Student Loan Payoff Calculator

What this page computes is one fixed monthly payment against one balance at one fixed rate: the date the loan ends, what it has cost in interest by then, and how both of those change when the payment is larger than it has to be. Income-driven repayment plans — SAVE, IBR, PAYE and ICR — forgiveness including PSLF, subsidized interest, deferment, forbearance and the capitalization that follows a period of non-payment are not modelled here. A schedule that assumed any of them would be a guess wearing the clothes of an answer.

That leaves a real question the page can answer exactly. A borrower on a standard ten-year schedule knows the payment and wants to know what happens if it goes up by $50 or $100 — which month the balance reaches zero, and how much interest never accrues because the principal came down sooner. Both numbers come from running two full schedules in whole cents and subtracting one from the other.

The other thing this page does not do is hold more than one loan. Most borrowers leave school with several disbursements at several rates, and the total payoff then depends on which loan the extra payment is directed at. The highest-rate loan is rarely also the smallest, so the choice is a real one. That ordering problem belongs to the debt payoff planner, which takes each balance and rate separately, applies one monthly budget across all of them, and rolls each freed payment into the next.

Every dollar above the scheduled payment is treated here as reducing the balance on the day it is paid. That is one of two things a lender can do with it. The other is to count it toward your next scheduled payment, which moves the due date forward and leaves the balance where it was — and the saving below is then not smaller, it is zero. The standard mortgage contract lets the lender choose; on a federal student loan choosing for you is the default. Send it as a principal-only payment, in writing, and check the next statement.

On a federal student loan, paying more than the amount due moves the due date by default. The money is applied — to fees, then outstanding interest, then principal — but the account is then paid ahead, so a later statement can read $0.00 due while interest keeps accruing daily. You have to ask the servicer not to advance the due date. The saving below assumes every extra dollar reduced the balance.

The payoff date is the date of the last row of the schedule, not the date the ten-year term was scheduled to end. With no extra payment those are the same day. Add anything extra and they separate, and the distance between them is the answer most people came for.

Early in a long schedule, most of the payment is interest. On the $35,000 example below, $190.46 of the first payment of $397.96 goes to interest and $207.50 to principal; by the last payment the interest is $2.15. This is why a dollar paid in year one is worth more than the same dollar paid in year eight — it stops accruing interest for every month that remains, and there are more of those months at the start.

The last payment is smaller than the others. The scheduled payment is rounded up to the next cent so that the schedule never runs past its term, which leaves the final payment only whatever balance is still standing. On the example, 119 payments of $397.96 are followed by one of $396.67.

Total interest comes from the schedule, not from the payment. Multiplying $397.96 by 120 and subtracting the balance gives $12,755.20. The schedule gives $12,753.91. The $1.29 difference is exactly the amount by which that final payment is short of a full one, and the schedule is the one that is right.

Interest saved is measured against the same loan with no extra payments — same balance, same rate, same scheduled payment, paid monthly to the end of its term. Nothing else moves underneath the comparison: the rate does not change, no plan is switched, and no forgiveness is assumed at any point.

M

the scheduled payment, rounded up to the next cent

P

the balance at the start, in cents

r

the periodic rate — the APR divided by 100 and by 12

n

the term, in months

bₖ₋₁

the balance before payment k

iₖ

the interest charged in period k, rounded half-up to the cent

The payment is rounded up so the schedule cannot run past the term. Rounding to the nearest cent instead leaves a stray final payment of a few dollars on a long loan.

The payoff date comes from running the schedule, not from the formula. The two agree on ordinary loans and can differ by several months when the payment barely exceeds the interest.

The rounding rule, the final-payment adjustment and the published test vectors are all on the methodology page.

One loan or several, fixed payment or revolving — that is the real question behind this family of calculators, and it decides which page answers yours.