 918934, 'deferred': 4595, 'payment': 86066}], ['sample 5', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 8560, 'deferred': 43, 'payment': 8607}], ['sample 6', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 991814, 'deferred': 0, 'payment': 48486}]]]
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: payments before forbearance{'balance': 95833, 'deferred': 0, 'payment': 4167}{'balance': 100000, 'deferred': 0, 'payment': 4167}Failed
regression: payments before forbearance, partial-repair probe{'balance': 98099, 'deferred': 0, 'payment': 4796}{'balance': 102071, 'deferred': 0, 'payment': 4990}Failed
sample 1{'balance': 983333, 'deferred': 0, 'payment': 16389}{'balance': 1000000, 'deferred': 0, 'payment': 16667}Failed
sample 2{'balance': 49996, 'deferred': 0, 'payment': 3846}{'balance': 54163, 'deferred': 0, 'payment': 4166}Failed
sample 3{'balance': 210379, 'deferred': 12624, 'payment': 22212}{'balance': 230288, 'deferred': 13818, 'payment': 22212}Failed
sample 4{'balance': 87012, 'deferred': 0, 'payment': 2255}{'balance': 88417, 'deferred': 0, 'payment': 2291}Failed
sample 5{'balance': 84151, 'deferred': 842, 'payment': 8885}{'balance': 92115, 'deferred': 921, 'payment': 8885}Failed

