Lesson 1 of 25 · 7 min

Credit-card APR as a daily rate

A card APR is a daily rate, and a monthly statement is thirty-one of those multiplications added.

A credit-card APR is an annual rate that is applied as a daily rate. Track 1 lesson 14 is that mechanism on a securities line: interest is computed every day, then summarised once a month, and the summary loses the path. A card statement is the same summary. This lesson does not reopen Act/360 against 365. Cards commonly divide by 365. The rest of the machine is the one already taught.

Wick & Pell Cards prints an illustrative 21.99 percent APR on a carried balance of $4,280. The daily rate is 21.99 percent ÷ 365 = 0.000602466. A 31-day month charges $4,280 × 0.000602466 × 31 = $79.94. That $79.94 is thirty-one multiplications added, not a twelfth of 21.99 percent of $4,280. A twelfth would be $4,280 × 0.2199 ÷ 12 = $78.43, which is a different day-count and a different month.

daily interest = balance × (APR ÷ 365) × days in the cycle

balance: The amount outstanding on the days being charged, including any interest already added.
APR: The annual percentage rate printed on the card. Illustrative in every figure here.
365: The day-count cards commonly use. Track 1 lesson 15 is the 360-day version; this lesson does not re-teach it.

The monthly line is a compression. Change the number of days and the charge moves even if the balance and the APR do not. A 28-day cycle on the same $4,280 is $4,280 × 0.000602466 × 28 = $72.20. A 31-day cycle is $79.94. The APR did not move. The clock did. That is Track 1 lesson 14's point on a household product: the printed month hides the daily product.

The APR is a year. The charge is a day times a balance times a day-count. The statement is the sum of those days.

Key terms

Card APR: An annual rate that a card applies as a daily rate, commonly APR divided by 365.
Daily rate: APR ÷ 365 on a typical card. The number multiplied by the balance each day.
Cycle charge: The sum of daily interest across the days in the statement period. One printed line, many multiplications.

Worked example

Thirty-one days on one balance

Wick & Pell Cards. Balance $4,280. Illustrative 21.99 percent APR. Cycle of 31 days. Day-count 365.

Daily rate: 0.000602466
One day's interest: $2.58
31-day charge: $79.94
Monthly twelfth, for contrast: $78.43
28-day charge, same APR: $72.20

The $79.94 is thirty-one daily products. It is not a twelfth of the year, and a shorter cycle prints a smaller line at the same APR.

Check yourself

A Wick & Pell card carries $2,640 at an illustrative 24.99 percent APR. The cycle is 30 days and the day-count is 365. What is the cycle's interest?

A card APR billed daily is the everyday version of daily accrual, which Track 1 lesson 14 shows a monthly statement hiding. Open Daily accrual, and why a monthly statement hides it →

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.