Student Loan Repayment Calculator and Payment Formula

This student loan repayment calculator estimates the fixed monthly payment and total interest for a loan when you enter its balance, annual percentage rate (APR), and repayment term. It uses standard amortization math; it does not determine a payment under a particular student-loan program or account for program rules.

Formula

The calculator treats the loan as a fixed-rate balance repaid in equal monthly installments. It first computes the monthly payment, rounds that payment to cents, then multiplies the rounded payment by the number of months and subtracts the original principal to estimate total interest.

• p = starting loan principal, in dollars.
• apr = annual percentage rate entered as a percentage per year.
• r = monthly interest rate, calculated as apr ÷ 1,200.
• n = total number of monthly payments, calculated as years × 12.
• pmt = monthly payment in dollars, rounded to the nearest cent.
• int = estimated total interest in dollars over the full term.

In symbols, pmt = round[p × r ÷ (1 − (1 + r)⁻ⁿ), 2]. Total interest is int = pmt × n − p. The APR is divided by 1,200 because it is expressed as a percentage per year and the calculation uses a monthly rate.

Worked Example

Using the calculator’s default inputs—$20,000 principal, 8% APR, and a five-year term:

1. Convert the APR to a monthly rate: 8 ÷ 1,200 = 0.0066667, or about 0.66667% per month.
2. Find the number of payments: 5 × 12 = 60 months.
3. Apply the payment formula: $20,000 × 0.0066667 ÷ [1 − (1.0066667)⁻⁶⁰] = approximately $405.53 per month after rounding.
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 total interest is $4,331.80. The final payment on a real account can differ because of daily interest calculations, payment dates, fees, or rounding by the servicer.

Assumptions

• The interest rate stays fixed for the full repayment period.
• Payments are equal, made monthly, and applied at the end of each monthly period.
• Interest is modelled monthly at APR divided by 12.
• The estimate excludes fees, late charges, deferment or forbearance, payment changes, capitalization, and any taxes or insurance.
• It does not model student-loan program rules, income-based payments, eligibility, forgiveness, or special repayment benefits.

How to Use the Estimate

Enter the principal you want to model, the APR stated for that balance, and a term in years. For an existing loan, use the current balance if you want a simplified estimate of payments from now onward; the result will not recreate past interest or account activity. If multiple loans have different rates or terms, calculate each separately rather than combining their figures into one loan.

The monthly payment is the amount this fixed-payment model would allocate each month to interest and principal. Early in repayment, interest generally makes up a larger share of each payment; over time, more of the payment reduces principal. The total-interest output is the modeled interest across all scheduled payments, not the total amount paid. Add principal to total interest to get the modeled total payments.

For example, if you are comparing two possible repayment periods, hold the balance and APR constant and change only the term. A longer term usually spreads repayment across more installments and increases the number of months during which interest can accrue; the exact payment and interest depend on the figures entered. This is an arithmetic comparison, not a determination of which arrangement is suitable.

Student Loan Repayment Plans and Calculator Limits

“Student loan repayment plan” can refer to the schedule for paying a loan or to a formal plan whose payment is determined using rules beyond principal, APR, and term. This calculator handles only the first, simplified case: a fixed balance, fixed APR, and equal monthly payments that fully amortize the loan.

It cannot calculate a payment based on income, household information, loan type, enrollment status, a changing interest rate, or program-specific eligibility. It also cannot determine whether a loan qualifies for a benefit or whether payments count toward a program requirement. Those details depend on the applicable program and the account’s records. Ask the loan servicer or program administrator for the rules and payment amount that apply to a particular loan; enter a verified balance, rate, and term here only to see a separate fixed-payment estimate.

Common Mistakes and Practical Checks

• Entering a whole-number rate incorrectly: enter 8 for 8% APR, not 0.08. The calculator converts the percentage to a monthly decimal internally.
• Using the original balance when the balance has changed: the original principal may not match what is currently owed, especially after payments, pauses, or added interest.
• Treating the result as a bill: a servicer’s amount can reflect account-specific accrual, payment timing, unpaid charges, or plan terms that are absent here.
• Assuming every student loan has one rate and schedule: separate loans can have distinct balances, rates, and repayment terms.
• Rounding intermediate figures: small differences can accumulate. The calculator rounds the monthly payment to cents and uses that rounded figure to calculate total interest.

For an adjustable-rate loan, a changing payment schedule, or a payment that does not fully repay the balance by the end of the entered period, this formula may not represent the account. It is also an estimate rather than a payoff quote: an exact payoff amount can depend on the date and interest accrued since the latest payment.

Frequently Asked Questions

How is a student loan monthly payment calculated?
The calculator converts APR to a monthly rate, then applies the fixed-payment amortization formula using the balance and number of monthly payments. It rounds the resulting payment to cents.

Does this calculator show an income-based student loan payment?
No. It uses only principal, APR, and term. It does not include income, family or household details, eligibility, or rules for any repayment program.

Why can my servicer’s payment differ from this estimate?
The servicer may use different payment dates or interest calculations, or the account may include a variable rate, fees, prior unpaid interest, a different term, or program-specific adjustments.

Does total interest include my original loan balance?
No. Total interest is the modeled amount charged for borrowing. Add it to the principal to get the calculator’s estimated total of all scheduled payments.

Can I use this for several student loans at once?
Only if they can reasonably be treated as one loan with a single balance, APR, and term. Otherwise, calculate each loan separately; combined rates and balances can conceal differences in repayment costs.

This result is an estimate for educational arithmetic; the lender’s or servicer’s disclosure gives the exact figures.

Related

• No-Down-Payment Auto Loan Calculator
• BSP Loan Repayment Schedule Calculator
• Loan Repayment Schedule: Calculate Monthly Payments

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 | $ | round(p * (apr / 1200) / (1 - (1 + apr / 1200) ^ -(yrs * 12)), 2) | 2
out int | Total interest | $ | pmt * yrs * 12 - p | 2