Student Loan Repayment Calculator and Monthly Payment Formula

Calculate an estimated monthly student loan payment by entering the loan balance, annual interest rate, and repayment term. The calculator uses a fixed-rate, level-payment formula and also estimates total interest over the full term; it does not model a particular loan program or repayment plan.

Formula

The monthly payment is the level payment that pays down principal and covers monthly interest over the selected number of payments:

Payment = P × r ÷ [1 − (1 + r)⁻ⁿ]

• P is the amount borrowed, in dollars.
• r is the monthly interest rate as a decimal: annual APR ÷ 1200. For an 8% APR, r = 8 ÷ 1200.
• n is the number of monthly payments: years × 12.

Total interest is calculated as the monthly payment multiplied by the number of payments, minus the original loan amount: Total interest = payment × n − P. The calculator displays the payment to cents, then uses that displayed, rounded payment for the interest estimate. This can create a small difference from a calculation that keeps extra decimal places throughout.

Worked Example

Using the calculator’s defaults: a $20,000 loan, 8% APR, and a five-year term.

1. Convert the annual APR to a monthly decimal rate: 8 ÷ 1200 = 0.0066667.
2. Convert the term to months: 5 × 12 = 60 payments.
3. Substitute into the payment formula: $20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)⁻⁶⁰] = $405.53 per month, rounded to cents.
4. Calculate total interest using the rounded payment: $405.53 × 60 − $20,000 = $4,331.80.

The estimated monthly payment is $405.53, and estimated interest across 60 payments is $4,331.80.

Assumptions

• The interest rate remains fixed for the entire repayment term.
• Payments are equal, made monthly, and paid at the end of each monthly period.
• Interest accrues monthly using the APR divided by 12.
• The estimate excludes fees, taxes, insurance, deferment, payment pauses, and changes to the balance or repayment schedule.

How to Use the Estimate

Enter the balance to be repaid, the annual percentage rate supplied for the loan, and the planned repayment term in years. The loan amount should reflect the amount on which repayment is calculated, not necessarily the original amount borrowed if payments or balance changes have already occurred. Use the APR as a percentage—for example, enter 6.5 for 6.5%, not 0.065.

The result is a mathematical estimate for a standard amortizing loan: each payment covers that month’s interest first, with the remainder reducing principal. Early in repayment, a larger share of the payment goes toward interest; as the balance falls, more goes toward principal. With a fixed rate and regular full payments, the balance is intended to reach zero at the end of the term, subject to rounding and the loan’s actual payment rules.

The total-interest figure assumes every scheduled payment is made on time and the rate and balance do not change. It is not the total amount paid: add the principal to interest to estimate total repayment. In this example, that is $20,000 + $4,331.80 = $24,331.80.

What Changes a Student Loan Payment?

• Principal: A larger balance increases the payment when rate and term stay the same.
• APR: A higher input rate increases the payment and generally raises total interest.
• Term: A longer term usually lowers each scheduled payment but extends the time interest can accrue, increasing total interest under this formula.
• Payment structure: A variable rate, graduated payments, interest-only periods, or payments tied to income do not follow this fixed-payment calculation.

For instance, comparing two terms is useful only when the balance and APR are held constant. The resulting figures describe the arithmetic trade-off between payment size and repayment duration; they do not establish which arrangement is suitable for any particular person. Get the actual rate, payment schedule, and any charges from the loan servicer or lender.

Limits and Common Calculation Errors

This calculator covers general loan arithmetic, not the detailed terms of a specific student loan. It does not determine eligibility, account for program-specific repayment rules, or estimate payment changes under an income-based arrangement. Program rules are not modelled; check the applicable program information or contact the servicer for details. It also does not account for a changing rate, unpaid interest added to principal, extra payments, skipped payments, or fees.

• Do not enter an APR in decimal form. The input is a percentage, so 8 means 8%.
• Do not confuse years with months. The term field is in years, and the formula converts it to months.
• Do not assume the displayed payment is an exact payoff quote. Cent rounding, due dates, accrued interest, and servicing rules can affect an actual final payment.
• Do not add a fee to the balance unless it is actually financed and included in the amount being repaid.

If the loan has multiple portions with different rates or terms, calculating each portion separately and summing the results may better represent the scheduled payment. Any result remains an estimate, not a statement of the balance or amount due on a particular date. This is estimate arithmetic for education, not financial advice; the lender’s disclosure gives the exact figures.

Frequently Asked Questions

How do I calculate a monthly student loan payment?
Convert APR to a monthly decimal by dividing the percentage by 1200, convert years to months, then use the level-payment formula shown above with the loan balance.

Does this estimate include interest?
Yes. The monthly payment includes principal and interest under the fixed-rate assumptions. The separate total-interest output estimates interest paid over all scheduled payments.

Why can my servicer’s payment differ?
The actual loan may have a different balance, rate, term, payment date, interest accrual method, fees, or repayment structure. Compare the calculator inputs with the current loan disclosure or statement.

Does a longer repayment term lower total cost?
Not necessarily. In this formula, a longer term generally reduces each monthly payment while increasing the number of months interest accrues, which can raise total interest.

Can I use this for an income-based repayment amount?
No. The calculator models equal monthly payments on a fixed-rate amortizing loan. It does not calculate payments set by income or other program-specific rules; check with the servicer or the program for those details.

Related

• Daily Student Loan Interest Calculator
• Student Loan Payment Calculator: Standard Monthly Payment

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in yrs | Loan term | years | 5 | 0.0833 | 50
out pmt | Monthly payment | $ | p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2