Two questions, one loan: what's the payment for a set term, or how long does a set payment take to clear it?
Estimates for planning, not financial, tax or legal advice. Figures use US rules unless the page says otherwise.
Fixed term: the payment formula
Payment = P × i ÷ (1 − (1 + i)−n)
P is the loan amount, i the monthly rate (APR ÷ 12) and n the number of payments. A $20,000 loan at 8% for 4 years (48 payments) costs $488.26 a month, with $3,436.41 in total interest.
Fixed payment: how long it takes
Solve the same formula for n:
n = −ln(1 − i × P ÷ M) ÷ ln(1 + i)
M is your monthly payment. Paying $250 a month on $10,000 at 9%: i = 0.0075, so n = −ln(1 − 0.0075 × 10,000 ÷ 250) ÷ ln(1.0075) = 47.73. That's 48 payments: 47 of $250 and a last one of $183.92. Total interest is $1,933.92.
When the payment is too small
Each month, interest is charged first: balance × i. If your payment isn't bigger than that, the balance never goes down. At 12% on $10,000, the first month's interest is $100, so a $100 payment would go on forever. The calculator tells you when that happens instead of showing a meaningless number.
Limitations
- For fixed-rate loans with monthly payments. Variable-rate loans change payment when the rate resets.
- Interest is charged monthly at APR ÷ 12. Loans that charge daily interest, like many student loans, come out a few cents to a few dollars different.
- Late fees, insurance and other charges aren't included.
Sources
How we checked this
Before every update, this calculator is run in a real browser with these known answers, and it must match all of them:
- $20,000 at 8% for 4 years: $488.26/month ✓
- $10,000 at 9% paying $250: 48 payments, last one $183.92 ✓
- $1,200 at 0% paying $100: 1 year ✓
- $10,000 at 12% paying $100 (only the interest): never pays off ✓
- $10,000 at 12% paying $100.01: 934 payments once interest is rounded to the cent ✓
- Payment bigger than the loan: 1 payment of $10,041.67 ✓
Last checked October 26, 2026. Spotted something wrong? The math is done in your browser with the formula shown on this page, so you can check any result by hand.
Questions people ask
How do I calculate a monthly payment?
Use Payment = P × i ÷ (1 − (1 + i)⁻ⁿ), where i is the APR divided by 12 and n is the number of months. Or enter the numbers above.
How long will it take to pay off my loan?
Switch to Find the payoff time and enter what you pay each month. The calculator gives the number of payments and the smaller final payment.
Why is my last payment smaller?
The payments rarely divide the balance exactly. The last one covers only what's left, plus that month's interest.
What payment do I need to pay off a loan faster?
Enter a shorter term in Find the payment mode. The difference from your current payment is the extra you'd need each month.