Source: https://guthlabs.ai/docs/instruments/student-loan-payoff-idr-estimate/mechanism/
instrument mechanism / verified-clean
# Student Loan Payoff & IDR Estimate mechanism
The inspectable method record for Student Loan Payoff & IDR Estimate, kept separate from implementation and qualification.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## 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
[01**Overview**]()[03**Implementation**]()[04**Qualification**]()
## 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`