Daily periodic rate: how card interest adds up

Turning an annual rate into a daily one

APR is expressed as a yearly rate, but interest actually accrues every day a balance is carried. Card issuers convert the APR into a daily periodic rate, commonly by dividing by 365, and apply that small daily rate continuously rather than waiting until the end of the month.

How the daily rate turns 24% APR into a monthly charge

Each day, the issuer takes that day's balance, multiplies it by the daily rate, and that's the interest charged for that one day. Those daily amounts accumulate across every day in the billing cycle to produce the total interest on the statement. If the balance changes mid-cycle, from a new purchase or a payment, each day still uses whatever the balance actually was on that day.

Working out a daily periodic rate by hand

The calculation is straightforward once broken into its parts.

1. Take the card's APR and divide by 365 to get the daily periodic rate.
2. Multiply that daily rate by the balance for a given day to get that day's interest.
3. Repeat for every day in the billing cycle if the balance changes during the month.
4. Add up every day's interest for the cycle to get the total interest charge.
5. Compare that total to the number on the statement to check your math.

Why the same APR can produce a different interest charge month to month

The APR staying fixed doesn't mean the interest charge does. A higher balance carried for more days in the cycle raises the total, and a longer billing cycle, more days, does too. A purchase made early in the cycle accrues interest for more days than one made near the end, even at the identical rate.

Where this shows up on a real statement

Statements typically list both the APR and the corresponding periodic rate the issuer actually used, along with the balance the rate was applied to. It's worth checking a specific card's own numbers rather than assuming every issuer rounds or divides the same way.

Common questions

Does every issuer divide by 365 exactly?

Not necessarily. Some use 360 or another variation, and the exact method is set out in the card's own terms. Check your card's agreement or statement to see the specific divisor and periodic rate it actually uses.

Why does my interest charge change even though my APR didn't?

Because the daily balance changed. Carrying a higher balance for more days in a given cycle, or having a cycle with more days than usual, both raise the total interest even without any change to the rate itself.

Does paying earlier in the billing cycle lower the interest charged?

Generally yes, since it lowers the balance the daily rate applies to for the remaining days in that cycle. The exact effect depends on when in the cycle the payment posts and how the issuer calculates the balance.