calculate-loan

01 Loan payments

US Student Loan Repayment Calculator and Guide

Calculator No. 01-4170 · Updated · Formula and assumptions shown below

Monthly payment $405.53
Total interest
$4,331.67
= Monthly payment × loan term × 12 − loan amount
Loan amount
$20,000
Input
Interest rate (APR)
8 %
Input
You enter
Loan amount ($), Interest rate (APR) (%), Loan term (years)
You get
Monthly payment ($), Total interest ($)
Rounding
2 dp

Estimate for education, not financial advice. The result follows from the numbers you enter and the formula shown. It is not a quote or an offer, and it does not include fees, taxes or insurance unless the calculator asks for them. Ask your lender for the exact figures.

This US student loan repayment calculator estimates a fixed-rate loan’s monthly payment and total interest from the balance, annual percentage rate (APR), and repayment term you enter. It uses standard monthly amortization; it does not calculate federal repayment-plan payments, income-based amounts, or forgiveness.

Formula

The calculator assumes equal monthly payments, a constant APR, and interest accruing monthly. The standard payment formula is:

Monthly payment = P × r ÷ [1 − (1 + r)−n]

  • P is the starting loan principal, in dollars.
  • r is the monthly interest rate as a decimal: annual APR ÷ 12 ÷ 100.
  • n is the number of monthly payments: years × 12.
  • Total interest is monthly payment × number of payments − principal.

The APR input is expressed as a percentage per year, so 8 means 8%, not 0.08. For this calculation, 8% APR gives a monthly rate of 0.08 ÷ 12, or about 0.006667. The formula presumes the calculated payment is made on schedule and does not change.

Worked Example

Using the calculator’s defaults—$20,000 principal, 8% APR, and five years—the number of monthly payments is 5 × 12 = 60. The monthly rate is 8 ÷ 1200 = 0.0066667.

Substitute those values into the payment formula:

Payment = 20,000 × 0.0066667 ÷ [1 − (1 + 0.0066667)−60] = $405.53 per month

The displayed payment is rounded to the nearest cent. Total interest is calculated using that rounded payment: $405.53 × 60 − $20,000 = $4,331.80. The resulting scheduled payments total $24,331.80, including principal and interest.

Assumptions

  • The interest rate remains fixed for the full term.
  • Payments are equal, made monthly, and begin on schedule; the formula does not model a payment date or grace period.
  • Interest is compounded monthly using APR divided by 12.
  • Fees, taxes, insurance, deferment, forbearance, missed payments, extra payments, and payment-plan changes are not included.

How US Student Loan Repayment Works

In the United States, “student loan repayment” can refer to paying down a private education loan or a federal student loan. Both may involve principal and interest, but the options and rules can differ. This calculator covers only the arithmetic of a single fixed-rate loan paid in equal monthly installments. It is not a substitute for a servicer’s payment schedule or an official repayment-plan estimate.

Federal loans may offer repayment plans or other provisions that change the required payment or the time it takes to repay. Some options depend on loan type, borrower circumstances, or program rules. Those details change over time and are not modelled here; check current information with the loan servicer or the relevant program. Private loan contracts can also specify different rates, payment structures, and conditions. Use the terms shown in the applicable loan disclosures rather than assuming every student loan follows this formula.

A borrower may have several loans with different balances, rates, or terms. This calculator treats the entered principal as one loan. For a rough combined estimate, calculate each loan separately and add the monthly payments, but do not assume that sum is the amount required under a particular repayment plan.

How to Use and Read the Estimate

  1. Enter the principal you want to model. For an existing loan, use its current balance if the goal is to estimate future payments from now; accrued unpaid interest or fees may affect the actual balance.
  2. Enter the annual APR as a percentage. Confirm whether the figure is fixed or variable and whether it includes costs that affect the loan’s disclosed APR.
  3. Enter the repayment term in years. Convert a term stated in months by dividing the number of months by 12.
  4. Read the monthly payment and total interest together. The first is the modeled scheduled payment; the second is the interest implied by making that rounded payment for the full term.

For example, a longer term generally spreads repayment across more payments, while interest has more time to accrue. This calculator shows the mathematical effect of the chosen inputs, not whether a term or payment arrangement is suitable for a particular person. To model a variable-rate loan, changing balance, or extra monthly amount, a different calculation is needed.

Common Questions and Misconceptions

Is this the payment I will owe? Not necessarily. A servicer’s required amount can reflect the loan’s current balance, due dates, plan terms, unpaid interest, fees, or other details that this simple model omits. Use the official account or disclosure for the amount due.

Does total interest include the amount borrowed? No. Total interest is the estimated cost of interest alone. Adding it to the starting principal gives the modeled total of payments. It is not a payoff quote, since a payoff amount can depend on the date and accrued interest.

Why might my result differ from a servicer’s estimate? The APR, balance, payment timing, rounding method, or term may differ. A loan may also have variable interest, fees, unpaid accrued interest, or a repayment structure that is not a level-payment schedule. Check that the inputs use the same figures and period as the servicer’s calculation.

Frequently Asked Questions

How is a student loan monthly payment calculated?
For a fixed-rate loan with equal monthly payments, the payment is principal multiplied by the monthly rate, divided by one minus the discount factor for all monthly payments. The calculator applies that standard amortization formula.

What does APR mean in this calculator?
APR is the annual percentage rate entered as a percentage. The formula converts it to a monthly rate by dividing by 1,200. The lender’s disclosure is the source for the applicable rate and how it is defined for a specific loan.

Can I use this for federal student loans?
You can use it to estimate ordinary fixed-rate amortization, but it does not calculate federal repayment-plan payments, eligibility, or forgiveness. Check current program details with the servicer or relevant program.

Does the estimate include extra payments?
No. It assumes the same scheduled payment each month and no extra principal payments. Extra payments can change the payoff timing and interest, but their effect depends on how they are applied to the loan.

Why is my actual total interest different?
Actual interest can differ because the balance, rate, payment dates, rounding, or repayment terms are not identical to the assumptions here. A variable rate or payment changes will also alter the result.

This result is an estimate, and the lender’s disclosure gives the exact figures.

Related

Formula used
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

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard loan formula for this calculation, fixed rate and monthly compounding unless stated, rounded as each result states. Not financial advice; no lender, rate or product is recommended. See formulas and assumptions, the disclaimer or report an error.

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