FA-58623 / Loan amortization schedules / Member archive

Rule of 78s early payoff rebate: total digits denominator · case 03

Rebates are overstated for every payoff.

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Case contract

x = {'term' n, 'paid' k, 'finance_charge', 'acq_fee' (fully earned up front), 'payment', 'min_rebate'}. Rebatable charge = finance_charge - acq_fee; remaining r = n - k; rebate = round_half_up(rebatable * r(r+1) / (n(n+1))), set to 0 when below min_rebate. Payoff = payment*r - rebate; earned = finance_charge - rebate. Return {'rebate', 'payoff', 'earned'}.

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.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression: total digits denominator	`{"earned": 23750, "payoff": 113750, "rebate": 96250}`	`{"earned": 27600, "payoff": 117600, "rebate": 92400}`	Failed

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