Student Loan Calculator Explained

One amortisation formula, two very different repayment systems

Strip away the acronyms — SAVE, PAYE, IBR, PSLF on the US side; Plan 1, Plan 2, Plan 4, Plan 5, Postgraduate on the UK side — and a student loan with a fixed monthly payment is the same arithmetic as any other instalment loan. The student loan calculator runs the standard amortisation formula in one line: enter the current balance, the APR, and the monthly payment, and it returns the years and months to clear the loan, the total amount paid, and the total interest. Add an optional extra monthly payment and the panel updates with how much faster the loan clears and how much interest you save.

What the calculator cannot do is decide whether you should pay the loan off voluntarily. For a US federal borrower pursuing Public Service Loan Forgiveness, voluntary prepayment is value-destroying — the money would have been forgiven. For a UK Plan 2 graduate whose career trajectory will not clear the balance before the 30-year statutory write-off, voluntary repayment is money that would otherwise not have left the bank account. The arithmetic is the easy part; the policy is the rest of this article.

The amortisation formula

Every fixed-rate instalment loan — mortgage, car finance, personal loan, federal student loan — follows the same month-to-month accounting:

1. Interest for the month = current balance × (APR ÷ 12).
2. Payment goes to interest first, then to principal.
3. New balance = old balance + interest − payment.
4. Repeat until balance reaches zero.

Running that loop month by month gives the same answer as the closed-form solution that the calculator uses:

k = −log(1 − B·r ÷ P) ÷ log(1 + r)

where B is the starting balance, r is the monthly rate (APR ÷ 12), and P is the total monthly payment (base plus any extra). The output k is the number of months until the loan is fully paid. When r is zero — an interest-free loan, which for student loans only exists for US Subsidised loans during deferment — the formula collapses to k = B ÷ P. If P is less than or equal to B·r, the payment cannot cover the monthly interest charge and the loan never amortises; the balance is flat (if P = B·r exactly) or growing (if P < B·r). The calculator detects this case and returns a “payment too small” flag instead of an infinite timeline.

A worked example: $30,000 at 6.5%

Take a typical US Direct Unsubsidised loan at the 2024–25 undergraduate rate: $30,000 balance, 6.53% APR, paying $340 per month. Monthly rate r = 0.0653 ÷ 12 = 0.005442. Plugging in:

• B·r = 30,000 × 0.005442 = $163.25 (month 1 interest)
• 1 − B·r ÷ P = 1 − 163.25 ÷ 340 = 1 − 0.4801 = 0.5199
• −log(0.5199) ÷ log(1.005442) ≈ 0.654 ÷ 0.005427 ≈ 120 months

The loan clears in 120 months — exactly the 10-year Standard Federal repayment term. Total paid = 120 × $340 = $40,800. Total interest = $40,800 − $30,000 = $10,800. That single round number is no accident: the $340/month payment is derived from the 10-year amortisation formula at 6.53%, so the calculator is round-tripping the same arithmetic the Department of Education uses to set the Standard payment.

Now add $50 extra each month, so the total payment is $390:

• 1 − 163.25 ÷ 390 = 0.5814
• −log(0.5814) ÷ log(1.005442) ≈ 0.542 ÷ 0.005427 ≈ 100 months

The loan clears in 100 months, or 8 years 4 months — 20 months faster. Total paid = 100 × $390 = $39,000. Total interest = $9,000. The extra $50 per month saves about $1,800 of interest and clears the loan nearly two years early. The calculator runs that comparison automatically in the result panel so you can see the before/after side by side.

US federal student loans: the rate table that matters

US federal Direct Loans are fixed-rate at first disbursement and carry that rate for life. The Department of Education sets new rates each July based on the May 10-year Treasury auction plus a margin defined in statute. The 2024–25 published rates (effective for loans first disbursed 1 July 2024 to 30 June 2025) are:

• Direct Subsidised and Unsubsidised, undergraduate: 6.53%
• Direct Unsubsidised, graduate and professional: 8.08%
• Direct PLUS (Grad PLUS and Parent PLUS): 9.08%

Loans first disbursed in earlier years have lower rates. Direct Loans from 2020–21 are 2.75% (undergraduate) or 4.30% (graduate). A borrower with several loans across multiple academic years typically has a portfolio of different rates; each loan amortises independently against the monthly payment, with the servicer allocating extra payments to the highest-rate loan unless the borrower instructs otherwise.

