# What is my credit card interest?

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.

- Page: https://www.acalculator.org/finance/credit-card-interest-calculator
- JSON spec: https://www.acalculator.org/finance/credit-card-interest-calculator.json
- Version: 09fc9e3648c8

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| balance | Card balance | The balance on the card that is charged interest. |
| apr | Purchase APR | The card’s annual percentage rate for the balance. |
| days | Days in the billing cycle | The number of days in one billing cycle, usually 28 to 31. |
| basis | Days in a year | The number of days the card divides the APR by to get the daily rate: 365 or 360. |
| payment | Monthly payment | A fixed amount you pay at the end of every billing cycle. Leave it empty to see one cycle’s interest. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| cycle | Interest this billing cycle | The interest the balance builds in one billing cycle at the daily periodic rate, compounded daily. |
| daily | Daily periodic rate | The APR divided by the days in a year. |
| effective | Effective yearly rate | What the APR really costs in a year when interest compounds daily: (1 + daily rate)^days in a year − 1. |
| months | Months to pay it off | How many monthly payments clear the balance, if no new charges are made. |
| interest | Total interest | All the interest paid until the balance is 0. |
| paid | Total of payments | The balance plus all the interest. |
| time | Time to pay it off | The number of payments in years and months. |

## 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.

## Assumptions

- 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.

## Worked examples

1. balance = $5,000.00, apr = 22%, days = 30, basis = 365, payment = $200.00 gives cycle = $91.21, months = 34, interest = $1,736.75, effective = 24.599415%. Source: hand calculation in content.mdx; Python 3 in docs/progress/WP-31/python/credit_card.py.
2. balance = $1,000.00, apr = 18%, days = 30, basis = 365 gives cycle = $14.90, daily = 0.049315%. Source: hand calculation in content.mdx: 1,000 × ((1 + 0.18 ÷ 365)^30 − 1).
3. balance = $2,000.00, apr = 24%, days = 31, basis = 360, payment = $2,100.00 gives months = 1, cycle = $41.75, interest = $41.75. Source: hand calculation in content.mdx: 2,000 × ((1 + 0.24 ÷ 360)^31 − 1).

## FAQ

### 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.

## Sources

- Consumer Financial Protection Bureau, How does my credit card company calculate the amount of interest I owe? https://www.consumerfinance.gov/ask-cfpb/how-does-my-credit-card-company-calculate-the-amount-of-interest-i-owe-en-51/
- Regulation Z (Truth in Lending), 12 CFR 1026.14(b), Annual percentage rate for periodic statements: each periodic rate times the number of periods in a year. https://www.consumerfinance.gov/rules-policy/regulations/1026/14/
- Compound interest and the number of payments: S. A. Broverman, Mathematics of Investment and Credit, chapters 1 and 3.