def estimated_aid(total_balance, household_size, household_income):
    """Estimate aid using a Massachusetts cost-adjusted poverty benchmark."""

    if household_size < 1:
        raise ValueError("household_size must be at least 1")
    if total_balance < 0 or household_income < 0:
        raise ValueError("balance and income cannot be negative")

    # Official 2026 federal poverty guideline for the contiguous states.
    federal_poverty_level = (
        15_960 + 5_680 * (household_size - 1)
    )

    # Massachusetts prices are approximately 5.757% above the
    # national average according to the latest available BEA data.
    massachusetts_cost_factor = 1.05757

    # This is an internal cost-adjusted benchmark, not the official FPL.
    adjusted_need_threshold = (
        federal_poverty_level * massachusetts_cost_factor
    )

    # Protect household income up to 200% of the adjusted benchmark.
    protected_income = 2.0 * adjusted_need_threshold

    # Only income exceeding the protected amount is considered available.
    discretionary_income = max(
        0.0,
        household_income - protected_income,
    )

    # Expect 10% of discretionary income to be available for school fees.
    expected_contribution = 0.10 * discretionary_income

    # Aid covers the remaining fee balance.
    estimated = total_balance - expected_contribution

    # Prevent negative awards or awards exceeding the fee balance.
    return round(
        max(0.0, min(total_balance, estimated)),
        2,
    )


def final_rebate(
    total_balance,
    household_size,
    household_income,
    amount_requested,
):
    """Return estimated aid capped by the request and fee balance."""

    if amount_requested < 0:
        raise ValueError("amount_requested cannot be negative")

    estimated = estimated_aid(
        total_balance,
        household_size,
        household_income,
    )

    return min(estimated, amount_requested, total_balance)