Lesson 7 of 25 · 7 min

What a gap of one missing statement costs

One skipped letter leaves the next month's interest accruing on an opening that is already eleven thousand dollars light.

Miss the March letter and the last confirmed balance is February's close, which is March's opening of $1,847,220.00. The March interest of $11,343.47 never becomes an official opening for April. If April is then accrued on $1,847,220.00 at 7.22 percent Act/360 for thirty days, the interest comes out at $1,847,220.00 × 0.0722 × 30 ÷ 360 = $11,114.11. The same thirty days on the true March close of $1,858,563.47 produce $11,182.36. The interest error is $68.25.

The closing error is larger, because it includes the missed March interest as well: $11,343.47 + $68.25 = $11,411.72. The trigger that belongs to that missed close is $11,411.72 ÷ 0.70 = $16,302.46 below the trigger computed from the true April close. One missing letter has moved the reconstructed trigger by the March interest, plus one month of interest on that interest, all divided by the threshold.

Even a reconstruction that remembers to accrue March still lacks the letter's confirmation of the reset on 12 March, of zero draws, and of unchanged units. The $16,302.46 is the cost if the old close is frozen. The unseeable cost is every intra-month event the missing letter would have itemised and the reconstruction has to assume away.

A gap of one statement is not a missing page of narrative. It is a wrong opening balance for every later accrual, and a missing list of the events that opening already includes.

Key terms

Missing-statement gap: The difference between a reconstruction that starts from the last letter you hold and one that starts from the letter you do not.
Wrong opening: An accrued balance that used an earlier close as if it were the current one. Every later day compounds that error.

Worked example

April accrued on February's close

Last confirmed balance $1,847,220.00. April treated as 30 days at 7.22 percent Act/360. True March close $1,858,563.47.

April interest on the stale opening: $11,114.11
April interest on the true opening: $11,182.36
Interest error: $68.25
Missed March interest: $11,343.47
Closing error: $11,411.72
Trigger error: $16,302.46

One skipped March letter is $11,411.72 of closing error and $16,302.46 of trigger error before any April price is considered.

Check yourself

March is missing. April's thirty days at 7.22 percent Act/360 are accrued on $1,847,220.00 instead of on $1,858,563.47. What is the trigger error at the April close, ignoring prices?

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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.