Lesson 9 of 25 · 6 min

Daily accrual: the charge that does not wait for the statement

Interest exists on the morning of the twelfth, whether or not a statement has been issued.

The statement is dated 2 April and covers 1 March to 31 March. Accrual does not wait for 2 April. Each day adds balance × rate ÷ 360 to a running total. On the Halden & Wren opening rate that daily addend is $1,847,220 × 0.0697 ÷ 360 = $357.642316…. On the closing rate it is $1,847,220 × 0.0722 ÷ 360 = $370.470233….

After eleven mornings the running total is 11 × $357.642316… = $3,934.065483…, which is period 1. After the next twenty mornings it has grown by 20 × $370.470233… = $7,409.404666…, which is period 2. The month-end print is the same addition you have already done, sliced by day rather than by leg. The legs are just runs of identical days.

The maintenance test does not use the 2 April document. It uses the balance plus what has accrued since the last capitalisation. On the morning of 12 March, before any April statement exists, $3,934.07 has already been earned on the line. Lesson 17 puts that $3,934.07 against the printed February close and shows the headroom it has already consumed.

A daily figure also explains why a 31-day month and a 28-day month differ by more than a rounding. Three extra days at $357.64 is $1,072.93 before the rate path is allowed to differ. February against March is lesson 13; the daily addend is the unit that comparison is made of.

Key terms

Daily addend: Balance × rate ÷ 360. $357.642316… at 6.97 percent and $370.470233… at 7.22 percent on the March opening balance.
Running total: The sum of daily addends since the last capitalisation. It exists on days the statement has not yet described.
Accrual: The daily earning of interest. Distinct from capitalisation, which is when that earning is added to the printed principal.

Worked example

Two daily addends, one month

Flat $1,847,220. Act/360. Rate 6.97 percent for eleven days, then 7.22 percent for twenty.

Daily addend at 6.97%: $357.642316…
Eleven of those days: $3,934.065483…
Daily addend at 7.22%: $370.470233…
Twenty of those days: $7,409.404666…
Month as a sum of days: $11,343.47

A leg is a pile of identical daily addends. The statement is a late description of a total that was already growing.

Check yourself

What is the daily addend on $1,847,220 at 6.97 percent, Act/360, and what has accrued by the morning of 12 March?

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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.