Lesson 10 of 25 · 5 min

Capitalisation: where this month's charge sits next month

Next month's opening balance is this month's closing balance, so today's charge is tomorrow's principal.

The March close is $1,858,563.47. That figure is the April opening. The $11,343.47 that March earned is no longer a charge sitting beside the principal. It is inside the principal. Every April day accrues on $1,858,563.47, not on $1,847,220.

The February chain is the same mechanism one month earlier. February opened at $1,837,260.01, ran 28 days at 6.97 percent, Act/360, and charged $1,837,260.01 × 0.0697 × 28 ÷ 360 = $9,959.990654…, which prints as $9,959.99. $1,837,260.01 + $9,959.99 = $1,847,220.00, the March opening to the cent. March's first daily addend already includes February's interest in its base.

April, illustrated at a flat 7.22 percent for its 30 days, charges $1,858,563.47 × 0.0722 × 30 ÷ 360 = $11,182.356877…, which prints as $11,182.36. The close is $1,869,745.83. Of that April product, the piece that sits on March's $11,343.47 of capitalised interest is $11,343.47 × 0.0722 × 30 ÷ 360 = $68.25. Last month's charge has begun to earn.

Capitalisation is why a year of statements is a chain rather than twelve independent products on a fixed base. Lesson 19 writes that chain in outline. The unit of the chain is this: the printed close becomes the next opening, and the next product uses the new opening as its balance.

Key terms

Capitalisation: Adding a period's interest to principal so the next period's product uses a larger balance.
Opening from a close: The next statement's opening balance is this statement's closing balance. March opens at February's $1,847,220.00.
Interest on interest: The slice of next month's product that sits on this month's charge. $68.25 of the illustrated April bill.

Worked example

February into March into April

Halden & Wren chain. February and March from the sample; April illustrated at 7.22 percent for 30 days.

February interest: $9,959.99
March opening: $1,847,220.00
March interest: $11,343.47
April opening: $1,858,563.47
April interest at 7.22%, 30 days: $11,182.36
Of which on March's $11,343.47: $68.25

Each close is the next opening. The $68.25 is March's charge earning a month of 7.22 percent, Act/360.

Check yourself

February charged $9,959.99 on $1,837,260.01. What is March's opening, and how much of March's first-day addend sits on February's interest?

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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.