Every loan has a finish date, and it is set by four numbers: the balance you still owe, the interest rate, the monthly payment you make, and any extra you add. Change any one of them and the date moves. The date is not guessed and it is not one formula applied once; it is the result of repeating the same small calculation month after month — charge interest on the balance, take the payment, reduce the balance — until the balance reaches zero. This guide works through that calculation, shows what moves the date and by how much, and explains how to solve the problem backwards: given a deadline, what payment does it need?

The four numbers that set the date

Four numbers decide when a loan clears. The balance is what you still owe. The rate is the annual percentage rate, which sets each month’s interest charge. The payment is what you actually send each month. And the extra is anything beyond the regular payment — a fixed monthly extra, a lump sum in a particular month, or the extra payment a biweekly schedule adds each year. Every payoff question is a question about these four numbers, and the calculator on this page takes exactly these four as its inputs.

Two things that look important are not among the four. The original loan amount does not matter — only the balance still owed. And the original term does not matter either — a loan taken over five years and a loan taken over seven years with the same balance, rate, and payment clear on the same date. The date depends on where the loan stands now, not on how it started.

How the date is worked out

The payoff date is found by simulation, not by a single formula. Each month, the lender charges interest on the balance that remains: monthly interest = balance × APR ÷ 1,200. The payment first covers that interest, and whatever is left reduces the balance. Then the next month repeats the same calculation on the smaller balance. The simulation continues until the balance reaches zero, and the number of months it took is the time to payoff.

The division by 1,200 is the annual rate turned into a monthly rate: APR ÷ 100 gives the yearly fraction, divided by 12 gives the monthly fraction, and 100 × 12 is 1,200. A 9% rate therefore charges 0.75% of the balance each month. The balance curve this produces bends downward faster near the end, because the interest slice shrinks as the balance falls and the principal slice grows — which is why the last months of a loan clear the balance so quickly, and why extra payments early on are worth more than extra payments late.

Worked example: $15,000 at 9%

Take a $15,000 balance at 9%, paid at $350 a month. The first month’s interest is $15,000 × 9% ÷ 1,200 = $112.50, so $237.50 of the payment reduces the balance to $14,762.50. By month 12 the interest has fallen to $92.15 and the principal slice has grown to $257.85, leaving $12,029.45. After 51 full payments of $350, a small balance of about $311 remains; month 52 charges roughly $2.33 of interest on it, so the final payment is just $313.62, bringing the total paid to $18,163.62, of which $3,163.62 is interest.

Table notes: monthly interest = balance × 9% ÷ 1,200; payment $350 a month; final payment is smaller because only the remaining balance plus its last interest is due. Total interest $3,163.62 over 52 months.

What moves the date

The payment moves the date most. On the $15,000 loan above, raising the payment from $350 to $375 a month brings the payoff from 52 months to 48, and cuts interest from $3,163.62 to $2,900.81 — saving $262.81 from $25 a month. Adding $100 a month brings it to 39 months with $2,325.99 of interest, saving $837.63 and 13 months. The companion guide on how to pay off a loan early compares the strategies in full.

The rate moves the date too, in the opposite direction: a higher rate raises each month’s interest charge, so less of each payment reaches principal and the payoff recedes. A rate cut has the reverse effect, which is why refinancing to a cheaper rate shortens a loan even when the payment stays the same. And a lump sum moves the date by the month it lands: $1,200 in month 6 of a $10,000 loan at 6% saves $327.34 of interest, while the same $1,200 in month 48 saves only $43.03, because by then there is little interest left to save.

Solving for a deadline

The question can also be run backwards: given a deadline, what payment does it need? The payment that clears a balance PV over n months at monthly rate r is P = r × PV ÷ (1 − (1 + r)⁻ⁿ), where r is the APR divided by 1,200. For the $15,000 loan at 9% over 36 months, r is 0.0075, and the payment is $477.00 a month — $127 more than the $350 that takes 52 months, and the total interest falls to $2,171.83.

To finish a year sooner than the 52-month baseline — in 40 months — the payment needs to be about $436 a month, or roughly $86 more than $350. The general pattern is worth remembering: each month cut from the term costs a little more than the last, because the payment must cover the same balance in fewer months. The calculator on this page solves the deadline directly: enter the date you want, and it returns the payment that gets you there.

When there is no payoff date

Some loans have no payoff date at all. If the monthly payment is no more than one month’s interest, the balance grows instead of shrinking, and the simulation never reaches zero. On the $15,000 example at 9%, one month’s interest is $112.50, so any payment at or below that figure cannot clear the loan. The balance rises each month, the interest charge rises with it, and the loan runs away.

The fix is not mysterious: the payment must exceed the monthly interest by enough that the principal slice is meaningful. Raising it by $25 or $50 a month is often enough to turn a loan that never clears into one with a real finish date. If the payment cannot be raised, the options are a lower rate, a lump sum to cut the balance below the point where the payment covers the interest, or a conversation with the lender about the terms — but a payment that does not cover the interest is a loan that is growing, and it should be treated as urgent.

Payoff amount vs balance

The payoff amount and the balance are different numbers, and confusing them is the commonest surprise in a payoff. The balance is what you owe today. The payoff amount is what you would owe on the day you actually pay the loan off: the balance plus the interest that accrues between today and that day. It is always a little more than the balance, and the further away the payoff date, the larger the difference.

That is why a lender’s payoff quote differs from this calculator’s balance, and why the quote carries a good-through date: the interest is counted to that date, and after it the figure is stale. When you compare a quote with the calculator, compare the quote with the balance plus the interest to the quote’s date, not with the balance alone — and when you send the payoff, send the quoted amount, not the balance, or a small residue of interest will remain and the loan will not close.

Sources: Worked examples computed by month-by-month simulation: interest = balance × APR ÷ 1,200 each month; payment covers interest first, remainder reduces principal. $15,000 at 9%, $350 a month: 52 months, $3,163.62 interest, final payment $313.62. $350 raised to $375: 48 months, $2,900.81. $477 a month clears the same loan in 36 months with $2,171.83 interest; about $436 a month clears it in 40 months. Payment formula: P = r × PV ÷ (1 − (1 + r)⁻ⁿ), r = APR ÷ 1,200.