How to Calculate Credit Card Minimum Payment

The formula, in one paragraph

Start with the balance, the APR, the card’s minimum-payment rule and the floor. The month’s interest is the balance times the APR divided by 12, the minimum is the larger of the floor and the interest plus 1% of the balance (or 2% of the balance, on a 2% rule card), and the payoff is the month-by-month simulation of the balance falling until it reaches zero.

Step 1: Work out the month’s interest

The interest is the balance times the APR divided by 12, because the APR is the yearly rate and the card charges a twelfth of it each month. At the example numbers that is $5,000 times 24.99% divided by 12, which is $104.13 of interest in month 1. At 18% the same balance costs only $75.00 of interest in month 1, which is $29.13 less.

Step 2: Work out the minimum payment

The minimum is the larger of the floor and the rule. Under the interest-plus-1% rule, add 1% of the balance to the month’s interest: $104.13 plus $50.00 is $154.13, which beats the $35 floor, so the first payment is $154.13. Under the 2%-of-balance rule the minimum is 2% of $5,000, which is $100.00 — below the month’s interest of $104.13, so the balance grows. The floor only matters on small balances: on a $1,000 balance the interest is $20.83 and 1% is $10.00, which is $30.83 together, below the $35 floor — so the first payment is $35.00.

Step 3: Simulate month by month

Each month, add the interest to the balance and subtract the payment, then work out the next month from the new balance. After month 1 the balance is $5,000 plus $104.13 minus $154.13, which is $4,950.00 — only $50.00 of the payment touched the balance. The payment shrinks with the balance, so the balance falls slower and slower, and the card takes 203 months to reach zero. A fixed payment never shrinks: a fixed $200 a month pays the same card off in 36 months, and a fixed $250 a month takes 27 months.

Step 4: Read the totals

Add up the interest over all the months for the total interest, and add the balance for the total paid. At the example numbers the interest over 203 months is $8,824.08, and the total paid is $5,000 plus $8,824.08, which is $13,824.08 — nearly three times the balance. A fixed $200 a month costs $2,135.16 of interest and $7,135.16 in all, and a fixed $250 a month costs $1,534.53 of interest and $6,534.53 in all.

That box is the whole formula.

What changes the payoff most

The balance moves the payoff fastest. A $2,500 balance takes 134 months and costs $3,617.84 of interest, and a $10,000 balance takes 272 months and costs $19,236.57. The APR is next: at 18% the $5,000 balance takes 189 months and costs $6,153.99, which is $2,670.09 less than at 24.99%. The floor matters more than it looks: a $25 floor lets the payment fall further, so the same card takes 236 months and costs $9,278.01 — $453.93 more than the $35 floor.

Minimum vs fixed: the same card, different numbers

A minimum payment and a fixed payment use the same first month’s interest: $104.13 either way. The numbers part company at the payment. The minimum is $154.13 in month 1 and shrinks with the balance, so the card takes 203 months and costs $8,824.08 of interest. A fixed $200 a month never shrinks, so the card takes 36 months and costs $2,135.16 — and a fixed $250 a month takes 27 months and costs $1,534.53. The fixed payment that clears the card in 24 months is $266.84 a month.

Work backwards from a payment you can afford

When the payment is fixed, run the formula in reverse. At $200 a month, the biggest balance gone in 12 months is $2,104.39, and at $250 a month the card takes 27 months. On a 2% rule card, check the payment against the interest first: at 24.99% the first payment of $100.00 is below the first month’s interest of $104.13, so the balance grows to $5,049.73 after 12 months and never pays off. At 18% the same 2% rule does pay off, but it takes 303 months and costs $11,258.89 of interest.

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