New module: StudentLoan.fs — UK Plans 1/2/4/5 and US IBR income-contingent repayment

[Copilot]

Adds a StudentLoan module modelling income-contingent student loan repayments for UK Plans 1, 2, 4, and 5 and the US IBR scheme.

Types

• Plan — UkPlan1 | UkPlan2 | UkPlan4 | UkPlan5 | UsIbr
• RepaymentRate — percentage of income above threshold applied annually
• ThresholdUprating — Fixed | Rpi | GovernmentPolicy
• InterestMethod — NoInterest | Fixed | RpiOnly | RpiPlusScaledMargin (Plan 2 linearly scales from RPI to RPI+3% between ~£27,295–£49,130)
• WriteOffCondition — years until remaining balance is written off
• WriteOffEstimate — FullyRepaid of year | PartialWriteOff of remainingBalance
• ProjectionYear — annual snapshot (income, threshold, repayment, interest charged, closing balance)

Core functions

• planDefaults — returns (RepaymentRate, WriteOffCondition, InterestMethod) for a given plan and RPI rate
• annualRepayment — rate% × max(income − threshold, 0)
• annualInterestRate — resolves the applicable rate for a given income and InterestMethod
• uprateThreshold — applies RPI or policy-rate uprating
• projectBalance — builds a ProjectionYear array up to write-off or full repayment
• estimatedWriteOff — top-level summary returning FullyRepaid or PartialWriteOff

Example

open FSharp.Finance.Personal.StudentLoan

// Project a Plan 2 borrower with £45,000 balance, £35,000 income, 2% income growth, 3.1% RPI
let (repRate, writeOff, interest) = planDefaults Plan.UkPlan2 (Percent 3.1m)

let projection =
    projectBalance
        4500_000L<Cent>          // £45,000
        3500_000L<Cent>          // £35,000 income
        2729_500L<Cent>          // Plan 2 threshold
        (Percent 2m)             // income growth
        (ThresholdUprating.Rpi (Percent 3.1m))
        repRate
        interest
        writeOff

let outcome = estimatedWriteOff ... // WriteOffEstimate.PartialWriteOff or FullyRepaid

All monetary values follow the existing int64<Cent> convention; percentages use Calculation.Percent.