The authoritative source is studentaid.gov — the Department of Education publishes the current and historical rate table there. For an exact APR on a specific loan, log into the servicer's portal (Mohela, Nelnet, Aidvantage, EdFinancial, MOHELA, or whichever Direct Loan servicer is assigned). Private student loans are issued by SoFi, Sallie Mae, Discover, College Ave, and others; they are either fixed or floating SOFR-linked and the rate depends on credit score, cosigner, and choice of in-school or after-graduation repayment.

UK student loans: five plans, one income-contingent design

UK student loans are administered by the Student Loans Company and structured as income-contingent loans. The monthly “payment” is set by salary, not by balance, deducted automatically via PAYE, and the loan is statutorily written off after a fixed number of years regardless of how much remains. There are five active plans:

• Plan 1 — pre-September 2012 English/Welsh undergraduates, plus most Northern Irish loans. Threshold £24,990 (2024–25), 9% above. Interest = RPI or Bank of England base + 1%, whichever is lower. Written off after 25 years, or at age 65.
• Plan 2 — September 2012 to July 2023 English/Welsh undergraduates. Threshold £27,295. Interest = RPI + 0–3% sliding scale with income, capped at the “prevailing market rate”. Written off after 30 years from the April after graduation.
• Plan 4 — Scottish undergraduates from any year. Threshold £31,395. Interest = RPI or BoE base + 1%, whichever is lower. Written off after 30 years, or at age 65.
• Plan 5 — post-August 2023 English undergraduates. Threshold £25,000. Interest = RPI only. Written off after 40 years.
• Postgraduate Loan — Master's and PhD loans across the UK. Threshold £21,000, 6% above. Interest = RPI + 3%. Written off after 30 years.

A graduate on Plan 2 earning £40,000 pays 9% × (£40,000 − £27,295) = £1,143.45 per year, or about £95 per month. That number is independent of whether the balance is £20,000 or £80,000 — the SLC takes the same payment either way and the rest of the balance accrues interest in the background. For most Plan 2 and Plan 5 graduates, the balance never reaches zero before write-off. The Institute for Fiscal Studies has projected that under Plan 5, around 65–70% of borrowers will repay in full over 40 years; under Plan 2, the share was closer to 17%.

The current applicable interest rate is published by the Student Loans Company at gov.uk. For Plan 2, the rate changes at least annually each September based on the previous March RPI, and is capped at the prevailing market rate when RPI runs above commercial unsecured lending rates.

When extra payments save money — and when they don't

Voluntary overpayments on a student loan earn a guaranteed risk-free return equal to the loan APR. On a US federal loan at 6.5%, that beats almost every cash savings account and compares well with equity-market expected returns after tax. For a Plan 2 UK graduate paying 7.7% on a balance that they will clear in full, the same logic applies.

There are three situations where the pure-maths answer is wrong:

1. You are pursuing US loan forgiveness. Public Service Loan Forgiveness wipes the remaining balance after 120 qualifying payments on an income-driven plan while working for a qualifying employer (government, 501(c)(3) non-profit). Income- driven repayment plans on their own forgive after 20–25 years. Voluntary prepayment shortens the timeline and shrinks the eventual forgiven amount — you are destroying the value the policy is designed to give you. The same logic applies to Teacher Loan Forgiveness, Perkins Loan cancellation, and the various state-specific programmes.
2. You are a UK Plan 2/4/5/Postgrad borrower who will not clear the loan before write-off. If your projected lifetime earnings mean the SLC will write the balance off after 30 or 40 years, every voluntary repayment is money that would never have been deducted via PAYE. The Money Saving Expert “should I repay my student loan early” tool models this in detail; the rough heuristic is that if you do not expect a high-earning trajectory (sustained income meaningfully above the upper threshold for the bulk of 30 years), do not overpay.
3. You have higher-rate debt or no emergency fund. Credit-card APRs of 20%+ destroy the maths advantage of a 6.5% student-loan overpayment. Clear those first. Then build a 3–6 month emergency fund. Then capture any employer 401(k) or pension match. Student-loan overpayments come after those three priorities — and only for borrowers in cases where the maths actually applies.

