Lesson 6 of 25 · 6 min

Adding the legs and matching the printed total

The printed total is just the two legs added, and the closing balance is that sum sitting on the opening.

Period 1 printed $3,934.07. Period 2 printed $7,409.40. Added, $11,343.47. That is the interest total on the Halden & Wren March statement. There is no third charge hiding in a blended rate, and there is no average of 6.97 and 7.22 being applied to 31 days. The printed page is two products and a sum, in that order.

The balance chain is the same addition in a different slot. Opening $1,847,220.00, plus draws of zero, minus repayments of zero, plus interest of $11,343.47, equals $1,858,563.47, which is the printed close. The interest did not leave the account. It sat on the balance. Next month's opening figure is this closing figure, which is the capitalisation lesson.

A naive 31-day product at the closing rate does not match. $1,847,220 × 0.0722 × 31 ÷ 360 = $11,484.58. That is $141.11 above the printed total. The $141.11 is eleven days of the 0.25-point gap running the wrong way: those eleven days were charged at 6.97 percent, and the naive product charges them at 7.22 percent. $1,847,220 × 0.0025 × 11 ÷ 360 = $141.11 exactly, once rounded.

Matching $11,343.47 is matching two products and a sum. It is not matching a monthly rate, because no single monthly rate appears in the arithmetic.

Key terms

Printed total: The sum of the legs after each has been rounded. On the sample, $3,934.07 + $7,409.40 = $11,343.47.
Naive closing-rate product: Charging the whole period at the header rate. Here $11,484.58, which is $141.11 too high.
Balance chain: Opening + draws − repayments + interest = closing. On this March, $1,847,220.00 + $11,343.47 = $1,858,563.47.

Worked example

Two legs, one total, one close

Halden & Wren March 2026. No draws, no repayments.

Period 1: $3,934.07
Period 2: $7,409.40
Interest total: $11,343.47
Naive 31 days at 7.22%: $11,484.58
Opening + interest: $1,858,563.47
Printed close: $1,858,563.47

The total and the close are the same two additions. The naive product fails because it rewrites period 1 at the closing rate.

Check yourself

Why is $1,847,220 × 0.0722 × 31 ÷ 360 = $11,484.58 larger than the printed $11,343.47, and by how much in rate-days?

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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.