SHA-256 / f58497bacad36db01f4fd5b99a7997e47f7225b5bd43fa9b6ded9e191be7cd84

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(2, 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: payments before forbearance', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'forbear': [1, 3], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 4167}], ['regression: payments before forbearance, partial-repair probe', {'principal': 100000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'capitalize'}, {'balance': 102071, 'deferred': 0, 'payment': 4990}], ['sample 1', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 3], 'mode': 'capitalize'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['sample 2', {'principal': 100000, 'rate_bp': 0, 'months': 24, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 54163, 'deferred': 0, 'payment': 4166}], ['sample 3', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 230288, 'deferred': 13818, 'payment': 22212}], ['sample 4', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [12, 3], 'mode': 'capitalize'}, {'balance': 88417, 'deferred': 0, 'payment': 2291}], ['sample 5', {'principal': 100000, 'rate_bp': 1200, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 92115, 'deferred': 921, 'payment': 8885}]], [['regression: payments before forbearance', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 801419, 'deferred': 24042, 'payment': 44321}], ['sample 1', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['sample 2', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 21406, 'deferred': 107, 'payment': 21517}], ['sample 3', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [6, 6], 'mode': 'defer'}, {'balance': 91665, 'deferred': 0, 'payment': 1667}], ['sample 4', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 1], 'mode': 'defer'}, {'balance': 231905, 'deferred': 1160, 'payment': 4833}], ['sample 5', {'principal': 250000, 'rate_bp': 1200, 'months': 12, 'forbear': [12, 6], 'mode': 'capitalize'}, {'balance': 23316, 'deferred': 0, 'payment': 23549}], ['sample 6', {'principal': 250000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'defer'}, {'balance': 240170, 'deferred': 3603, 'payment': 11080}]], [['regression: payments before forbearance', {'principal': 1000000, 'rate_bp': 600, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 975088, 'deferred': 0, 'payment': 44985}], ['sample 1', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [6, 6], 'mode': 'capitalize'}, {'balance': 859545, 'deferred': 0, 'payment': 49898}], ['sample 2', {'principal': 100000, 'rate_bp': 1200, 'months': 60, 'forbear': [1, 1], 'mode': 'capitalize'}, {'balance': 101000, 'deferred': 0, 'payment': 2247}], ['sample 3', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 100000, 'deferred': 0, 'payment': 1667}], ['sample 4', {'principal': 100000, 'rate_bp': 1200, 'months': 12, 'forbear': [6, 6], 'mode': 'capitalize'}, {'balance': 63367, 'deferred': 0, 'payment': 9418}], ['sample 5', {'principal': 250000, 'rate_bp': 1200, 'months': 60, 'forbear': [6, 6], 'mode': 'capitalize'}, {'balance': 248449, 'deferred': 0, 'payment': 5895}], ['sample 6', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 6], 'mode': 'capitalize'}, {'balance': 238865, 'deferred': 0, 'payment': 4978}]], [['regression: payments before forbearance', {'principal': 250000, 'rate_bp': 600, 'months': 60, 'forbear': [6, 3], 'mode': 'capitalize'}, {'balance': 235385, 'deferred': 0, 'payment': 4906}], ['sample 1', {'principal': 250000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 1], 'mode': 'capitalize'}, {'balance': 20837, 'deferred': 0, 'payment': 20837}], ['sample 2', {'principal': 250000, 'rate_bp': 600, 'months': 12, 'forbear': [1, 1], 'mode': 'defer'}, {'balance': 250000, 'deferred': 1250, 'payment': 21517}], ['sample 3', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 1], 'mode': 'capitalize'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['sample 4', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 6], 'mode': 'defer'}, {'balance': 962927, 'deferred': 57774, 'payment': 47073}], ['sample 5', {'principal': 100000, 'rate_bp': 0, 'months': 12, 'forbear': [12, 6], 'mode': 'defer'}, {'balance': 8337, 'deferred': 0, 'payment': 8333}], ['sample 6', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}]], [['regression: payments before forbearance', {'principal': 100000, 'rate_bp': 0, 'months': 60, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 98333, 'deferred': 0, 'payment': 1667}], ['sample 1', {'principal': 1000000, 'rate_bp': 0, 'months': 60, 'forbear': [1, 6], 'mode': 'defer'}, {'balance': 1000000, 'deferred': 0, 'payment': 16667}], ['sample 2', {'principal': 100000, 'rate_bp': 600, 'months': 60, 'forbear': [12, 3], 'mode': 'defer'}, {'balance': 83837, 'deferred': 1257, 'payment': 1933}], ['sample 3', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [6, 3], 'mode': 'defer'}, {'balance': 59058, 'deferred': 885, 'payment': 8607}], ['sample 4', {'principal': 1000000, 'rate_bp': 600, 'months': 12, 'forbear': [2, 1], 'mode': 'defer'}, {'balance': 918934, 'deferred': 4595, 'payment': 86066}], ['sample 5', {'principal': 100000, 'rate_bp': 600, 'months': 12, 'forbear': [12, 1], 'mode': 'defer'}, {'balance': 8560, 'deferred': 43, 'payment': 8607}], ['sample 6', {'principal': 1000000, 'rate_bp': 1200, 'months': 24, 'forbear': [2, 3], 'mode': 'capitalize'}, {'balance': 991814, 'deferred': 0, 'payment': 48486}]]]
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: payments before forbearance{'balance': 100000, 'deferred': 0, 'payment': 4167}{'balance': 100000, 'deferred': 0, 'payment': 4167}Passed
regression: payments before forbearance, partial-repair probe{'balance': 106000, 'deferred': 0, 'payment': 5182}{'balance': 102071, 'deferred': 0, 'payment': 4990}Failed
sample 1{'balance': 1000000, 'deferred': 0, 'payment': 16667}{'balance': 1000000, 'deferred': 0, 'payment': 16667}Passed
sample 2{'balance': 58330, 'deferred': 0, 'payment': 4487}{'balance': 54163, 'deferred': 0, 'payment': 4166}Failed
sample 3{'balance': 250000, 'deferred': 15000, 'payment': 22212}{'balance': 230288, 'deferred': 13818, 'payment': 22212}Failed
sample 4{'balance': 89811, 'deferred': 0, 'payment': 2327}{'balance': 88417, 'deferred': 0, 'payment': 2291}Failed
sample 5{'balance': 100000, 'deferred': 1000, 'payment': 8885}{'balance': 92115, 'deferred': 921, 'payment': 8885}Failed

SHA-256 / f90f2120ecebd3f8398a5802ca405b5302020253161a06ed4ed2df39b5174329

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 2026-09-29T14:46:29.369886+00:00.

Case digest / 054a44b0253e0a4f6a014fb6acc0a15b6fc7b3dd841e4593840b5f78d2f4ca21