Student Loan Calculator

How the Student Loan Calculator works

Use this calculator to understand the arithmetic behind a student-loan balance, payoff scenario, or school borrowing projection before checking Federal Student Aid tools, your servicer, private lender documents, school financial-aid materials, or tax sources. Use Loan Payment for a generic fixed-payment loan, Debt Payoff for multiple debts, Budget for monthly cash flow, and official sources for federal repayment plans, forgiveness, deferment, forbearance, subsidy eligibility, tax deductions, and account-specific instructions.

Simple mode rounds remainingTermYears * 12 + remainingTermMonths into payment months, converts Interest rate to a monthly decimal with interestRate / 100 / 12, then uses PMT = P * m / (1 - (1 + m)^-n). Repayment mode runs month-by-month interest on the current balance, applies the entered monthly payment, adds extraPayment every month for extra-monthly, every twelfth payoff month for extra-annual, once before the simulation for one-time, or treats payoff-now as an immediate balance payoff. Projection mode adds annualLoanAmount at the start of each school year, optionally capitalizes monthly interest during school and grace when Pay interest during school is No, then amortizes the balance after grace over loanTermYears.

Student Loan Calculator formula

This formula page covers the app's Student Loan Calculator: simple fixed-rate repayment for an existing balance, repayment simulation with normal or extra payments, and a school-borrowing projection through graduation and grace period. It does not calculate federal income-driven repayment, forgiveness, subsidy eligibility, deferment, forbearance, consolidation, refinancing, lender approval, tax deductions, private-loan disclosures, or jurisdiction-specific student-finance rules.

Step by step

1. For simple mode, round remaining years and months into payment months with max(1, round(remainingTermYears times 12 plus remainingTermMonths)).
2. Convert the entered annual interest rate into a monthly rate by dividing by 100 and then by 12.
3. If the monthly rate is 0, divide the loan balance by the payment count.
4. Otherwise, solve the fixed-payment amortization formula PMT = P times r divided by 1 minus (1 + r) raised to negative N.
5. Calculate simple-mode total payments as the required monthly payment times N, and total interest as total payments minus the starting balance.
6. For repayment mode, first simulate a baseline payoff using the entered monthly payment with no extra payment.
7. For the selected repayment option, apply payoff-now as an immediate payment of the loan balance with zero modeled interest.
8. For a one-time payment, subtract up to the extra payment amount from the balance before the monthly loop starts.
9. For extra-monthly, add the extra amount to every monthly payment in the loop.
10. For extra-annual, add the extra amount only on simulated months divisible by 12.
11. Each simulated month adds interest to the balance, caps the payment at balance plus current-month interest, subtracts that payment, and adds the interest to total interest.
12. If the first monthly payment plus any first-month extra does not cover first-month interest, the helper returns zero payoff fields rather than projecting endless negative amortization.
13. Calculate interest saved as the positive difference between baseline interest and selected-option interest.
14. For projection mode, start with current balance, add the estimated annual loan amount at the start of each school year, and simulate 12 months of interest for each year.
15. When Pay interest during school is No, monthly interest is capitalized during school and grace period; when it is Yes, the app does not add that interest to the projected balance.
16. After the rounded grace-period months, solve a fixed repayment payment from balance after grace period over round(loanTermYears times 12) months.
17. Use Federal Student Aid, CFPB, IRS, lender disclosures, or local regulator sources before adding repayment-plan, subsidy, forgiveness, tax, private-loan, or jurisdiction-specific claims.

Worked example

Default examples: simple repayment, extra payment, and school projection

The calculator has three different operating modes, so the formula page uses one fixture from each: a simple existing-balance payment, an extra-payment payoff simulation, and a school-borrowing projection.

1. Simple mode with a $30,000 balance, 6 percent annual interest, and 10 years gives N = 120 and r = 0.06 / 12.
2. The fixed-payment formula reports a $333.06 monthly payment.
3. Total payments are reported as $39,967.38, and total interest is $9,967.38.
4. Repayment mode with the same $30,000 balance, 6 percent interest, a $350 monthly payment, and a $150 extra monthly payment uses $500 as the displayed monthly payment with extra.
5. The extra-monthly simulation pays off in 72 months, reports $35,756.90 of total payments, and reports $5,756.90 of total interest.
6. The baseline schedule from the entered $350 payment takes 113 months, so the selected extra-monthly case reports $3,514.20 of interest saved.
7. Projection mode with $10,000 borrowed at the start of each school year for 4 years at 5.5 percent, no in-school interest payments, and a 6-month grace period borrows $40,000 in total.
8. Because interest is capitalized during school and grace in that fixture, the balance is $45,968.05 after graduation and $47,246.74 after grace period.
9. Solving repayment of that post-grace balance over 10 years reports a $512.75 monthly payment, $61,530.16 in total payments, and $21,530.16 in total interest.

The examples show the app's mechanics, not a federal repayment-plan result or lender quote. Small differences in disbursement timing, interest subsidy, capitalization, fees, or repayment-plan rules can materially change real student-loan outcomes.

Assumptions and what this calculator ignores

Geographic scope: works globally. The math is currency-agnostic, so enter amounts in your own currency; local taxes, fees, and product rules are not included.

