If you calculate the interest on swaps, bonds, or loans and check payment amounts, you work it out under the day count convention set in the contract.

Interest is calculated by converting the period into years

Interest is the principal times the rate times the period expressed in years. Consider a hypothetical example in which a principal of 100 million yen is invested at 2% from March 15 to August 31, 2026. The period has 169 actual days. Dividing 169 days by 360 gives 0.469444 years, so the interest is 100 million yen × 2% × 169 ÷ 360, or 938,889 yen. Dividing by 365 gives 0.463014 years and interest of 926,027 yen1.

For the same period and rate, the interest differs by a little over 12,000 yen depending on how many days make up a year. The rule that sets how to count the days in a period, and what fraction of a year they represent, is called a day count convention. The European Banking Federation (EBF) and other associations provide a contract form, the European Master Agreement, that uses a day count fraction to calculate interest2. The interest on the fixed rate side is the product of three numbers: the principal, the fixed rate, and the day count fraction the parties choose3. This is simple interest: within the period, no interest is earned on interest, unlike compound interest.

The days in a period include the start date but not the end date4. In the example, March contributes the 17 days from the 15th to the 31st, April through July contribute 30, 31, 30, and 31 days, and August contributes the 30 days from the 1st to the 30th. That makes 169 days in total.

Act/360 and Act/365F

Act/360 and Act/365F count the actual number of days in the period and convert it into years by dividing by 360 (Act/360) or 365 (Act/365F)5. The F in Act/365F stands for "Fixed" and means the divisor stays 365 even in a leap year. It is also written as Actual/365(Fixed) or Actual/Fixed 365.

For the same number of actual days, Act/360, which divides by 360, gives a longer year fraction, and so more interest when the rate is positive. The ratio is 365 ÷ 360, or about 1.014. For the 365 days from January 1, 2026, to January 1, 2027, with a principal of 100 million yen at 2%, Act/365F gives one full year of interest, 2,000,000 yen. Act/360 treats the period as 365 ÷ 360 = 1.013889 years, so the interest is 2,027,778 yen.

Deep diveConventions that count a leap year as 366 days

Separately from Act/365F, some conventions divide by 366 in a leap year. The convention called "Actual/365 or Actual/Actual" in the EBF contract form divides the actual number of days by 365, or by 366 in a leap year. When part of the period falls in a leap year, the days in the non-leap-year part are divided by 365, the days in the leap-year part are divided by 366, and the two results are added6. Because Act/365F divides by 365 even in a leap year, the two conventions give different results for periods that fall in a leap year.

30/360 and 30E/360

30/360 and 30E/360 count days as if every month had 30 days and every year 360 days, regardless of the actual calendar. Under Rule G-33 of the Municipal Securities Rulemaking Board (MSRB), which writes rules for the US municipal securities market, the number of days is the difference in years times 360, plus the difference in months times 30, plus the difference in days7. In the example, the difference in years is 0 and the difference in months is 5 (March to August), so the months contribute 150 days.

The two conventions differ in how they treat the 31st. Under 30/360, a start date on the 31st is changed to the 30th. An end date on the 31st is changed to the 30th only if the start date is the 30th or 31st7. 30E/360 counts every month as 30 days whatever the start and end dates are. So a start date or end date on the 31st is treated as the 30th89.

Step 30/360 30E/360
Difference in years × 360 (days) 0 0
Difference in months × 30 (days) 150 150
Start day (after adjustment) 15 15
End day (after adjustment) 31 30
Difference in days (days) 16 15
Days in the period (days) 166 165

In the example, the start date is the 15th, so 30/360 leaves the end date of the 31st unchanged and the difference in days is 16. 30E/360 changes the end date to the 30th, so the difference in days is 15.

Worked example: comparing the interest under four conventions

For the example of 100 million yen at 2% from March 15 to August 31, 2026, the four conventions put Act/360 highest and 30E/360 lowest. The interest is the principal of 100 million yen times the 2% rate times the year fraction.

Convention Days in the period (days) Days in a year (days) Year fraction (years) Interest (yen)
Act/360 169 360 0.469444 938,889
Act/365F 169 365 0.463014 926,027
30/360 166 360 0.461111 922,222
30E/360 165 360 0.458333 916,667

The gap between the highest, Act/360, and the lowest, 30E/360, is 22,222 yen1. Interest is proportional to the principal and the rate, so with a principal ten times larger, 1 billion yen, the gap is also ten times larger, 222,222 yen.

Which convention gives more interest depends on the period

Which convention gives the most interest changes with the months the period covers. For the month from February 15 to March 15, 2026, there are 28 actual days, but 30/360 and 30E/360 count 30. On 100 million yen at 2%, the interest is 166,667 yen under both 30/360 and 30E/360, 155,556 yen under Act/360, and 153,425 yen under Act/365F. The two conventions that count 30 days give the most.

