Lesson 25 of 25 · 6 min
What agreeing with the printed figure does and does not prove
Matching the printed total proves the arithmetic is consistent with the inputs you used, and nothing beyond that.
You have rebuilt $3,934.07, $7,409.40, $11,343.47 and $1,858,563.47. The chain residual is zero. The inversion recovers the total. That is a real finding. It is also a bounded one. A match proves that the four inputs you used produce the printed products. It does not prove that those were the only inputs the month contained, or that the month is finished.
What the match does not reach:
- A hidden intra-period rate wiggle that nets to the same two-leg total would also match.
- A backward-effective revision can reopen February, as lesson 15 did with $357.24 arriving in April.
- Collateral values, advance rates and headroom are a different reconstruction. Matching interest says nothing about Calder's 35 percent advance.
- The convention was an input you brought. Matching Act/360 products does not independently prove the agreement says Act/360.
- Demand rights, notice, and the eight terms from Track 5 are not arithmetic objects at all.
The useful remainder is still large. A $141.11 gap is a rewritten period 1. A 1.39 percent gap is a 365-divisor. A one-cent gap is a rounding split. A residual of $185.00 is a named hole in the chain. Each of those is a smaller question than whether the statement 'looks right'. The match you have on March is the first of those questions answered: these four factors, on this path, produce this page.
Agreement with a printed figure is consistency with the inputs in hand. Completeness, finality and fairness are different claims, and they have different evidence.
Key terms
- Consistency
- The printed products equal the four-factor reconstruction. The finding this track can make.
- Completeness
- A claim that no other rate segment or balance change occurred. A match does not establish it.
- Finality
- A claim that a closed period will not be recomputed. A prior-period adjustment is the counter-example.
Worked example
Four findings a match cannot make
The sample March, already reconstructed to the cent.
- What matched
- $3,934.07 + $7,409.40 = $11,343.47, close $1,858,563.47
- Hidden third rate that nets to the same total
- Not ruled out by the match
- February reopened at 6.72 percent
- $357.24 later, March still matches
- Calder advance rate 35 percent
- Untouched by the interest products
- Naive 31 days at 7.22 percent
- $11,484.58, rejected by the same match
The match is decisive against $11,484.58 and silent on Calder, on February's later revision, and on any path that happens to add to $11,343.47.
Check yourself
You have reproduced $11,343.47 and $1,858,563.47 to the cent. Which claim does that establish, and which of these does it not: that March is final, that no other rate applied, that Act/360 is in the agreement, that Calder's advance rate is 35 percent?
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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.