How a standard student loan repayment is calculated
A student loan on a standard repayment plan is an amortizing loan like any other. The monthly payment comes from payment = P * i * (1 + i)^n / ((1 + i)^n - 1), where P is the balance, i is the annual rate divided by 12, and n is the repayment term in months. The default term on federal loans is ten years, which is why this calculator starts at ten.
Each month, interest accrues on the outstanding balance and the rest of the payment reduces principal. Federal student loans use simple daily interest rather than monthly compounding, so a real servicer computes interest as balance times the annual rate divided by 365, times the days since the last payment. The monthly approximation used here differs by a small amount, usually a few dollars over the life of the loan, and can differ more if payments arrive at irregular times.
The calculator also supports an extra payment. When you enter one, it simulates the loan month by month at the base payment plus the extra, stops when the balance reaches zero, and reports both the shortened term and the interest saved compared with the unchanged schedule.
Worked example: 30,000 at 5.5 percent over ten years
Using the defaults of a 30,000 balance, a 5.5 percent rate, and a ten year term, the monthly rate is 0.055 / 12 = 0.00458333 and n is 120. The payment is 325.58. Across 120 payments that is 39,069.46 in total, with 9,069.46 of it interest.
The first payment breaks down as 30,000 * 0.00458333 = 137.50 in interest and 325.58 - 137.50 = 188.08 in principal. Unlike a 30 year mortgage, a ten year loan puts most of each payment toward principal from the beginning, which is why the total interest is a modest fraction of the amount borrowed.
Adding 100 a month changes the picture considerably. Paying 425.58 clears the loan in 86 months instead of 120, nearly three years early, and total interest falls to about 6,316 from 9,069, a saving of roughly 2,753. Stretching instead to a 20 year term drops the payment to 206.37 but raises total interest to 19,528, more than double.
Federal repayment plans this calculator does not model
The standard ten year plan is only one option on federal loans. Graduated plans start with a lower payment that rises every two years. Extended plans stretch to 25 years for borrowers above a balance threshold. Income driven plans set the payment as a percentage of discretionary income, recalculated annually, with any remaining balance forgiven after a set number of years. None of these are modeled here, because each depends on income, family size, and current program rules.
Income driven plans in particular behave differently in a way the arithmetic here cannot show. When the required payment is smaller than the monthly interest, the balance grows rather than shrinks, and the amount ultimately repaid depends on income growth and the forgiveness rules rather than on an amortization formula. Anyone on such a plan should use the official federal loan simulator rather than a fixed payment calculator.
Public Service Loan Forgiveness, teacher loan forgiveness, and the treatment of forgiven balances for tax purposes are also outside this tool. If you expect forgiveness, minimizing total interest paid is not the objective, and the extra payment feature here may be actively counterproductive.
Multiple loans, capitalization, and what the single balance hides
Most borrowers have several loans rather than one, often at different rates from different academic years, sometimes mixing subsidized, unsubsidized, and private debt. Entering the total balance with an average rate gives a reasonable summary but hides the fact that paying the highest rate loan first is cheaper than spreading extra payments evenly.
Capitalization is the other thing a single balance hides. Unpaid interest that accrues during deferment, forbearance, or a grace period is added to the principal at certain events, after which interest accrues on the larger balance. Entering your current principal after any capitalization has already occurred is the right approach; the calculator does not model future capitalization.
Private student loans differ further. Many carry variable rates tied to a benchmark, some have terms longer than ten years, and they lack the federal protections around deferment and income driven repayment. A variable rate loan cannot be described accurately by a fixed rate model over a long term.
The mistake people make with extra payments on student loans
The most common mistake is sending extra money without telling the servicer what to do with it. By default, many servicers apply an overpayment to future scheduled payments, placing the account into a paid ahead status. Interest savings in that case are zero or close to it, because the balance was not reduced early. A written instruction to apply the overpayment to the current principal balance is what produces the result this calculator shows.
The second is targeting the wrong loan when several exist. If the extra 100 in the example goes to a 3 percent loan while a 7 percent loan sits untouched, the interest saved is less than half what it would have been. Order matters more than amount when the rates differ.
The third is prepaying while carrying higher cost debt or no emergency savings. Student loan rates are frequently below credit card rates by a wide margin, and federal loans carry protections that cash savings do not replace. The arithmetic of prepayment is straightforward; the question of whether it is the best use of the money is not one this calculator answers.