The basic formula: loan amount, interest rate, and loan term

Your monthly payment depends on three numbers: how much you borrowed, what interest rate you're charged, and how many months you have to repay. The standard formula multiplies your loan balance by a factor that accounts for both the interest rate and the repayment timeline. If you know these three pieces, you can work out what you owe each month—or verify what your servicer is charging you.

The calculation itself is straightforward algebra, but the numbers that go into it vary depending on your loan type and repayment plan. Federal loans use one formula. Private loans use another. Income-driven repayment plans use a third. Understanding which applies to you matters because the same $30,000 loan can produce monthly payments ranging from $200 to $600 depending on the plan you choose.

Key Takeaways

  • Standard repayment on federal loans uses a fixed monthly payment calculated over 10 years; the formula multiplies your loan balance by an interest factor based on your rate.
  • Income-driven plans calculate payments as a percentage of your discretionary income (usually 10 to 20 percent), not based on the loan amount itself.
  • Private loans use the same mathematical formula as federal standard repayment, but the interest rate is often variable and can change annually.
  • You can calculate your payment by hand using the amortization formula, or use your loan servicer's calculator, which accounts for any existing payments already made.
  • The longer your repayment term, the lower your monthly payment but the more interest you pay overall.

Federal loans on the standard 10-year plan

Federal loans on standard repayment use a fixed monthly payment spread over 120 months (10 years). The payment is calculated using the amortization formula, which divides your loan balance by a factor that reflects both your interest rate and the number of months remaining.

The formula is: M = P × [r(1 + r)^n] / [(1 + r)^n − 1], where M is your monthly payment, P is your principal (the amount borrowed), r is your monthly interest rate (annual rate divided by 12), and n is the number of months (120 for standard repayment).

Example: You borrowed $25,000 at 5.5 percent annual interest. Your monthly rate is 0.055 ÷ 12 = 0.00458. Over 120 months, this produces a monthly payment of approximately $483. If you borrowed $50,000 at the same rate, your payment would be approximately $966. The payment scales directly with the loan amount.

Your loan servicer (the company that collects your payments) calculates this for you and shows it on your bill. You do not need to do the math yourself unless you are comparing scenarios or checking their work. Most servicers also provide an online calculator where you enter the loan amount and rate and it shows you the payment.

Income-driven repayment plans: a different calculation entirely

Income-driven plans—Revised Pay As You Earn (REPAYE), Pay As You Earn (PAYE), Income-Based Repayment (IBR), and Income-Contingent Repayment (ICR)—do not use the loan amount to calculate your payment. Instead, they use your income and family size.

The formula is: Monthly payment = (Discretionary income) × (Percentage rate) ÷ 12. Discretionary income is your adjusted gross income minus 150 percent of the federal poverty line for your family size. The percentage rate varies by plan: REPAYE and PAYE use 10 percent; IBR uses 10 or 15 percent depending on when you took out the loan; ICR uses 20 percent.

Example: You earn $50,000 per year, you are single, and the poverty line is $14,580. Your discretionary income is $50,000 − (1.5 × $14,580) = $28,130. On REPAYE at 10 percent, your annual payment would be $28,130 × 0.10 = $2,813, or about $235 per month. This is true whether you borrowed $20,000 or $100,000.

Income-driven plans recalculate your payment each year based on your current income. If you earn less, your payment drops. If you earn more, it rises. After 20 to 25 years of payments (depending on the plan), any remaining balance is forgiven, though you may owe income tax on the forgiven amount.

Private student loans: variable rates and shorter terms

Private loans use the same amortization formula as federal standard repayment, but with two important differences: the interest rate is often variable (meaning it changes), and the repayment term is typically shorter—5 to 15 years instead of 10.

A variable rate is tied to a market index (usually the prime rate or LIBOR) plus a margin set by the lender. If the index rises, your rate rises, and your payment may increase. Some private loans lock in a fixed rate, which works like federal loans. Check your promissory note to see whether your rate is fixed or variable.

