Two questions, one formula
Every fixed-payment debt has the same relationship between four quantities: balance, rate, payment and time. Fix any three and the fourth follows.
Solving for the payment
- M
- Monthly payment
- P
- Balance owed
- r
- Monthly rate — APR ÷ 12 ÷ 100
- n
- Number of months
Solving for the time
The second has a hard limit worth understanding. If your payment is less than or equal to the first month's interest, the expression is undefined — the balance grows rather than shrinks, and no amount of time clears it.
A worked example
Raise the payment to $400 and the debt clears in 26 months with $2,128 of interest — $959 saved for $95 more a month. The relationship between payment and interest is steeply non-linear, which is why paying above the minimum matters so much.
The minimum payment trap
Credit card minimums are typically 1% to 3% of the balance plus that month's interest, with a floor around $25 to $35. The minimum falls as the balance falls, which stretches repayment out almost indefinitely.
| Payment | Months | Total interest |
|---|---|---|
| Interest + 1% minimum | ~23 years | $13,593 |
| $250 | 49 | $4,191 |
| $305 | 37 | $3,087 |
| $400 | 26 | $2,128 |
| $500 | 20 | $1,628 |
| $700 | 13 | $1,063 |
Since the 2009 CARD Act, US card statements must show how long the balance would take to clear at the minimum, and what payment would clear it in three years. It is worth reading — the contrast is usually stark.
Two payoff strategies
- Avalanche. Pay minimums on everything, then put every spare pound or dollar against the highest-rate debt. Mathematically optimal — it always costs least.
- Snowball. Attack the smallest balance first. Costs slightly more, but the early wins improve the odds of sticking with it. Research suggests it works better in practice for many people.
For general loan modelling, use the loan calculator. For Indian EMIs, the EMI calculator.
Frequently asked questions
How do I calculate a monthly payment?
Use M = P × [r(1+r)ⁿ] ÷ [(1+r)ⁿ − 1], where P is the balance, r is the monthly rate and n is the number of months.
On $8,000 at 21.99% over 36 months, that is $304.94.
How long will it take to pay off my credit card?
Switch to "find the time" mode and enter what you can pay. The calculator solves the logarithmic form.
If your payment is at or below the first month's interest, the balance never falls — the calculator will tell you the minimum needed.
Why do minimum payments take so long?
Because the minimum is a percentage of the balance, it falls as the balance does. Most of each payment covers interest, so the principal barely moves.
On $8,000 at 21.99%, a typical interest-plus-1% minimum takes roughly 23 years and costs about $13,600 in interest.
Should I pay off the highest rate or smallest balance first?
Highest rate — the avalanche method — always costs least mathematically. Smallest balance first, the snowball, costs a little more but produces early wins that help people stay with the plan.
If the difference is small, choose the one you will actually finish.
Is a balance transfer worth it?
Often, if you can clear the balance within the promotional period. A 0% offer for 18 months with a 3% transfer fee costs $240 on $8,000 — far less than the $1,500 or so of interest you would otherwise pay.
The risk is not clearing it in time, since the rate after the promotion is usually high.