Lesson 23 of 25 · 7 min

Reading the same number in two places

A figure that appears twice and still reconciles is a check; a figure that appears once is a claim.

A statement is full of numbers that are printed once and derived twice. The second appearance is sometimes another cell and sometimes an identity you have to form. When both appearances agree, the page is internally consistent. When a figure has only one appearance, it is an input — a claim the page asks you to accept from outside itself.

Pairs on the March page that are the same quantity in two places:

Interest charged $11,343.47 is also $3,934.07 + $7,409.40.
Closing drawn balance $1,858,563.47 is also $1,847,220.00 + $11,343.47.
Stated rate 6.97% is also 5.12% + 1.85%; stated rate 7.22% is also 5.37% + 1.85%.
Calder market $1,840,005.00 is also 3,100 × $593.55; Calder lending $644,001.75 is also $1,840,005.00 × 0.35.
Total market $6,032,795.00 is the five market cells; total lending $3,277,251.25 is the five lending cells.
Blended advance 54.32% is $3,277,251.25 ÷ $6,032,795.00; LTV 30.81% is $1,858,563.47 ÷ $6,032,795.00.
Undrawn at open $552,780.00 is $2,400,000.00 − $1,847,220.00.

The once-only figures are the inputs those identities consume: the two index fixings, the 1.85 point spread, the 11 and 20 day counts, each row's units, prices and advance rates, the $2,400,000.00 limit, the 70% threshold, the $1,847,220.00 opening as far as this page alone is concerned. The opening becomes a twice-appearing figure only when February's close is on the desk.

Reading a statement is walking the pairs. A broken pair is a broken page. An unbroken pair is not yet a true page — it is a consistent one. Truth against the world is a later question, for marks and fixings fetched elsewhere. Consistency against itself is the question this document can answer, and it answers it only in the places a number appears twice.

Key terms

Pair: The same quantity printed or implied in two places. $11,343.47 as a total and as $3,934.07 + $7,409.40 is a pair.
Input (on the page): A figure with one appearance and no parent identity on the document. Calder's 35% and the 1.85 point spread, taken as a printed line, are inputs.
Internal consistency: Every pair agrees. It is a property of the document, not a property of the market.

Worked example

Seven pairs, one morning

The March statement treated as a set of identities rather than a set of facts.

Interest pair: $3,934.07 + $7,409.40 = $11,343.47
Balance pair: $1,847,220.00 + $11,343.47 = $1,858,563.47
First-rate pair: 5.12% + 1.85% = 6.97%
Calder market pair: 3,100 × $593.55 = $1,840,005.00
Blend pair: $3,277,251.25 ÷ $6,032,795.00 = 54.32%
Undrawn pair: $2,400,000.00 − $1,847,220.00 = $552,780.00
A once-only figure, for contrast: 70% of market value

Six identities confirmed the arithmetic. The 70% remains a claim about the agreement. Both readings are useful, and they are not the same reading.

Check yourself

Name two March figures that appear twice, show the arithmetic that joins each pair, and name one March figure that appears only once.

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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.