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How ACT/360 and Other Day-Count Conventions Measure Interest

Article Quant Q&A · Author: Lay González
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Summary

The document explains what the ACT/360 day-count convention means when calculating interest. A year is treated as 360 units for the calculation, while elapsed time is counted in actual calendar days. As a result, a 365-day period accrues interest for 365/360 years; the convention does not make calendar days shorter or longer. The answer notes that 360 was a convenient round number before widespread computer use.

The discussion briefly distinguishes ACT/360 from 30/360, but does not explain the latter convention or provide worked rate calculations. It points readers toward a reference on interest-rate instruments and market conventions. The exchange gives a concise conceptual clarification rather than evidence from market data, and its historical rationale is presented informally. For practical calculations, the exact day-count rule should be checked for the instrument and market in question.

Key ideas

  • ACT/360 counts actual calendar days and divides the elapsed period by 360 to express a year fraction.
  • A 365-day period therefore represents 365/360 years under ACT/360.
  • The convention changes the interest year fraction, not the length of a calendar day.
  • The document mentions 30/360 but does not explain how that convention handles dates.

Tags

Fixed incomeStatistics
Full text
# When computing with rates, how long is a year? how long is a day?


# When computing with rates, how long is a year? how long is a day?












The convention says that when computing with rates, $1$ year has $360$ days. Does this mean that, when computing with rates, $1$ year has $360$ normal days or 1 day is $\frac{365 \times 24}{360} = 24.33$ hours long?

I hope it is clear, tell me if my question is confusing.

## Answer by FinanceGuyThatCantCode (score 1)

https://quant.stackexchange.com/a/34143

When the convention is ACT/360, it means that 365 calendar days of interest is calculated as 365/360 years. I knows it seems stupid, but before industrial use of computers, it was convenient for a year to be a nice round number like 360.

I forget how the 30/360 convention is handled - I once coded up all the conventions, but they have worked really well for me and I don't remember what they all mean!

Try this reference:

https://developers.opengamma.com/quantitative-research/Interest-Rate-Instruments-and-Market-Conventions.pdf

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.