Loan Calculator Based on Payment Amount: How Long to Pay It Off

This calculator works out how long a loan takes to repay when you choose the monthly payment. Enter the balance, the APR and the payment; you get the number of months, the same in years and the total interest paid.

Formula

n = −ln(1 − r × P ÷ M) ÷ ln(1 + r), rounded up to a whole month, with r = APR ÷ 1200. The last payment is smaller: it is the balance after n − 1 payments plus one month of interest. Total interest = M × (n − 1) + last payment − P.

Worked Example

A $15,000 balance at 6% APR, paying $400 a month.

1. r = 0.005; r × P ÷ M = 0.005 × 15,000 ÷ 400 = 0.1875
2. n = −ln(0.8125) ÷ ln(1.005) = 41.63, rounded up to 42 months (3.5 years)
3. Total interest, counting the smaller last payment = $1,652.87

Assumptions

• Fixed interest rate for the whole term; payments of equal size at the end of each month.
• Interest compounds monthly at APR ÷ 12.
• No fees, taxes or insurance unless the calculator has a field for them.

How to read the result

If the payment does not cover the first month’s interest (M ≤ r × P) the balance never falls, and the calculator shows “Cannot compute”. Raise the payment to see a finite payoff time.

Limits and common mistakes

• Use the balance you owe now, not the original loan amount.
• Lenders may require a minimum payment; this calculator does not know it.

Frequently Asked Questions

How long does $400 a month take to repay $15,000 at 6%?

42 months (3.5 years), with about $1,653 of interest.

Why does it say “Cannot compute”?

The payment is too small to cover the interest, so the balance would never be repaid.

Is the last payment the same?

No, it is smaller; it clears whatever is left.

in p | Loan balance | $ | 15000 | 1 | 100000000
in apr | Interest rate (APR) | % | 6 | 0.01 | 100
in m | Monthly payment | $ | 400 | 0.01 | 100000000
out n | Months to pay off | months | ceil(round(-ln(1 - (apr / 1200) * p / m) / ln(1 + apr / 1200), 6)) | 0
out yrs | Years to pay off | years | n / 12 | 1
out int | Total interest | $ | m * (n - 1) + (p * (1 + apr / 1200) ^ (n - 1) - m * ((1 + apr / 1200) ^ (n - 1) - 1) / (apr / 1200)) * (1 + apr / 1200) - p | 2