← Reconstructing the arithmetic

Lesson 4 of 25 · 6 min

Reconstructing period 1 of the March statement

Eleven days at 6.97 percent on the opening balance is the whole of the first printed interest line.

The sample statement sits above this lesson so the printed figures are in view. Period 1 is the stretch from 1 March to the reset on 12 March: eleven days. The rate in force is the opening rate, 5.12 percent index plus 1.85 percent spread, which is 6.97 percent. The balance does not move. Those are the four inputs.

Rebuild it from the opening balance. $1,847,220 × 0.0697 × 11 ÷ 360 = $3,934.065483…. The statement prints $3,934.07. The match is to the cent. Nothing from period 2 belongs in this product: not the 7.22 percent closing rate, not the twenty remaining days, not the $7,409.40 that those twenty days produce.

A common miss is to start the twenty-day clock on 12 March and still charge 12 March at 6.97 percent, or to count 1 March to 12 March as twelve days. The sample names eleven days at the opening rate and twenty at the closing rate, and 11 + 20 = 31, which is the length of March. The reset date is the first day of the new rate, not an extra day of the old one.

Once this leg matches, period 2 is a second product of the same shape. Adding them is lesson 6. The only arithmetic this page has to do is the one product, and the statement already printed the answer you are aiming at.

Key terms

Period 1
1 March to 11 March 2026 on the sample. Eleven days at 6.97 percent on $1,847,220.
Reset date
12 March 2026. The first day the closing rate applies, and therefore not a twelfth day of period 1.
Opening rate
Index 5.12 percent plus spread 1.85 percent, which is 6.97 percent. In force for the first eleven days.

Worked example

Period 1 against the printed line

Halden & Wren sample, 1 March 2026 – 31 March 2026. First interest line only.

Index + spread
5.12% + 1.85% = 6.97%
Days at that rate
11

1 March through 11 March.

Balance
$1,847,220.00
Product
$3,934.065483…

$1,847,220 × 0.0697 × 11 ÷ 360.

Printed period 1
$3,934.07

The first interest line is this product rounded to the cent. A match here is a match of four inputs, not a match of a monthly average.

Check yourself

Why is period 1 eleven days rather than twelve, given that the reset is dated 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.

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