Student Loan Payoff & IDR Estimate mechanism

Model scope

The standard amortization algorithm is mathematically sound under the stated fixed-rate, monthly-payment assumptions. The IDR calculation is only a configurable educational approximation, not a universal federal formula. Before production use, specify the exact plan convention, HHS guideline year and jurisdiction, AGI definition, rate/payment timing, and precise meaning of payoff time. The existing educational-only and servicer-disclaimer labeling is appropriate but should explicitly state the assumed IDR percentage and poverty multiplier.

• The standard amortization formula is correct only when rate periodicity, payment frequency, fixed term, and end-of-period payments are explicitly defined.
• The IDR formula is not uniquely determined by 'plan type': the percentage of discretionary income and poverty multiplier vary by federal plan and sometimes loan-borrower circumstances. The spec does not define either parameter.
• The stated discretionary-income formula needs a nonnegative floor: max(0, AGI - poverty guideline × multiplier).
• The input says income, but the formula requires AGI; gross income, taxable income, and AGI are not interchangeable.
• Payoff time is undefined: it could mean the stated standard term, payoff under the standard payment, or IDR repayment/forgiveness timing. IDR payments generally change with income, family size, recertification, interest accrual, and plan rules.
• Federal poverty guidelines require a year, geographic jurisdiction, and household-size definition. The specification does not identify these.

Units and conventions

• Balance is in U.S. dollars.
• Annual interest rates are nominal rates compounded monthly; monthly rate equals annual rate divided by 12.
• Income is annual AGI in U.S. dollars.
• Poverty guidelines use the HHS 2024 annual guideline for the contiguous 48 states and District of Columbia.
• Family size is an integer household size matching the HHS table.
• The test IDR convention is a simplified 10% of positive annual discretionary income above 150% of the applicable poverty guideline, paid monthly.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "balance_usd": 0,
    "annual_rate": 0.05,
    "term_months": 120,
    "annual_agi_usd": 20000,
    "family_size": 1,
    "plan_type": "simplified_10pct_150pct_poverty",
    "idr_percent": 0.1,
    "poverty_multiplier": 1.5
  },
  "expected_outputs": {
    "standard_monthly_payment_usd": 0,
    "estimated_idr_monthly_payment_usd": 0,
    "standard_payoff_time_months": 0
  },
  "reference_data": {
    "hhs_2024_poverty_guideline_usd_family_1": 15060,
    "source_convention": "HHS 2024 Poverty Guidelines, contiguous 48 states and District of Columbia"
  },
  "working": "Monthly rate = 0.05 / 12 = 0.0041666667. Standard payment = 0 × 0.0041666667 / [1 − (1.0041666667)^(-120)] = 0.00. Poverty threshold = 15060 × 1.5 = 22590. Annual discretionary income = max(0, 20000 − 22590) = 0. IDR payment = 0 × 0.10 / 12 = 0.00. With zero balance, payoff time = 0 months."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The literal standard amortization formula is undefined at a zero interest rate because its denominator becomes zero, and the simplified IDR formula has unspecified behavior for zero balances and negative discretionary income.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json