Lesson 16 of 25 · 5 min

Checking the balance chain: open + draws − repayments + interest = close

Opening plus draws minus repayments plus interest is the closing balance, or the residual is the finding.

The chain is one addition. Closing equals opening plus draws minus repayments plus interest, plus any fee or adjustment you can name. On the sample March every optional term is zero: $1,847,220.00 + $0 − $0 + $11,343.47 = $1,858,563.47. The printed close matches. There is no residual.

close = open + draws − repayments + interest ± fees ± adjustments

open: The previous close. February's $1,847,220.00 is March's opening.
draws: Amounts advanced in the period. Zero on the sample; $184,000 in lesson 11.
repayments: Amounts applied to principal. Zero on the sample; $63,400 in lesson 12.
interest: The period's charge, ideally the figure the legs already reproduced.

The invented draw month closes at $2,031,220 + $11,786.30 = $2,043,006.30, which is also $1,847,220 + $184,000 + $11,786.30. The invented repayment month closes at $1,783,820 + $11,040.07 = $1,794,860.07, which is $1,847,220 − $63,400 + $11,040.07. Both chains are the same sentence with different numbers in the slots.

A residual is a number. Invent an April close printed at $1,869,930.83 against an opening of $1,858,563.47 and verified interest of $11,182.36. The chain expects $1,869,745.83. The residual is $185.00. That $185.00 is a fee, an unlabelled adjustment, or a question. The arithmetic does not name it. It isolates it. Five lines of addition produced a specific dollar figure attached to a named period. Matching the printed close without naming every term in the chain is not a check at all; it is an assumption that the unlabelled terms were zero.

Key terms

Balance chain: The identity linking one close to the next opening through the period's activity. It uses addition, not the agreement's rate clause.
Residual: The unexplained difference after every named item is applied. The output of the check.

Worked example

Three months, one identity

Sample March, the lesson-11 draw, and an April with a $185.00 residual.

Sample March: $1,858,563.47
March with the $184,000 draw: $2,043,006.30
Expected April close: $1,869,745.83
Invented printed April close: $1,869,930.83
Residual: $185.00

A match is a closed identity. A residual is a dollar figure attached to a named period, which is a different object from a feeling that the balance looks high.

Check yourself

Opening $1,858,563.47, verified interest $11,182.36, no draws, no repayments, printed close $1,869,930.83. What is the residual?

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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.