• The calculator uses a fixed user-entered interest rate and whole-month timing. It does not look up federal loan data, current rates, servicer balances, disbursement dates, payment due dates, IDR payments, graduated or extended repayment schedules, consolidation, refinancing, deferment, forbearance, default, forgiveness, fees, subsidy eligibility, tax treatment, or lender-specific payment rules.
• Repayment mode assumes extra payments reduce the simulated balance according to this app's schedule. Real servicers may apply payments first to fees, then interest, then principal, and extra payments can be handled differently unless the borrower gives account-specific instructions.
• Projection mode is a simplified borrowing model. It adds the same estimated loan amount at the start of each school year, capitalizes interest monthly only when the interest-during-school option is No, and applies the selected grace period before repayment. Federal Student Aid, CFPB, IRS Publication 970, private lender disclosures, school financial-aid materials, and local regulatory sources are needed before making federal-plan, capitalization, grace-period, private-loan, tax, legal, borrower-rights, product-specific, or jurisdiction-specific claims. Scoped independent comparator checks pass 4 of 4 scoped fixtures for overlapping simple, repayment, and projection outputs. Results are educational estimates, not financial, tax, legal, lending, student-aid, borrower-rights, regulatory, or personalised advice.

What this formula does not include

• The calculator uses a fixed annual interest rate converted to a monthly rate. It does not look up federal, state, school, servicer, or private-lender rates.
• Simple mode is a standard amortization estimate from balance, rate, and remaining term. It does not include fees, subsidy status, repayment-plan eligibility, or statement-specific servicing rules.
• Repayment mode simulates monthly interest and payments. It does not model exact due dates, daily interest accrual, payment posting order, capitalization events, servicer rules, late fees, skipped payments, auto-debit discounts, or prepayment allocation instructions.
• The extra-payment input is shared across extra-monthly, extra-annual, and one-time modes. The independent comparator exposes separate extra-monthly, annual, and one-time fields, so the interfaces are not identical.
• Payoff-now is modeled as paying the current loan balance immediately with no future scheduled interest. It is not a payoff quote and does not include accrued unpaid interest, fees, or servicer payoff instructions.
• If the entered payment cannot cover first-month interest, the payoff helper returns zero payoff fields. Users should treat that as a warning that the inputs do not amortize under this simple model.
• Projection mode adds the estimated annual borrowing amount at the start of each school year. Other calculators, schools, or lenders may assume different disbursement timing.
• Projection mode capitalizes monthly interest during school and grace only when Pay interest during school is No. It does not determine whether a real loan is subsidized, unsubsidized, deferred, in forbearance, or eligible for an interest subsidy.
• Projection validation currently compares amount borrowed for the independent comparator projection fixture because the independent comparator appears to use a different annual disbursement or capitalization timing convention.
• The app does not calculate income-driven repayment, graduated repayment, extended repayment, deferment, forbearance, consolidation, refinancing, public service forgiveness, default consequences, tax deductions, or private-lender disclosures.
• Federal Student Aid and CFPB sources are needed before making federal repayment-plan, grace-period, capitalization, borrower-rights, or private-loan context claims. IRS Publication 970 is needed before discussing US student-loan interest tax deduction treatment.
• Scoped independent comparator checks currently pass 4 of 4 scoped fixtures for simple monthly repayment, normal repayment, extra-monthly repayment, and in-school projection, with the projection fixture scoped as noted above.
• The result is an educational estimate from the entered assumptions, not financial, tax, legal, lending, student-aid, borrower-rights, regulatory, or personalised advice.

Common mistakes to avoid

• Using Simple mode as if it were an official federal repayment-plan result. It is fixed-rate amortization math and does not model income-driven repayment, graduated payments, extended repayment, forgiveness, or subsidy rules.
• Assuming every extra payment will be applied exactly like this simulation. Real payment allocation, paid-ahead status, fees, accrued interest, and servicer instructions can change how much principal is reduced.
• Reading Projection mode as a financial-aid award, school cost estimate, lender quote, tax answer, or eligibility decision. The model uses the entered annual borrowing amount and interest assumption; real balances depend on actual disbursement timing, subsidy status, capitalization events, lender terms, and tax rules.

Key terms

Capitalized interest

Interest added to the unpaid principal balance, so later interest can be charged on a larger balance. Projection mode capitalizes monthly interest during school and grace only when Pay interest during school is set to No.

Extra-payment simulation

A month-by-month payoff model that adds the selected extra-payment pattern to the regular payment. It helps compare timing in the app, but a real servicer's allocation rules and instructions may differ.

Grace period

A period after leaving school before repayment begins, if the loan terms provide one. The calculator uses the months entered on the page; real federal and private loan grace rules depend on loan type and documents.

Frequently asked questions

Methodology, sources, and disclaimer

This calculator is an original three-mode student-loan model: simple amortization, extra-payment repayment simulation, and a school-years borrowing projection with grace-period interest capitalization, validated by deterministic fixtures and edge-case tests. It is not copied from a single source.

Fixtures pin the interest-saved comparison, capitalization through school and grace, and the balance-after-graduation trace. The result remains an educational estimate, not a federal repayment-plan result or a servicer statement.

Formula version 2026.05.22-generic-student-loan. The version marks the calculation logic and validation fixture set used for this estimate.

• Federal Student Aid Loan Simulator and repayment-plan materials should be used when copy discusses federal repayment-plan context, standard repayment, graduated repayment, extended repayment, income-driven repayment, grace periods, consolidation, deferment, forbearance, default, or forgiveness.
• Federal Student Aid subsidized and unsubsidized loan and interest materials should be used when copy discusses interest accrual, capitalization, subsidy eligibility, in-school status, or grace-period interest for US federal student loans.
• CFPB student-loan materials should be used when copy discusses borrower-facing repayment-start timing, private student loans, repayment problems, servicer context, or consumer student-loan rights.
• IRS Publication 970 should be used before copy discusses US student-loan interest tax deduction treatment.
• Private lender disclosures and relevant local regulator or government sources should be used before copy makes private-loan, product-specific, jurisdiction-specific, approval, fee, prepayment, refinancing, tax, legal, or regulated student-finance claims.

Results are educational estimates, not advice. Read the full disclaimer.

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