acalculator

What is my credit card interest?

See how much interest your card balance builds each month, and how long a fixed payment takes to pay it off.

Your numbers

Days in a year
Interest this billing cycle
$91.21

A $5,000.00 balance at 22% APR builds $91.21 of interest in a 30-day billing cycle.

Daily periodic rate
0.06027%
Effective yearly rate
24.6%
Months to pay it off
34
Total interest
$1,736.75
Total of payments
$6,736.75
Time to pay it off
2 years, 10 months
Months
34

Interest this billing cycle: $91.21. A $5,000.00 balance at 22% APR builds $91.21 of interest in a 30-day billing cycle.

How much more than the balance will you pay?

How fast does the balance fall?

What does every billing cycle look like?

The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use

How to calculate

Computes the interest a credit card balance builds in one billing cycle at the daily periodic rate, and how long a fixed monthly payment takes to pay it off.

Example with the default inputs (Card balance $5,000.00, Purchase APR 22%, Days in the billing cycle 30, Days in a year 365, Monthly payment $200.00): A $5,000.00 balance at 22% APR builds $91.21 of interest in a 30-day billing cycle.

Method: Daily periodic rate d = APR ÷ days in a year; interest for a cycle of D days = balance × ((1 + d)^D − 1); each cycle the interest is added and the payment is taken off until the balance is 0.

  • Interest compounds daily at the daily periodic rate, and the balance does not change during the cycle.
  • The payment is made at the end of each billing cycle, and every cycle has the same number of days.
  • No new purchases, fees, or promotional rates; the APR does not change.
  • The last payment is whatever is left. Values are not rounded to the cent between cycles.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Card balance $5,000.00, Purchase APR 22%, Days in the billing cycle 30, Days in a year 365, Monthly payment $200.00 gives Interest this billing cycle $91.21, Months to pay it off 34, Total interest $1,736.75, Effective yearly rate 24.599415%.Source: hand calculation in content.mdx; Python 3 in docs/progress/WP-31/python/credit_card.py
  2. Card balance $1,000.00, Purchase APR 18%, Days in the billing cycle 30, Days in a year 365 gives Interest this billing cycle $14.90, Daily periodic rate 0.049315%.Source: hand calculation in content.mdx: 1,000 × ((1 + 0.18 ÷ 365)^30 − 1)
  3. Card balance $2,000.00, Purchase APR 24%, Days in the billing cycle 31, Days in a year 360, Monthly payment $2,100.00 gives Months to pay it off 1, Interest this billing cycle $41.75, Total interest $41.75.Source: hand calculation in content.mdx: 2,000 × ((1 + 0.24 ÷ 360)^31 − 1)

How it works

Write B for the balance, a for the APR as a decimal, Y for the days in a year the card uses (365 or 360), D for the days in the billing cycle, and P for the monthly payment.

  1. Daily periodic rate: d = a ÷ Y.
  2. Interest factor for one cycle: g = (1 + d)^D − 1. Interest is added to the balance every day, so the cycle's interest on a balance that does not change during the cycle is B × g. This is the same as the average daily balance (with the daily interest included) times d times D.
  3. Interest this billing cycle: B × g.
  4. Effective yearly rate: (1 + d)^Y − 1.
  5. Paying it off (when a payment is entered): each cycle, interest = balance × g is added and P is paid at the end of the cycle. The exact number of cycles is n* = −ln(1 − B × g ÷ P) ÷ ln(1 + g) (at 0%, n* = B ÷ P). If P is not more than B × g, the balance never falls and there is no answer; the page also gives no answer when n* is more than 600 (50 years). The number of payments is n* rounded up (a value within 10^−6 above a whole number counts as that number, because n* cannot be computed more closely than about 10^−8 near 600 cycles). The last payment is the balance plus that cycle's interest, so it is usually smaller than P.
  6. Totals: total interest is the sum of every cycle's interest; total of payments is B plus the interest; time is the number of payments in years and months.

With no payment entered, the page shows one cycle only: the interest, the daily rate, and the effective rate.

Assumptions

  • The balance stays the same during each cycle: no purchases, cash advances, fees, or credits, and no grace period.
  • Every cycle has D days, and the payment is credited at the end of the cycle.
  • The APR does not change, and there are no promotional rates.
  • Values are not rounded to the cent between cycles; only the display is rounded.

Worked examples by hand

$5,000 at 22% APR, 30-day cycles, 365-day year, $200 a month. d = 0.22 ÷ 365 = 0.0602740% a day. g = 1.000602740^30 − 1 = 0.0182411, so the first cycle's interest is 5,000 × 0.0182411 = $91.21. B × g ÷ P = 91.206 ÷ 200 = 0.456028, so n* = −ln(0.543972) ÷ ln(1.0182411) = 33.68, which is 34 payments. Running the cycles, the interest adds up to $1,736.75. The effective yearly rate is 1.000602740^365 − 1 = 24.60%.

$1,000 at 18% APR for one 30-day cycle. d = 0.18 ÷ 365 = 0.049315%. (1 + d)^30 = 1.0149008, so the interest is 1,000 × 0.0149008 = $14.90.

$2,000 at 24% APR, a 31-day cycle, 360-day year, paying $2,100. d = 0.24 ÷ 360 = 0.066667%. (1 + d)^31 = 1.0208747, so the cycle's interest is 2,000 × 0.0208747 = $41.75. The balance plus interest is $2,041.75, less than $2,100, so one payment of $2,041.75 clears it and the total interest is $41.75.

Other questions people ask

How is credit card interest calculated?

Most cards charge interest every day at the daily periodic rate: the APR divided by 365 (some use 360). Each day's interest is added to the balance, so the next day's interest is a little larger. Over a billing cycle of D days the interest is the balance × ((1 + daily rate)^D − 1). A $1,000 balance at 18% APR builds $14.90 in a 30-day cycle.

What is the daily periodic rate?

It is the APR divided by the number of days in the year the card uses. At 22% APR and 365 days it is 0.06027% a day. Regulation Z defines the APR the other way round: the periodic rate times the number of periods in a year.

Why is my interest charge different from this page?

Your card charges interest on the average daily balance, which changes with every purchase and payment during the cycle, and some purchases may be in a grace period. This page assumes the balance stays the same through the cycle and no new charges are made. It also leaves out fees, promotional rates, and cash advance rates.

How long will it take to pay off my card?

Enter a fixed monthly payment. Each cycle the page adds the interest and takes off the payment, until the balance is 0. At 22% APR, a $5,000 balance with $200 a month takes 34 payments and $1,736.75 of interest, if you make no new charges.

What if I pay only the minimum?

The minimum payment usually falls as the balance falls, so paying only the minimum can take many years and cost much more interest. Your statement shows how long the minimum takes. A fixed payment, like the one here, pays the card off much faster.

What is the effective yearly rate?

Because interest compounds daily, a card costs a bit more than its APR over a full year: (1 + daily rate)^365 − 1. A 22% APR is an effective 24.60% a year on a balance that is never paid down.