Lesson 18 of 25 · 6 min

When two consecutive statements disagree

March's close is April's opening; any other printed pair is a difference you can name in dollars.

Two consecutive letters are a chain. March's close of $1,858,563.47 is April's opening if no document between them rewrites the loan. When an invented April letter prints an opening of $1,858,540.12, the pair disagrees by $23.35. That $23.35 is not a rounding story until you have recomputed it; it is first a difference between two printed numbers that the chain says should be equal.

The same April letter prints interest of $11,190.50. Thirty days at 7.22 percent Act/360 on the true March close is $11,182.36. The interest disagreement is $8.14 the other way. Opening plus printed interest is $1,858,540.12 + $11,190.50 = $1,869,730.62. The reconstructed close from March is $1,869,745.83. The close-to-close gap is $15.21, which is $23.35 − $8.14: the two disagreements partly offset.

A disagreement is a measured pair, not a verdict. It can be a day-count difference, a restated opening, a mid-month draw the reconstruction missed, or a typesetting error. The mechanism is the subtraction. March close minus April opening, reconstructed interest minus printed interest, reconstructed close minus printed close. Three named differences, three places the chain can fail to join.

Consecutive statements are an equation. When the two sides differ, the content of the month is the difference, not the later letter alone.

Key terms

Chain break: A printed opening that does not equal the previous printed close, or a printed interest that does not equal the reconstructed accrual.
Offsetting disagreements: Two breaks of opposite sign whose net is smaller than either side. Here $23.35 and $8.14 net to a $15.21 close gap.

Worked example

An invented April letter that does not join March

March close $1,858,563.47. April letter prints opening $1,858,540.12 and interest $11,190.50. Reconstructed April interest $11,182.36.

Opening disagreement: $23.35
Interest disagreement: $8.14
Printed April close: $1,869,730.62
Reconstructed April close: $1,869,745.83
Close-to-close gap: $15.21

Three subtractions locate the break. The later letter is one side of an equation, not a replacement for the earlier one.

Check yourself

March closes at $1,858,563.47. April prints an opening of $1,858,540.12 and interest of $11,190.50 against a reconstructed $11,182.36. What is the close-to-close gap?

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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.