Daily accrual, and why a monthly statement hides it

Interest is computed every day, then summarised once a month, and the summary loses the detail.

Interest on these facilities accrues daily. Each day the lender takes your balance that day, multiplies by the daily rate, and adds the result to what you owe. Thirty of those small numbers are then added together and printed as one line on a statement.

Compressing thirty numbers into one loses two kinds of information. It loses the balance path — a month where you drew heavily on day two and a month where you drew the same amount on day twenty-eight produce different interest but similar-looking statements. And it loses the rate path — if the rate reset mid-month, the single figure blends two rates, and the printed rate at the top of the statement may match neither.

daily interest = balance × (rate ÷ day-count basis)

balance: The amount outstanding on that specific day, including interest already added.
rate: The annual rate in effect on that day, not the average for the month.
day-count basis: The number the annual rate is divided by, typically 360 or 365. The next lesson is about this choice.

The reason this is not merely pedantic: the only way to verify a monthly interest figure is to reconstruct the daily accruals. If you cannot state your balance and rate for each day of the period, you cannot check the number, and an unverifiable charge is one you are accepting on trust. Track 5 walks through the reconstruction step by step.

There is also a compounding effect. If accrued interest is added to the balance rather than paid, the next day's interest is computed on the larger figure. On a small balance over a month this is a rounding detail; on a large balance over years it is not.

Key terms

Accrual: Interest earned by the lender day by day, whether or not it has been billed or paid.
Balance path: The sequence of daily balances over a period. Two months with the same average balance can have different paths and different interest.
Capitalisation: Adding unpaid interest to principal, so future interest is computed on a larger balance.

Worked example

Same money, different month

A 30-day month, 6.5% annual rate, Act/360 basis. Daily rate 0.0180556%.

Case A: $200,000 drawn on day 1: $1,083.33
Case B: $200,000 drawn on day 21: $361.11
Difference: $722.22
What both statements show: One interest line

The interest line is a summary of a path, and the path is not printed. Verifying the summary requires rebuilding the path.

Check yourself

Two borrowers each averaged a $200,000 balance over the same month at the same rate. Must their interest charges be equal?

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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.