Methodology

A financial calculator that will not show its working is asking for trust it has not earned. This page contains everything needed to reproduce any figure the tool produces, and everything needed to find it wrong.

Policy constants in force on this page: version 2026-08-25. Every result screen carries that stamp, so a printed result can be checked against the rules it was produced under.

1. Standard amortization

The level payment that retires a principal over a fixed term:

M = P × [ r(1 + r)ⁿ ] / [ (1 + r)ⁿ − 1 ]

where P is principal, r is the annual rate divided by twelve, andn is the number of monthly payments. When r is zero the formula divides by zero, so that case is handled separately as M = P / n.

Worked example, computed live by the engine

The Department of Education published an example comparing the old ten-year Standard plan with the fifteen-year Tiered Standard plan on a $30,000 balance, giving roughly $341 and $262. Running that through this engine at 6.5%:

These reproduce the published figures. The same case is asserted in the test suite, so a change that broke it would fail the build rather than ship quietly.

2. Income-driven plans

Income-driven plans cannot be evaluated with a closed-form formula, because the payment changes annually with income, unpaid interest behaves differently on each plan, and the loan may end in forgiveness rather than payoff. The engine simulates month by month.

Repayment Assistance Plan

Applicable base payment by AGI band, from 34 CFR 685.209(b)(2), divided by twelve, less $50 per dependent, then the spousal proration if applicable, then a$10.00 floor applied last. The full band table is on the RAP page.

Two provisions that most models omit, and that change the answer materially:

• Interest waiver, 34 CFR 685.209(h)(4)(i). Accrued interest not covered by an on-time payment is not charged. The engine therefore never accumulates unpaid interest under RAP.
• Matching principal payment, 34 CFR 685.209(o)(2)(i). Where an on-time payment reduces principal by less than $50.00, the Department makes up the difference up to the lesser of $50.00 and the payment.

Forgiveness at 360 qualifying payments over at least thirty years.Assumption: the projection assumes every payment is made on time, because a late payment forfeits both provisions for that month and we have no way to predict lateness. That assumption is stated on every result that uses it.

IBR, PAYE and ICR

Discretionary income is income less a multiple of the poverty guideline for family size: 150 percent for IBR and PAYE, and 100 percent for ICR. The ICR figure is frequently misreported as 150 percent. Because the multiple is subtracted from income, using the larger figure leaves less discretionary income and so understates ICR payments, which makes an ICR path look cheaper than it is.

IBR takes 15 percent of discretionary income, or 10 percent for borrowers with "new borrower" status, capped at what the ten-year standard payment would have been at election. PAYE takes 10 percent under the same cap. ICR takes the lesser of 20 percent of discretionary income and a twelve-year fixed amortization adjusted by an income percentage factor.

Under legacy plans, interest that a payment does not cover accrues as unpaid interest on principal and does not compound monthly, because under income-driven repayment interest capitalizes on defined events rather than every month. Compounding it would overstate the cost of staying federal.

Poverty guidelines

2026 HHS figures, from ASPE:

3. Forgiveness and tax

PSLF forgives after 120 qualifying payments and isnot taxable federally. Income-driven and RAP forgivenessis taxable federally for discharges from 1 January 2026, because the American Rescue Plan exclusion expired on 31 December 2025 and was not extended.

The engine applies your stated federal and state marginal rates to income-driven forgiveness and nothing to PSLF forgiveness. Valuing both identically, which every calculator we audited for this site does, overstates income-driven forgiveness by roughly a quarter to two fifths and understates PSLF's relative advantage.

4. Present value, and why it is not optional

Comparing "interest saved over the next ten years" against "a balance forgiven in year thirty" without discounting is not a comparison. It treats a dollar in 2056 as identical to a dollar today. This is the largest single modelling error in the market, and correcting it is why this tool's headline figure is a present value rather than a raw total.

PV = amount / (1 + d/12)^months

Every payment in every scenario is discounted individually and summed, as is any tax due on forgiveness at the month it falls.

