Day-count conventions: ACT and 30/360 for dates and bonds
Ninety-two days or ninety? How ACT and 30/360 count time differently, why leap years matter, and how the dates worksheet bridges Gregorian and Jalali calendars.
Interest is rent for time, and finance needs an unambiguous way to count time. A 'year' on a bond is not always 365 days, and a 'month' is not always 30. Day-count conventions fix the rule, and the two families you meet everywhere are ACT (actual days) and 30/360 (a stylized month of 30 days). The difference sounds cosmetic — it is not: it changes the cash.
ACT: the calendar, honestly counted
ACT counts the actual number of calendar days between two dates and divides by an actual year (365, or 366 in a leap year, or 365.25 in some variants). The engine-verified examples: 2024-01-01 to 2025-01-01 spans 366 days because 2024 is a leap year; the same dates a year earlier span 365. And from May 15 to August 15 of 2024 the actual count is 92 days.
30/360: every month is 30 days
The 30/360 convention pretends each month has 30 days and each year 360 — making every year exactly twelve equal twelfths. Dates are adjusted (day 31 becomes 30, with a few special cases) and the count follows. For the same May 15 → August 15 span, 30/360 reports 90 days: three flat months. And January 1 to July 1 is exactly 180 days, half a year, year-fraction 0.5 — a cleanness ACT can never offer (it counts 182 in 2024).
| Span | ACT | 30/360 | Year fraction (30/360) |
|---|---|---|---|
| 2024-01-01 → 2025-01-01 | 366 | 360* | 1.0 |
| 2024-01-01 → 2024-07-01 | 182 | 180 | 0.5 |
| 2024-05-15 → 2024-08-15 | 92 | 90 | 0.25 |
*Under a strict 360-day year the 366 actual days of the leap year still count as 360/360 = one full year — the convention simply refuses to see the extra day.
Where each convention lives
- US corporate & municipal bonds: 30/360 — coupons are equal-sized by design.
- US Treasuries: ACT/ACT — the calendar rules, so coupons vary with actual days.
- Money-market instruments (deposits, T-bills, repos): ACT/360 — lender-favorable counting.
- Many loans and mortgages: ACT/365 or monthly-period TVM, depending on the contract.
Why it changes money
Accrued interest multiplies the coupon by the year fraction. On a 4.00 semi-annual coupon, the verified 91/182 elapsed period pays 2.00 of accrued interest under ACT; under a 30/360 lens the same settlement date would count 90 days of a 180-day period and again give 2.00 — but settle one day either side and the two conventions part ways, one paying for 91 real days, the other for 90 contract days. Over thousands of settlements, the basis is worth real basis points.
The Jalali bridge
Frequently asked questions
Why do ACT and 30/360 give different day counts?
ACT counts real calendar days (the May 15 → August 15, 2024 span is 92 days), while 30/360 assumes every month has 30 days and reports 90 for the same span. The conventions exist for different purposes: 30/360 gives equal coupons and clean half-years, ACT reflects the true passage of time including leap days.
How does a leap year affect interest?
Under ACT conventions a leap year contributes 366 days, so year fractions shrink slightly and daily accruals differ from a 365-day year — the verified 2024-01-01 → 2025-01-01 span is 366 days. Under 30/360 nothing changes: every year is 360 contract days regardless of the calendar.
How does FinScope handle Jalali dates in day counts?
The dates worksheet converts Jalali dates to Gregorian internally — 1403-01-01 is exactly 2024-03-20 — and then applies the chosen ACT or 30/360 arithmetic. Leap-year status is computed for the Jalali year itself (1403 leap with Esfand 30, 1404 common with Esfand 29), so contract dates never need manual conversion.
Practice it live
Open the matching worksheet and reproduce every number in this article.
Open calculator