Skip to content

Years to payoff calculator

By Jude Wallis

At $400 a month, a $12,000 balance at 21.99 percent takes 44 months to clear, which is 3.67 years. Total paid is $17,577.09, of which $5,577.09 is interest.

Months to payoff

44

3.67 years. Total paid $17,577.09.

Months
44
Years
3.67
Total paid
$17,577.09
Interest
$5,577.09
$
%
$

Put this on a class page: one iframe, free, for Google Sites, Canvas, WordPress or Notion.

On this page

The formula

n=−ln⁡(1−iBM)ln⁡(1+i)n=\frac{-\ln\left(1-\frac{iB}{M}\right)}{\ln(1+i)}

BB is the balance, ii the monthly rate and MM the monthly payment. The payment must exceed iBiB, the first month's interest, or the balance never falls.

The payment decides everything, and not gently

Interest on $12,000 at 21.99 percent is 12000×0.2199/12=219.9012000 \times 0.2199 / 12 = 219.90 in the first month. A $400 payment sends the rest at the balance, and the loan clears in 44 months with $5,577.09 of interest.

The relationship between payment and time is not proportional. Doubling the payment cuts the term by far more than half, because each extra dollar removes interest for every remaining month rather than just the current one.

Below the interest line, nothing happens

If the payment is smaller than that first month's interest, the balance grows and there is no payoff date at all. Just above it, the term stretches into decades. That narrow band is where minimum payments live, and it is the reason a minimum payment schedule can run longer than a mortgage.

The credit card payoff calculator runs the same maths on a card balance, and how credit card payoff works explains the minimum payment trap in full.

Rate and balance both matter, and differently

The second example, $8,000 at 18 percent with $250 a month, also takes 44 months, but the interest is $2,980.45 rather than $5,577.09. Same term, roughly half the interest, because both the balance and the rate are lower.

When several debts compete for one budget, the order matters. Snowball against avalanche sets the two orderings side by side, and this calculator gives the term for any single debt inside either plan.

What the schedule assumes

A fixed balance, a fixed rate and a fixed payment made every month, with nothing new charged to the account. That is what makes the 44 months exact rather than approximate: it is the point where the simulated balance reaches zero. How years to payoff works covers the same arithmetic in prose. This is educational material, not financial advice.

Worked examples

\$12,000 at 21.99 percent, paying \$400

A $12,000 balance charges 21.99 percent a year and $400 is paid every month. How long does it take?

  1. First month interest: 12000×0.2199/12=219.9012000 \times 0.2199 / 12 = 219.90, so about 180 of the payment reaches the balance.
  2. Run that forward and the balance reaches zero after 44 months, which is 3.67 years.
  3. Total paid: 17577.09, so interest is 17577.09−12000=5577.0917577.09 - 12000 = 5577.09.

It takes 44 months, or 3.67 years. Total paid is $17,577.09 and interest is $5,577.09.

A smaller balance at a lower rate

$8,000 at 18 percent, paying $250 a month.

  1. The balance reaches zero after 44 months, again 3.67 years.
  2. Total paid: 10980.45, so interest is 10980.45−8000=2980.4510980.45 - 8000 = 2980.45.

It also takes 44 months, but total paid is $10,980.45 and interest is only $2,980.45.

Dividing the balance by the payment

$12,000 over $400 suggests 30 months. The real answer is 44, because $5,577.09 of interest is added along the way. Ignoring interest understates the term by nearly half on a rate like this one.

Common questions

What if the payment is below the monthly interest?

The balance grows and there is no payoff date. The payment has to clear the interest before it can clear anything else.

Does new spending change the answer?

Yes, completely. The calculation assumes a closed balance with nothing added.

Is this financial advice?

No. It is educational material for the payoff term identity.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.