Lesson 7 of 25 · 6 min

Finding the day-count convention

The divisor that turns an annual rate into a daily charge is a term, not a rounding choice.

The day-count convention is the rule that turns an annual stated rate into a daily fraction. On this page it is printed in the header as Act/360: count the actual days in the segment, divide the annual rate by 360. The 360 is a contractual divisor. It is not a rounding convenience and it is not a description of how many days March contains.

March contains 31 actual days. The two legs use those 31. The divisor is still 360. That combination — actual days in the numerator's day count, 360 in the denominator — is why a quoted 6.97% costs more over a real year than 6.97% divided by 365 would. Track 1 lesson 15 put the relative gap at about 1.39 percent, the ratio 365/360 − 1.

segment interest = balance × stated rate × actual days ÷ 360

balance: The drawn amount outstanding for the whole segment. Here, $1,847,220.00 on both legs.
stated rate: Index plus spread for that segment, as a decimal. 0.0697 then 0.0722.
actual days: Calendar days in the segment. 11, then 20.
360: The Act/360 year. A term of the facility, printed in this header.

Finding the convention is reading the header line, then refusing to replace 360 with 365 because March has 31 days or because the calendar year has 365. A rebuild that swaps the divisor will miss the printed legs by that 1.39 percent signature, and the miss will look like an error in the charge. The convention is doing that work on every day of the facility, not only on the two March legs.

Key terms

Day-count convention: The rule for counting days and choosing the year divisor. This header prints Act/360.
Act/360: Charge for every actual day in the segment, using an annual rate divided by 360. The 31 and the 360 are different inputs.
Divisor: The number the annual rate is divided by to make a daily fraction. Here, 360. Replacing it with 365 is a different convention.

Worked example

The same 11-day leg, two divisors

Opening drawn balance $1,847,220.00, stated rate 6.97%, eleven days. Only the year changes.

Act/360, as printed: $1,847,220 × 0.0697 × 11 ÷ 360 = $3,934.07
Same inputs, divisor 365: $1,847,220 × 0.0697 × 11 ÷ 365 = $3,880.17
Gap: $3,934.07 − $3,880.17 = $53.90
Gap as a share of the printed leg: $53.90 ÷ $3,934.07 = 1.37%
What the statement charged for those 11 days: $3,934.07

The 360 is doing money work. It is not a description of March, and March's 31 days do not license a 365.

Check yourself

The header prints Act/360. Rebuild the second March leg on $1,847,220 at 7.22% for 20 days using 365 as the divisor. What figure do you get, and what is the gap to the printed $7,409.40?

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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.