Lesson 13 of 25 · 6 min

Reconstructing a 28-day February against a 31-day March

February is cheaper than March by more than the three missing days, because the rate path differs too.

February 2026 has 28 days and no reset on the sample chain. It opens at $1,837,260.01, runs at 6.97 percent, Act/360, and charges $1,837,260.01 × 0.0697 × 28 ÷ 360 = $9,959.990654…, which prints as $9,959.99. It closes at $1,847,220.00. March charges $11,343.47. The gap is $1,383.48. Three extra calendar days do not explain all of it.

Split the $1,383.48 into three named products. First, February's $9,959.99 already sits inside March's opening, so 28 March days at 6.97 percent cost more than 28 February days at 6.97 percent: $1,847,220 × 0.0697 × 28 ÷ 360 = $10,013.98, which is $53.99 more. The $53.99 is 28 days of 6.97 percent on February's $9,959.99.

Second, March has three extra calendar days. At the 6.97 percent daily addend on the March opening those three days are 3 × $357.642316… = $1,072.93, and $10,013.98 + $1,072.93 = $11,086.91, the flat-rate 31-day March. Third, twenty of March's days ran 0.25 points higher: $256.56. $11,086.91 + $256.56 = $11,343.47. The three pieces are $53.99 + $1,072.93 + $256.56 = $1,383.48.

A shorter month is not a cheaper month in any fixed proportion. The missing days, the capitalised opening, and the rate path each have their own product.

Key terms

Month-length gap: The extra calendar days of a 31-day month against a 28-day one. On this March opening at 6.97 percent, three days are $1,072.93.
Base gap: The extra product from a larger opening after capitalisation. Here $53.99: 28 days of 6.97 percent on February's $9,959.99.
Path gap: The extra product from a reset the shorter month did not contain. Here $256.56.

Worked example

Three products that turn February into March

February $9,959.99 against March $11,343.47. Same facility, Act/360.

February printed: $9,959.99
28 days at 6.97% on March's opening: $10,013.98
Three extra days at 6.97%: $1,072.93
Flat 31-day March at 6.97%: $11,086.91
Twenty days of an extra 0.25 points: $256.56
March printed: $11,343.47

$1,383.48 is three named products, not 31/28 times February. The ratio 31/28 would have predicted $11,027.13 and missed the reset and the larger base.

Check yourself

February charged $9,959.99. Scaling that figure by 31/28 gives $11,027.13. March printed $11,343.47. What did the ratio miss?

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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.