5. The verdict

The engine compares the present-value cost of the cheapest federal path against refinancing.

• If refinancing costs materially more, the verdict says refinancing is likely a mistake.
• If refinancing costs materially less, the verdict says it looks favourable on cost, and still lists what is forfeited.
• If the gap is smaller than a material margin, the verdict declines to call it.

The material margin is the greater of $2,500 and five percent of the federal balance. It exists because the protections we deliberately refuse to price are real and can plausibly be worth more than a thin advantage. Announcing a winner on a gap smaller than the value of the things we could not measure would be false confidence.

The verdict never says "you should". It reports what the numbers you entered imply. That is a deliberate constraint, enforced in the test suite, not a stylistic preference.

Where the verdict is anything other than clearly favourable, the affiliate slot isnot rendered at all. It is absent from the page, not hidden with styling.

6. Known limitations

Everything here is a real limitation of this tool, stated plainly.

• Variable rates are held flat. A variable-rate projection assumes today's rate for the entire term, which it will not do. Real variable rates move, and usually not in the borrower's favour when they move a lot.
• Income growth is a single smooth rate. Real incomes step, stall and fall. A steady three percent is a modelling convenience.
• Multiple loans are combined at a balance-weighted average rate for each scenario rather than amortized individually. This is accurate for totals and slightly inaccurate for the shape of the payoff when rates differ widely.
• No origination fees or capitalization events from switching plans are modelled.
• The three-year subsidized interest waiver on IBR and PAYE is not modelled.34 CFR 685.209(h)(2)(i) provides that the Secretary does not charge uncovered accrued interest on Direct Subsidized Loans for the first three consecutive years of repayment under those plans. This tool collapses a portfolio to one balance and one weighted rate, so the subsidized share is not tracked and the waiver cannot be applied. For a subsidized borrower on IBR or PAYE this overstates the cost of staying federal, by up to three years of the uncovered interest. It also makes RAP's own interest waiver look more distinctive than it is.
• The RAP matching principal payment is paid every month. 685.209(o)(2)(i) suspends it during deferment and forbearance. Since periods of deferment are not modelled at all, the match is never suspended, which slightly understates a RAP balance over time.
• Deferment and forbearance are not modelled. Neither their effect on the balance nor the months of forgiveness credit some of them carry under 685.209(k)(8)(i)(C)(7). The pages describe the rules; the projection does not apply them.
• Months already served on an income-driven plan are taken from a single fieldand applied to the whole balance. A borrower whose loans entered repayment at different times has more than one clock, and this models the one they enter.
• The ICR income percentage factor is unmodelled, as described above.
• The IBR knockout for post-July-2026 loans is unresolved for older loans. A loan made on or after 1 July 2026 is outside IBR, PAYE and ICR on either reading of 34 CFR 685.209(d)(5), and the engine applies that. Whether taking such a loan also removes IBR from a borrower's older loans is the open question; the engine takes the less restrictive reading for those and flags the uncertainty on screen. Seethe July 2026 page.
• Employer eligibility for PSLF is your own assessment. The tool takes your answer at face value. Use the Department's PSLF Help Tool to check an employer.
• No lender rates are published on this site. We have no way to verify that any advertised rate is the one you would actually be offered, so the tool asks for the offer you have.

7. How this is tested

The calculation engine has an automated test suite that runs on every build. It asserts against hand-worked amortization examples, the Department's own published Tiered Standard figures, the RAP band table and each of its cliffs, the ordering of the RAP formula, the poverty guideline figures, the IBR standard-payment cap, and the Tiered Standard PSLF threshold. It also asserts behavioural rules: that a defaulted borrower keeps RAP and IBR availability, that the verdict never contains the phrase "you should", and that the affiliate slot cannot appear on an unfavourable result.

If you find a figure you believe is wrong, say so and include the inputs you used. Corrections are published with a date on theeditorial policy page.