The average daily balance method worked through one statement cycle, with what the timing of a payment is worth.
Most cards charge interest on the average daily balance: divide the APR by 365 to get a daily rate, multiply by the balance on each day of the cycle, and add up. On a £2,400 balance at 22.9 per cent, with a £300 purchase on day 11 and a £500 payment on day 16, the average daily balance is £2,350 and the month's interest is £44.23. Paying the same £500 on day 1 instead would cut it to £39.53.
Worked in full in Personal Finance for Beginners by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
One 30-day statement cycle on a card that already carries a balance from last month, so there is no interest-free period on new purchases. All figures are illustrative. Card agreements differ in detail, including whether interest compounds daily or is added once a month, so your statement may differ by a few pence; the method is the same. One point on labels: the daily rate comes from the card's annual interest rate on purchases. In the UK the headline representative APR also folds in compounding and any fees, so it can sit slightly above the rate the card actually divides by 365. Use the purchase rate printed on the statement.
| Input | Value |
|---|---|
| Annual interest rate, purchases | 22.9% |
| Days in the year | 365 |
| Days in the cycle | 30 |
| Balance brought forward | £2,400 |
| Purchase on day 11 | £300 |
| Payment on day 16 | £500 |
Daily periodic rate = APR ÷ 365 = 22.9% ÷ 365 = 0.0627% a day (0.000627 as a decimal)
One day on £2,400 costs £1.51
Write down the balance at the end of each day and average it. Because the balance only changes on the days something happens, the cycle splits into three blocks.
| Days | Number of days | Balance | Balance × days |
|---|---|---|---|
| 1 to 10 | 10 | 2,400 | 24,000 |
| 11 to 15, after the purchase | 5 | 2,700 | 13,500 |
| 16 to 30, after the payment | 15 | 2,200 | 33,000 |
| Total | 30 | 70,500 |
Average daily balance = sum of daily balances ÷ days = 70,500 ÷ 30 = £2,350.00
Interest = average daily balance × daily rate × days in the cycle
= 2,350.00 × 0.000627 × 30 = £44.23
Excel, with daily balances in B2:B31: =AVERAGE(B2:B31)*22.9%/365*30
The closing balance is the £2,200 left after the payment plus £44.23 of interest: £2,244.23. If the card compounds daily, adding each day's interest to the balance before the next day's charge, the month's interest is £44.65, 42 pence more. Over one cycle compounding barely matters; over a year it is the difference between 25.46 per cent and 25.73 per cent effective, against the 22.9 per cent headline APR.
You can rebuild the bill from any statement in about ten minutes, and it is worth doing once to see where your money goes.
If your figure and the card's differ by more than a few pence, look for a cash advance or a balance transfer charged at a different rate, a fee added to the balance, or interest compounding daily. Each rate is calculated on its own balance and the results are added together.
The only lever inside a cycle is timing. The same £500 payment, moved across the month, with the purchase still on day 11:
| Payment day | Average daily balance | Interest | Against day 16 |
|---|---|---|---|
| 1 | 2,100.00 | 39.53 | −4.71 |
| 6 | 2,183.33 | 41.09 | −3.14 |
| 11 | 2,266.67 | 42.66 | −1.57 |
| 16 | 2,350.00 | 44.23 | 0.00 |
| 21 | 2,433.33 | 45.80 | +1.57 |
| 26 | 2,516.67 | 47.37 | +3.14 |
| 30 | 2,583.33 | 48.62 | +4.39 |
Each day £500 sits on the card costs £0.31, so paying ten days earlier saves £3.14 a month. It is real money over a year but small next to the rate itself:
| APR | Daily rate | Month's interest | A year at this balance |
|---|---|---|---|
| 17.9% | 0.0490% | 34.57 | 421 |
| 22.9% | 0.0627% | 44.23 | 538 |
| 29.9% | 0.0819% | 57.75 | 703 |
Carrying an average £2,350 for a year at 22.9 per cent costs about £538. That is the figure to hold against any decision to leave a balance on a card, and against the fee on a 0 per cent balance transfer.
The first is the shortcut: balance times APR divided by twelve. On the £2,400 brought forward it gives £45.80; on the £2,200 closing balance £41.98. Neither is the bill, because neither knows when money moved. The daily method charges for the purchase from the day it was made and credits the payment only from the day it arrived.
The second is assuming new purchases are interest-free. Most cards give an interest-free period on purchases only when the previous statement was paid in full. Once you carry a balance, the £300 purchase on day 11 attracts interest from day 11, as it does here. That is why carrying even a small balance is more expensive than it looks: it switches off the interest-free period on everything new.
The arithmetic cannot make a balance cheap. It can only show what it costs. If this month's interest is close to your payment, see what a minimum payment actually does.
To see how much of your own payment is interest and how long one debt takes to clear, use the blank calculator in the free workbook for this case.
Divide the APR by 365 to get the daily periodic rate, then multiply by the balance for that day. At 22.9 per cent the daily rate is 0.0627 per cent, so one day on a £2,400 balance costs £1.51. Over a cycle, multiply the average daily balance by the daily rate and the number of days.
Yes, if you carry a balance, because interest is charged on each day's balance. Moving a £500 payment from day 16 to day 1 of a 30-day cycle cuts the average daily balance from £2,350 to £2,100 and the month's interest from £44.23 to £39.53 at 22.9 per cent. Each day £500 sits on the card costs about £0.31.
If interest is added monthly, (1 + 0.229 / 12) to the power 12 minus 1 gives 25.46 per cent. If it compounds daily, (1 + 0.229 / 365) to the power 365 minus 1 gives 25.73 per cent. So carrying a balance costs more than the simple 22.9 per cent rate. A UK representative APR already includes this compounding, which is why it reads higher than the purchase rate.
Getting out of debt is worked in the workbook for chapter 7 of Personal Finance for Beginners. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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