Extra Payment Calculator

The three kinds of extra payment are not interchangeable, and the difference between them is not the amount. A recurring extra is added to every payment. A one-off is a single amount attached to one payment number. A lump sum is a single amount attached to a date, which the page converts to a payment number before it computes anything. All three reduce the balance in the period they fall in; what varies is which period that is, and on a fixed-rate loan the period is worth more than the size of the payment.

The page runs two schedules and subtracts them. The first is the loan with no extra at all — same balance, same rate, same scheduled payment, paid monthly to the end of its term. The second is the same loan with the extras entered. Months saved is the difference in the row counts, interest saved is the difference between the two interest columns, and neither figure comes out of a formula. Both schedules are run to the cent and every row of the second one is on the page.

An extra payment shortens the loan; it does not shrink the monthly payment. The scheduled payment stays at whatever the original term implies, the extra sits on top of it, and the loan ends on an earlier row. That is why the total handed over falls rather than rises: on the example below, paying $100 a month extra means paying $22,444.36 over the life of the loan instead of $23,199.35.

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.

Every extra is added to the payment due in its own period, never taken out of it. The amount due in a month is the scheduled payment plus the recurring extra plus any one-off that falls that month, and when two extras land in the same period they add. Interest is charged on the balance first, and whatever the payment exceeds it by comes off the principal — so a $5,000 one-off in a month whose interest is $83.83 takes $5,302.83 off the balance, counting the scheduled payment alongside it.

A lump sum's date becomes a payment number before anything else happens. With a first payment on 1 October 2026, a lump dated 1 September 2027 lands on payment 12: (2027 − 2026) × 12 + (9 − 10) + 1. The day of the month is ignored, so 30 September 2027 gives the same payment 12. Two edge cases follow from that arithmetic and the page states both rather than absorbing them: a lump dated before the first payment resolves to a payment number below one and is applied to payment 1, and a lump dated after the loan is already clear — 1 January 2031 on the example below, which resolves to payment 52 against a 45-payment schedule — is not applied at all, and the panel says so instead of dropping it.

The final payment absorbs whatever is left, so it is rarely a full one. The scheduled payment is rounded up to the next cent, which keeps the schedule from running past its term, and the last row only has to clear the remaining balance plus that month's interest. With a $100 recurring extra on the example the forty-sixth payment is $486.66 and the forty-seventh is $58.00. The rounding rule and the final-payment adjustment are set out in full on the methodology page.

Months saved and interest saved are measured against the same loan with no extras. The baseline does not move when an extra is entered: same balance, same rate, same scheduled payment, sixty payments to the end of the term. Changing the extra changes the second schedule and nothing else, which is what makes two different extras comparable on the same screen.

The same money saves more the earlier it arrives. A dollar taken off the balance stops accruing interest for every remaining month of the loan, so the saving depends on how many months are left when it lands rather than on how large the payment was. That is the whole of the result below: $5,000 paid once in the twelfth month saves more than $6,000 paid in sixty instalments, and doubling an extra never quite doubles what it saves.

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.