Student Loan Payoff Calculator

How to use

1. 01

   Enter the balance and the interest rate. If several loans sit with one servicer, either run them one at a time or enter the combined balance at a balance-weighted average rate — a single rate across mismatched loans is an approximation, not the schedule.

2. 02

   Enter the payment you actually make each month, not the payment you intend to make. The date the tool returns is only as honest as that number.

3. 03

   Add anything extra you can put on top each month in the extra field. Leave it at zero first so you can see the base timeline before the extra changes it.

4. 04

   Read the two timelines against each other: the headline is the date at payment plus extra, while the first insight gives the date at the base payment alone. The gap between them is what the extra is buying.

5. 05

   Open the year-end schedule to see where the balance stands at the end of each year at the base payment, then tell your servicer in writing to apply anything extra to principal without advancing the due date.

Formula

The calculator clears a single loan with a level monthly payment and reports the date, the interest, and what an extra amount each month takes off the end. Monthly rate r = annual interest rate / 100 / 12. Months to clear a balance B at a payment P: n = ceiling of [ -ln(1 - B x r / P) / ln(1 + r) ] With no interest at all (r = 0) it is simply B / P rounded up. The never-clears rule: if P is less than or equal to B x r, the payment does not cover the first month's interest, the balance cannot fall, and the tool reports 'Never at this payment' rather than a date. Total interest is not a formula but a simulation. The engine walks the months one at a time, adding that month's interest (balance x r), subtracting the payment, and summing every interest charge until the balance reaches zero. That is why the total is exact rather than approximate, and why the final payment is smaller than the rest. The tool runs this twice. Once at your payment alone, giving the base months and the base interest. Once at payment plus extra, giving the headline date and the interest stat. Time saved by the extra is the difference between the two month counts; interest saved is the difference between the two interest totals. The total you repay is the balance plus the interest on the payment-plus-extra path.

Example

Inputs: balance $35,000, interest rate 6.5%, payment $400 a month, extra $100 a month. Step 1 - The monthly rate. 6.5% / 12 = 0.541667% a month, or 0.00541667. Step 2 - Check the floor. The first month's interest is $35,000 x 0.00541667 = $189.58. A $400 payment clears that with $210.42 left over for principal, so the loan will finish. Step 3 - The base timeline, at $400 with nothing extra. n = -ln(1 - 35,000 x 0.00541667 / 400) / ln(1.00541667) = 118.95, which rounds up to 119 months. The tool reports 9y 11m, with $12,565 of interest along the way and $47,565 repaid in total. Step 4 - The timeline with the extra, at $500 a month. n = -ln(1 - 35,000 x 0.00541667 / 500) / ln(1.00541667) = 88.24, which rounds up to 89 months. The tool reports 7y 5m as the headline, $9,122 of interest, and $44,122 repaid in total. Step 5 - What the extra bought. 119 - 89 = 30 months, which the tool shows as 2y 6m saved. The interest saved is $3,444. Note that it is not exactly $12,565 - $9,122 = $3,443: those two are rounded for display and the saving is taken from the unrounded figures. Read that back in plain terms. An extra $100 a month, which comes to $8,900 of extra payments across the 89 months, ends the loan two and a half years earlier and cancels $3,444 of interest. Doubling the extra to $200 a month does it again: 5y 11m, $7,180 of interest, $42,180 repaid, 4 years and $5,386 saved. And the other direction, so the floor is not abstract. Drop the payment to $200 with no extra and the loan still clears, but it takes 45y 7m and costs $74,400 in interest — more than twice what was borrowed — because for the first several years almost the whole payment is going to the $189.58 of monthly interest. At the end of year five the balance is still $34,264.

Definitions

Balance

The principal currently outstanding on the loan. On a federal loan this is the figure the servicer calls the current principal balance, which may already include interest capitalized at an earlier event.

Interest rate

The annual rate on the loan. Federal Direct Loans carry a rate fixed for the life of the loan, set each year under 34 CFR 685.202(a) from the high yield of the 10-year Treasury note plus a statutory add-on and capped by statute.

Payment each month

The level monthly amount the schedule assumes. It has to exceed the first month's interest — balance times the annual rate divided by twelve — or the balance never falls.

Extra each month

An additional amount paid alongside the regular payment. The engine simply adds it to the payment, which is why the effect compounds: it lowers the balance, which lowers next month's interest, which frees more of the following payment.

Total interest

The sum of every monthly interest charge from the first payment until the balance reaches zero, on the payment-plus-extra path. It is the price of the borrowing, separate from the principal you would have repaid anyway.

Capitalization

Adding unpaid accrued interest to the principal balance, defined at 34 CFR 685.202(b)(1). It matters here because it resets the balance this page starts from: after a capitalizing event you are paying interest on interest.

Prepayment

Any amount paid above what is due. 34 CFR 685.211(a)(2) lets a borrower prepay all or part of a Direct Loan at any time without penalty, and (a)(3)(ii) advances the next due date unless you ask the servicer not to.

Frequently asked questions