Lesson 1 of 25 · 6 min

The four numbers an interest charge is made from

An interest line is four inputs multiplied, and the statement usually prints only the product.

A printed interest figure looks like a fact about the month. It is a product. Four numbers go in: the balance that was outstanding, the annual rate in force, the number of days that pair applied, and the day-count divisor. Multiply the first three and divide by the fourth. The statement typically shows the answer and hides at least one of the inputs.

On the Halden & Wren March statement the first of those inputs is $1,847,220, the opening balance. The second is 6.97 percent for eleven days, then 7.22 percent for twenty. The third is those day counts, not the 31 on the period label. The fourth is 360, because the facility is Act/360. The printed total, $11,343.47, is what those four produce when the month is split at the reset.

What each factor is, and where it lives:

Balance — the amount outstanding on the days being charged. It moves when you draw, repay, or capitalise a prior charge.
Rate — the annual percentage in force on those days. Index plus spread, and either piece can move.
Days — the length of the stretch during which both balance and rate were constant.
Divisor — 360 on this facility. It is a term of the agreement, not a property of the calendar.

The reconstruction habit is to name the four before trusting the product. A later lesson rebuilds each March leg. A different facility, or a different month, uses the same four. On a $412,800 balance at 6.40 percent for nine days, Act/360, the product is $412,800 × 0.0640 × 9 ÷ 360 = $660.48. Same shape, different sizes.

Key terms

Interest product: Balance × rate × days ÷ divisor. The printed charge is this product, often after a split into legs.
Input: One of the four numbers that make a charge. The statement may omit the one that changed.
Divisor: The year-length used to turn an annual rate into a daily one. 360 on an Act/360 facility.

Worked example

Four inputs, one small product

A $412,800 balance, 6.40 percent, nine days, Act/360. Invented figures, same shape as Halden & Wren.

Balance: $412,800
Rate: 0.0640
Days: 9
Divisor: 360
Product: $660.48

The statement would print $660.48. The four numbers that made it are what a reconstruction recovers.

Check yourself

A statement prints $660.48 of interest and a closing rate of 6.40 percent. Which of the four inputs does that pair fail to identify on its own?

The divisor, which might be 360 or 365, and the days and balance that actually applied.
Only the balance, because the rate and the days are on the page.
Only the divisor, because 6.40 percent and $660.48 fix the rest.

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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.