How card interest is calculated (APR → daily rate → average daily balance) ⚙

The situation

Your card says “24% APR.” You carry a $5,000 balance for a month. Quick: how much interest do you owe? Most people guess wildly — and the card company is counting on you not knowing. The actual math is completely learnable, and once you see it, that 24% stops being a mystery number and becomes a cost you can predict.

The idea

This is the same compounding engine from Phase 6 — but now it’s running against you. Three pieces:

1. APR → daily periodic rate. Your APR (Annual Percentage Rate) is the yearly cost of borrowing. But cards don’t charge once a year — they charge every day. So they split the APR into a daily periodic rate (DPR): APR ÷ 365. A 24% APR becomes about 0.0658% per day. Tiny — but it hits every single day.

2. Average daily balance. The card doesn’t charge interest on your starting balance or your ending balance. It charges on the average daily balance (ADB) — what you owed each day, added up and divided by the days in the cycle. Carry $5,000 flat all month and your ADB is $5,000. Pay some down halfway through and the average drops, because your balance was lower for the back half.

3. Put them together. The cycle’s interest is:

average daily balance × daily periodic rate × days in the cycle

That’s it. Average balance, times the daily slice, times the number of days.

The rule of thumb: a carried balance costs you ADB × (APR ÷ 365) × days — roughly 2% of the balance every month at a 24% APR. This is the “bucket with a hole.” A balance just sitting there leaks interest every day it sits.

One more thing this explains: why paying earlier in the cycle helps. Since interest rides on the average, knocking the balance down sooner means it’s lower for more days, which pulls the average — and the interest — down. Timing matters.

By the numbers

Here’s the calculator from the last lesson, now with the grace toggle OFF — you’re carrying a balance, so the bucket has a hole. Same $5,000, same 24% APR:

The scenario: $5,000 average daily balance, 30-day cycle, 24% APR, grace period lost.

Step by step:

Step	Math	Result
Daily periodic rate	24% ÷ 365	≈ 0.0658% per day
Average daily balance	$5,000 carried flat	$5,000.00
Cycle interest	$5,000 × 0.0658% × 30 days	≈ $98.63

People think card interest is one step — “the APR.” It’s a four-step chain, and every step is doing work:

flowchart LR
  accTitle: How a credit card turns an APR into a dollar amount
  accDescr: The APR is divided by 365 to get the daily periodic rate. That daily rate is multiplied by the average daily balance, and then by the number of days in the billing cycle. The result is the interest charged for that cycle.
  A["APR"] --> B["Divide by 365"]
  B --> C["Daily periodic rate"]
  C --> D["Times the average daily balance"]
  D --> E["Times the days in the cycle"]
  E --> F["Interest charged for the cycle"]

That $98.63 is what one month of carrying $5,000 costs. Keep it up all year and you’re paying roughly $1,184 — and that’s before the balance compounds on itself, which it does. You’d be handing the card company about $1,184 a year for the privilege of carrying a balance you could have paid off.

Now play with the calculator. Watch what happens when you add a payment mid-cycle — the average daily balance drops, and the interest drops with it, more if the payment lands earlier. Add a purchase mid-cycle and the average climbs. This is the live version of “interest rides on the average, and timing matters.” The number you saw as $0.00 in the last lesson (grace on) is the same engine — the only difference is whether the hole in the bucket is open.

Where this fits

You now know exactly what a carried balance costs and why: a daily rate, applied to your average balance, every day. That’s the engine. The next lesson points it at the cruelest setting of all — what happens when you pay only the minimum and let that engine run for years.