Refinancing trade-offs

US federal borrowers can refinance with a private lender to get a lower rate, but the new private loan loses every federal protection — no IDR plans, no PSLF, no death and disability discharge, no future forgiveness programmes that may be enacted. Refinancing is mostly attractive for high-earning graduate-school borrowers (medicine, law, MBA) with stable incomes who will never qualify for IDR forgiveness and want a lower headline rate. For everyone else, the federal protections are worth more than the rate spread.

UK student loans cannot be refinanced — they are not consumer credit and there is no private replacement. The only real lever is voluntary overpayment, and the write-off horizon decides whether that is sensible. UK graduates with substantial savings sometimes ask whether they should clear the balance in a lump sum; the answer is the same heuristic as above. If you would clear the loan through PAYE deductions anyway over the next decade, the lump-sum payoff saves you the interest that would have accrued. If you would not, it is a charitable donation to HMT.

How the calculator handles edge cases

The student loan calculator deliberately models the “fixed payment, voluntary payoff” scenario, not the income-driven repayment path. A few things to know about how it behaves at the edges:

• Payment too small. If the monthly payment is less than or equal to the monthly interest accrual (B·r), the calculator returns a “payment too small” flag instead of attempting to divide by zero. The break-even monthly payment at APR is B × APR ÷ 12.
• Zero interest. If you enter 0% APR, the calculator uses k = B ÷ P, rounded up to the next whole month.
• Extra payment. The extra-payment field adds to every month's payment from month 1. To model a one-time lump sum, instead reduce the starting balance by the lump sum and keep the regular monthly payment.
• Variable rates. The calculator uses a single fixed APR. For UK Plan 2 and Plan 5 with annual rate resets, either use the current applicable rate as a near-term snapshot or use a long-run RPI assumption plus the plan margin.
• Multiple loans. The calculator handles one loan at a time. For a portfolio of US federal loans at different rates, model each loan separately, or enter the weighted-average APR and the combined balance for a rough portfolio-level view.

Where to get the real numbers

Garbage in, garbage out — the answer is only as good as the balance and APR you feed it. For US borrowers, the authoritative source is studentaid.gov for federal loans and the servicer dashboard (Mohela, Nelnet, Aidvantage, EdFinancial) for live balances and APRs on each individual loan. Private-loan balances are on the lender's portal (SoFi, Sallie Mae, Discover, College Ave).

For UK borrowers, sign in to the Student Loans Company portal at gov.uk for the current balance and applicable interest rate. HMRC only knows about deductions taken via PAYE within the current tax year; the SLC has the running balance.

Related calculators

Once the student-loan plan is set, a handful of adjacent calculators help with the rest of the personal-finance picture:

• Amortisation calculator — takes a loan term in years and returns the level monthly payment. Useful for confirming what a US Standard 10-year repayment payment should be from a given balance and APR.
• Personal loan calculator — monthly payment and total cost on a fixed-term consumer loan, useful for comparing private student-loan refinance offers.
• Compound interest calculator — models the inverse problem of how a balance grows when nobody is making payments, which is exactly what is happening to the unrepaid portion of a UK Plan 2 or Plan 5 loan.
• Debt avalanche calculator — when student-loan overpayment is the right call, this orders multiple debts so the highest-APR loan is cleared first.
• Budget calculator — works out how much of monthly take-home can be allocated to debt repayment without breaking the rest of the household budget.

The short version

A student loan with a fixed monthly payment amortises like any other instalment loan; the calculator runs the closed-form formula in one step. The interesting questions are policy, not arithmetic: whether to pursue US forgiveness, whether your UK earnings trajectory means voluntary repayment is destroying value, and where student-loan overpayment sits in the personal-finance priority stack. The maths is the easy part — use the calculator for that, and treat the rest as a separate decision.