The shorter term means a higher monthly payment but less interest paid overall. A $30,000 private loan at 6 percent fixed over 5 years costs about $580 per month. The same loan over 10 years costs about $316 per month. Over 15 years, it drops to about $237 per month. The trade-off is always the same: shorter term, higher payment; longer term, lower payment but more total interest.

How to calculate payments when you have multiple loans

Most borrowers have more than one loan. You calculate the payment for each loan separately using the formula that applies to it, then add them together for your total monthly obligation.

Example: You have two federal loans totaling $25,000 at 5.5 percent (payment $483) and one private loan of $15,000 at 6.5 percent over 10 years (payment $159). Your total monthly payment is $483 + $159 = $642. If you switch one of the federal loans to an income-driven plan, that loan's payment changes but the other two stay the same.

Your loan servicer (or servicers, if you have loans from multiple companies) will show you each loan's payment separately on your bill. If you consolidate your federal loans into a Direct Consolidation Loan, they become one loan with one payment, but the calculation method remains the same.

What changes your payment and what does not

Your monthly payment is locked in on federal loans under standard repayment and on private loans with a fixed rate. It does not change unless you change your repayment plan or refinance. Making extra payments toward principal does not lower your monthly payment—it only shortens how long you pay.

On income-driven plans, your payment changes every year when you recertify your income. On private loans with a variable rate, your payment may change annually when the index rate adjusts. On federal loans, changing plans changes your payment: switching from standard to REPAYE, for example, could cut your payment in half or more, depending on your income.

Interest accrues (builds up) every day on unpaid balances. If you do not pay the full interest that accrues each month, the unpaid interest capitalizes—it gets added to your principal, and you then pay interest on that interest. This happens most often on income-driven plans when your payment is lower than the monthly interest charge.

Using online calculators and checking your servicer's math

The Federal Student Aid office provides a loan payment calculator on studentaid.gov. You enter your loan amount, interest rate, and repayment plan, and it shows you the monthly payment. This calculator works for federal loans only.

Your loan servicer also provides a calculator on their website. Navient, Mohela, Great Lakes, and other servicers all have them. These are more detailed because they can account for loans you have already been paying on (where some principal is gone) and show you how much of each payment goes to interest versus principal.

To verify your servicer's math: ask them for your current principal balance, interest rate, and remaining term. Plug those into the formula or an online calculator. If the payment they show does not match, contact them and ask why. Errors are rare, but they happen, and you have the right to understand what you are being charged.

Frequently Asked Questions

Why is my payment different from what the calculator shows?

The most common reason is that you have already made some payments, so your principal balance is lower than what you entered in the calculator. Your servicer's calculator accounts for this automatically. Also check whether you have unpaid interest that has capitalized—this increases your balance and your payment. If you switched repayment plans recently, your payment may not have updated yet.

Can I lower my monthly payment without changing my repayment plan?

On federal loans, switching to an income-driven plan is the main way to lower your payment. On private loans, refinancing with a different lender at a lower rate will lower your payment, but you lose federal protections like income-driven repayment and forbearance. Extending your repayment term also lowers the monthly payment but increases total interest paid.

What happens if I pay more than my monthly payment?

The extra amount goes toward your principal balance. This shortens your repayment timeline and reduces the total interest you pay, but it does not lower your required monthly payment. Your servicer will still expect the same payment next month unless you formally change your repayment plan.

How do I know if my interest rate is fixed or variable?

Check your promissory note or loan agreement—it will state whether your rate is fixed or variable. If it is variable, it will also say what index it is tied to and what margin the lender adds. Your servicer can also tell you if you call and ask.

Do I need to recalculate my payment every month?

No. On standard federal repayment and fixed-rate private loans, your payment stays the same for the life of the loan. On income-driven plans, you recertify your income once per year, and your servicer recalculates your payment based on your new income. On variable-rate private loans, your payment may change once per year when the interest rate adjusts.