Lesson 2 of 25 · 6 min

Opening balance × rate × days ÷ divisor

The charge is a product, not a rate, and any one of the four factors can be the one that moved.

The formula is short enough to write in one line and easy to apply to the wrong stretch. Interest for a run of days on which both the balance and the rate were constant is opening balance × rate × days ÷ divisor. The Halden & Wren first March leg is that product and nothing else.

interest = balance × rate × days ÷ 360

balance: The amount outstanding on every day of this stretch. $1,847,220 on the first March leg.
rate: The annual rate as a decimal. 0.0697 for the eleven days before the 12 March reset.
days: The count of calendar days in the stretch, not the count printed on the period label.
360: The Act/360 divisor. Replacing it with 365 scales every charge down by 360/365.

Work the first Halden & Wren leg. $1,847,220 × 0.0697 = $128,751.234. Times eleven days is $1,416,263.574. Divide by 360 and the unrounded product is $3,934.065483…. Rounded to the cent, $3,934.07. That is the figure the statement prints for period 1. The same four-factor shape produces period 2 when the rate becomes 0.0722 and the days become twenty.

The formula does not average anything. A 31-day label does not go in the days slot if the rate changed on day twelve. A closing rate does not go in the rate slot for days that preceded the reset. Putting either of those in produces a different product, and the difference is not a rounding error. Lesson 7 measures that gap on this same month. The four factors are a list of facts about one stretch, and a fact taken from a different stretch is a different charge.

Key terms

Leg: One stretch during which balance and rate were both constant. Each leg is its own four-factor product.
Unrounded product: The exact quotient before it is taken to the nearest cent. Period 1 is $3,934.065483… before it becomes $3,934.07.

Worked example

Period 1, written as a product

Halden & Wren, 1 March to 11 March 2026. Balance flat at $1,847,220. Rate 6.97 percent. Act/360.

Balance × rate: $128,751.234
Times eleven days: $1,416,263.574
Divide by 360: $3,934.065483…
Printed period 1: $3,934.07

Four numbers and one rounding produced the first interest line. Nothing else about March enters this product.

Check yourself

On $1,847,220 at 6.97 percent, Act/360, what is eleven days of interest, and what changes if you put 31 in the days slot?

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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.