What you are calculating
A debt payoff calculation answers two questions: with a fixed monthly payment, how many months until the balance hits zero, and what is the total interest paid over that time.
Every month, interest is added to the balance first and your payment is applied second. Whatever is left of the payment after interest is the only part that reduces what you owe. That single sentence explains why minimum payments on a high-rate card feel like running in place.
The payoff formula
n = −log(1 − (r × B) / P) / log(1 + r)
- n = number of monthly payments
- B = current balance
- r = monthly interest rate (APR ÷ 12, as a decimal)
- P = fixed monthly payment
- Total interest = (P × n) − B
Spreadsheet version: =NPER(APR/12, -payment, balance). If the payment is below r × B, the formula has no solution — the debt never clears.
Step-by-step calculation
- List the balance you owe. Use the current statement balance for each debt, e.g. $6,400 on a credit card.
- Convert the APR to a monthly rate. Divide the annual percentage rate by 12. A 22.9% APR becomes 0.229 ÷ 12 = 0.01908 per month.
- Decide the fixed monthly payment. Pick an amount you can pay every month without fail. It must exceed one month of interest or the balance will never fall.
- Check the interest floor. Multiply balance by the monthly rate: $6,400 × 0.01908 = $122. Any payment at or below $122 never clears the debt.
- Apply the payoff formula. Months = −log(1 − (r × B) ÷ P) ÷ log(1 + r), where B is the balance, r the monthly rate, and P the monthly payment.
- Work out total interest. Multiply the monthly payment by the number of months, then subtract the original balance. That difference is the cost of the debt.
Three worked examples
1. A credit card at 22.9% APR
Balance $6,400, monthly rate 0.229 ÷ 12 = 0.01908. Compare two fixed payments.
| Monthly payment | Months to clear | Total paid | Interest cost |
|---|---|---|---|
| $150 | ~104 | $15,600 | ~$9,200 |
| $200 | ~55 | $11,000 | ~$4,600 |
| $300 | ~27 | $8,100 | ~$1,300 |
Adding $100 a month to the $200 payment cuts more than two years off the debt and saves roughly $3,300. The payment is only 50% larger; the interest is nearly 3.5× smaller, because the balance spends far less time accruing.
2. A car loan at 7.4% APR
$19,000 borrowed over 60 months. Monthly rate 0.074 ÷ 12 = 0.006167. Rearranging the same formula for the payment gives about $380 per month, or $22,800 in total — roughly $3,800 of interest. Round the payment up to $420 and the loan clears in about 53 months, saving close to $500.
3. Two debts, one budget
You owe $2,000 at 26% APR and $7,500 at 11% APR, with $500 a month available. Both need their minimums; the surplus goes to one of them.
| Strategy | First debt cleared | All debt cleared | Total interest |
|---|---|---|---|
| Avalanche (26% first) | Month 5 | Month 21 | ~$1,180 |
| Snowball (smallest first) | Month 5 | Month 21 | ~$1,180 |
Here the smallest balance is also the highest rate, so both methods agree. When they disagree, avalanche wins on cost and snowball wins on momentum.
Snowball vs avalanche
- Avalanche — order debts by interest rate, highest first. Mathematically optimal, lowest total interest.
- Snowball — order by balance, smallest first. Each cleared debt frees its payment for the next one and provides visible progress.
- Hybrid — clear one small nuisance balance for momentum, then switch to strict avalanche.
- In most real cases the total-cost difference is a few hundred dollars. The method you will actually finish is the right one.
Common mistakes
- Letting the minimum float down. Fix your payment in cash terms and keep it there as the balance falls.
- Using the APR as a monthly rate. Always divide by 12 first.
- Ignoring new spending. A payoff plan only works if the card stops being used mid-plan.
- Forgetting fees. Balance transfer fees and annual fees belong in the balance before you calculate.
- Draining the emergency fund entirely. Without a buffer, the next surprise goes straight back on the card.
Use the calculator
The debt payoff calculator runs this formula for you, including extra payments and multiple debts. To find the monthly payment on a fixed-term loan instead, use the loan calculator, and to build the room in your budget, start with budgeting for beginners.
Frequently asked questions
How do I calculate how long it will take to pay off my debt?
Use Months = −log(1 − (r × B) ÷ P) ÷ log(1 + r), where B is the balance, r is the APR divided by 12, and P is the fixed monthly payment. In a spreadsheet the same answer comes from =NPER(rate, -payment, balance).
Why does paying the minimum take so long?
A credit card minimum is typically 1–3% of the balance, and most of it covers interest in the early months. As the balance falls, the minimum falls with it, so the payoff date keeps sliding. Fixing the payment amount is what actually ends the debt.
What is the difference between the snowball and avalanche methods?
Avalanche pays the highest interest rate first and costs the least in total interest. Snowball pays the smallest balance first and clears individual debts faster, which many people find easier to stick with. The gap in total cost is usually modest.
How much interest will I save by paying an extra $100 a month?
It depends on the rate and balance, but on a $6,400 balance at 22.9% APR, going from $200 to $300 a month cuts the payoff from about 55 months to 27 and saves roughly $3,300 in interest.
Should I pay off debt or invest first?
Compare rates honestly. Consumer debt above roughly 8–10% almost always beats an uncertain expected market return, so clearing it first is the higher-confidence move. Keep any employer retirement match — that is an immediate return no debt rate matches.
Does a balance transfer change the maths?
Yes. A 0% promotional period means the entire payment reduces the balance, so divide the balance by the number of promo months to find the payment that clears it before the standard rate returns. Include the transfer fee, usually 3–5%, in the balance.
Put this into practice
Open a real ticker, generate a personalized budgeting insight, and track what you learn — all in one calm workspace.