Student loan payoff calculator

How the formula works

The standard repayment plan is a fully amortizing loan, exactly like a mortgage: you pay the same amount \(M\) every month, and it is set so the balance reaches zero after \(N\) months. Interest is charged on the balance that remains, so early payments are mostly interest. The payment is:

where \(B\) is the balance, \(r\) the annual rate as a decimal and \(T\) the term in years. An extra payment changes the arithmetic in the borrower's favour. There is no separate formula for it — the calculator simulates the payoff month by month — but the mechanism is simple: an extra dollar paid this month is a dollar of principal that never accrues interest again. If it would otherwise have sat in the balance for \(k\) more months at rate \(i\), paying it now skips:

which is why extra payments made early in the loan save the most — that dollar had the longest interest tail ahead of it. On federal loans and most private student loans there is no prepayment penalty, so every extra dollar lands directly on principal and shortens the loan.

What each input means

Loan balance — \(B\)

What you owe today across the loan (or the group of loans) you are modelling. Interest that has already capitalised is part of the balance; this model does not add new capitalisation.

Interest rate — \(r\)

The annual rate on the loan. Federal student loans carry a fixed rate set at disbursement; private loans may be fixed or variable. A variable rate is not modelled — the calculator holds the rate constant.

Repayment term — \(T\)

The length of the standard plan. Federal loans default to 10 years; extended and consolidated plans can run 15, 20 or 25. A longer term lowers the required payment but raises total interest, because the balance falls more slowly.

Extra monthly payment

Any amount you add on top of the standard payment, applied straight to principal every month. This is where the calculator earns its keep: it shows what a modest, steady extra does to the payoff date and the interest bill.

A worked example

The worksheet's defaults: a $35,000 balance at 6.5% on the standard 10-year plan, with $100 added to each payment.

• Monthly rate: \(i = 0.065/12 = 0.005417\); over \(N = 120\) months the growth factor is \((1+i)^{120} = 1.9122\).
• Standard payment: $35,000 × 0.005417 × 1.9122 / (1.9122 − 1) = $397.42 a month. Left alone, that clears the loan in 120 months and $12,690 of interest.
• Add $100 a month — paying $497 instead of $397.42 — and the loan is gone in 89 months (7.4 years) with $9,186 of interest.
• The extra costs $100 × 89 = $8,900 in additional principal over the run, but it retires the loan 31 months early and saves $3,504 in interest — money that would otherwise have been paid for nothing but time.

Assumptions and limits

• The rate is fixed for the whole term. Federal student loans are fixed; private loans may be variable, in which case the payoff shifts with the index.
• Standard amortization only. Income-driven repayment (IDR) plans set the payment as a share of discretionary income, not the balance, and can end in forgiveness — the math there is entirely different and this tool does not model it. Public Service Loan Forgiveness (PSLF) is a separate program again.
• No deferment or forbearance, and no interest capitalisation during them, is modelled. In reality unpaid interest can be added to principal and then accrue interest itself.
• Taxes, forgiveness and any interest deduction are ignored. This is arithmetic on the stated inputs, not advice — whether to pay extra, refinance or pursue forgiveness depends on your whole situation.

Questions people ask

How much do extra payments actually help?

More than most people expect, because every extra dollar skips all the future interest it would otherwise have carried. On the worked example — $35,000 at 6.5% over 10 years — adding $100 a month retires the loan 31 months early and saves $3,504 in interest. The effect is largest early in the loan, when each dollar has the longest interest tail ahead of it, and there is no prepayment penalty on federal or most private loans.

Standard versus income-driven repayment — what's the difference?

The standard plan (modelled here) sets a fixed payment that clears the balance over the term. Income-driven repayment (IDR) instead caps the payment at a percentage of your discretionary income, so it can be much lower — and after 20 to 25 years of qualifying payments, any remaining balance is forgiven. IDR can mean paying more interest overall if your income is high, or far less if it stays low; it is a different calculation entirely, not a variant of this one.

Should I refinance my federal loans to a lower rate?

Be careful. Refinancing federal loans with a private lender can lower the rate, but it converts them to private debt and permanently gives up federal protections: income-driven plans, generous deferment and forbearance, and forgiveness programs including PSLF. For someone with secure income and no interest in those programs the interest saving can be real; for anyone who might need the safety net or forgiveness, the lost options usually outweigh a point or two of rate.

What is PSLF?

Public Service Loan Forgiveness cancels the remaining balance on federal Direct Loans after 120 qualifying monthly payments (about 10 years) made while working full time for a government or qualifying non-profit employer. Payments generally must be on an income-driven plan. For borrowers on track for PSLF the optimal strategy is often the opposite of this calculator's — pay the minimum, not extra, since the balance will be forgiven.

Does paying extra hurt me if I might get forgiveness?

It can. If you are pursuing PSLF or IDR forgiveness, extra payments reduce a balance that was going to be cancelled anyway — so the extra money is simply lost. The nuance: forgiveness is not guaranteed until the payment count is complete, and IDR forgiveness (unlike PSLF) may be taxable in some years. If forgiveness is uncertain, some borrowers hedge by saving the extra instead of paying it, keeping the option open. Paying extra is a clear win only when you intend to pay the loan off in full.