Lesson 21 of 25 · 6 min
30/360 against Act/360 on the same March
Thirty over 360 pretends March has thirty days, and the missing thirty-first is a full day's accrual.
30/360 counts every month as thirty days and still divides by 360. A 30/360 March at a flat 6.97 percent on $1,847,220 is $1,847,220 × 0.0697 × 30 ÷ 360 = $10,729.2695, which prints as $10,729.27. The Act/360 March at the same flat rate is 31 days: $11,086.91. The gap is $357.64, which is the 31st of March at the daily addend $1,847,220 × 0.0697 ÷ 360. 30/360 dropped a day that actually elapsed.
Against the printed two-rate Act/360 total of $11,343.47 the 30/360 flat-6.97 product is short by $614.20. That $614.20 is the dropped 31st ($357.64) plus the twenty-day reset ($256.56). Two different inputs, one combined gap. Isolating the convention means holding the rate flat, which is why $10,729.27 against $11,086.91 is the clean comparison.
February runs the other way. 30/360 still counts thirty days. Act/360 counts 28. On the sample February opening, 30/360 at 6.97 percent is $1,837,260.01 × 0.0697 × 30 ÷ 360 = $10,671.4186…, which prints as $10,671.42. Act/360 printed $9,959.99. 30/360 is larger by $711.43, which is two invented days: 2 × ($1,837,260.01 × 0.0697 ÷ 360) = $711.4279…. The same convention that understated March overstated February.
April has thirty actual days, so the two conventions agree on the day count. $1,858,563.47 × 0.0722 × 30 ÷ 360 = $11,182.36 either way. A 30-day month is the one month on which 30/360 and Act/360 do not disagree about days. They still disagree in any month that is not 30 days long, and most months are not.
Key terms
- 30/360
- Every month counted as 30 days, year as 360. Drops the 31st in March and invents two days in February.
- Dropped day
- A calendar day Act/360 charges and 30/360 does not. 31 March at 6.97 percent on this balance is $357.64.
- Invented days
- Days 30/360 charges that the calendar did not contain. Two of them in a common February, worth $711.43 on the sample opening.
Worked example
March short, February long, April agreed
Same balances as the sample chain. Flat 6.97 percent on February and March so the convention is isolated; April at 7.22 percent.
- March 30/360, 30 days at 6.97%
- $10,729.27
- March Act/360, 31 days at 6.97%
- $11,086.91
- Dropped 31 March
- $357.64
- February 30/360, 30 days at 6.97%
- $10,671.42
- February Act/360, 28 days
- $9,959.99
- April, either convention, 30 days at 7.22%
- $11,182.36
30/360 is not uniformly cheaper. It is cheaper in 31-day months and dearer in 28-day ones, and silent in April.
Check yourself
On the sample March at a flat 6.97 percent, what does 30/360 charge, what does Act/360 charge, and what is the gap in days and in dollars?
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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.