In the March-to-August example, Act/360 gave more interest because the period had many 31-day months, so the actual days exceeded the days counted at 30 per month. On the other hand, over a month that spans the end of February, such as February 15 to March 15, February has fewer actual days (28, or 29 in a leap year) than 30, so the conventions that count 30 days per month give more days. The order of Act/360 and Act/365F does not change with the period.

SimulatorHow the day count convention changes the interest
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Interest on a principal of 100 million yen (yen)

Act/360938,889Act/365F926,02730/360 (ISDA)922,22230E/360916,667
Act/360 (169 days ÷ 360 = 0.469444)
Interest 938,889, discount factor 0.9907
Act/365F (169 days ÷ 365 = 0.463014)
Interest 926,027, discount factor 0.9908
30/360 (ISDA) (166 days ÷ 360 = 0.461111)
Interest 922,222, discount factor 0.9909
30E/360 (165 days ÷ 360 = 0.458333)
Interest 916,667, discount factor 0.9909

Simplifications

  • The principal is 100,000,000 (100 million yen). Interest is simple, and the discount factor is 1 ÷ (1 + rate × year fraction).
  • 30/360 (ISDA) follows Section 4.16(f) of the 2006 ISDA Definitions and 30E/360 follows 4.16(g). End-of-February adjustments, which differ between contract forms (including the one in 30E/360 (ISDA)), are not covered.
  • No business day adjustment (moving dates that fall on holidays) is applied.

This simulator uses simplified calculations for learning. It cannot be used for valuing actual transactions or managing their risk. (Disclaimer)

About this simulator

Changing the start date, end date, and rate changes each convention's number of days, year fraction, interest, and simple-interest discount factor. This simulator labels 30/360 as "30/360 (ISDA)." Moving the start date to March 30, 2026, makes 30/360 (ISDA) also change the end date of the 31st to the 30th, so the two 30/360 conventions count the same number of days. Setting the start date to February 15, 2026, and the end date to March 15 makes the two conventions that count 30 days give the most interest.

Conventions set by contracts, clearing house conditions, and rules

The parties choose the convention in the contract for each transaction5. For some transactions, a clearing house's conditions or an industry rule sets the convention. In addition, the Federal Reserve Bank of New York, which publishes SOFR, the US dollar overnight rate, says it calculates the SOFR Averages and Index in line with US dollar money market convention10.

Transaction Day count convention Basis
The floating rate side of yen interest rate swaps cleared by Japan Securities Clearing Corporation (JSCC) Act/365F JSCC's conditions for transactions eligible for clearing11
US dollar money market (calculation of the SOFR Averages and Index) Act/360 The Federal Reserve Bank of New York's description of the SOFR Averages and Index10
Calculation of accrued interest and other amounts in US municipal securities transactions 30/360 MSRB Rule G-3312

JSCC says that the fixed rate side may use any convention defined in the ISDA Definitions and does not require it to match the floating rate side11. In a calculation example for a yen OIS, the fixed rate payment is 10 billion yen × 0.08% × 14 ÷ 365, or 306,849 yen. The actual days are divided by 36513.

Assumptions and limits

The worked examples count days between fixed start and end dates. In actual transactions, the contract may set a business day convention that moves a payment date falling on a holiday to a business day. JSCC's clearing conditions list the business day conventions that can be used15. When a date moves, the number of days in the period changes too. Business day conventions are covered in Business Day Conventions and Holiday Calendars. The simulator does not apply business day conventions. Some contract forms also have a separate rule for periods ending on the last day of February16, and the simulator does not apply that rule either.

The floating rate of a yen OIS is the uncollateralized overnight call rate, compounded over a fixed period17. The day count convention is also used in this day-by-day calculation. In the formula for a yen OIS, if Monday is not a holiday, Friday's rate is multiplied by a period of 3 days, including Saturday and Sunday, divided by 3654. Compounding the daily rates is covered in Compounding in Arrears.

Notes

  1. Year fractions are rounded to six decimal places and interest to the nearest yen. Interest is calculated from the unrounded year fractions. ↩ ↩2

  2. European Banking Federation, "EUROPEAN MASTER AGREEMENT (EMA)." The formal name is the Master Agreement for Financial Transactions, and it is provided in cooperation with the European Savings Bank Group and the European Association of Cooperative Banks. ↩

  3. European Banking Federation, "Master Agreement for Financial Transactions: Supplement to the Derivatives Annex, Interest Rate Transactions" (Edition 2020), Section 4(1), "Fixed Amounts," page 2. ↩

  4. Study Group on Risk-Free Reference Rates, "日本円ＯＩＳ（Overnight Index Swap）─取引の概要と活用事例─" (Yen OIS: overview of transactions and examples of use, April 2018, in Japanese), "基本的な取引方式" (Basic trading terms), page 5. The actual days are counted as "起算日算入、満期日不算入" (start date included, maturity date excluded; our translation), and Friday's rate covers 3 days including Saturday and Sunday. ↩ ↩2

  5. EBF, the Supplement, Section 4(7), "Day Count Fraction," items (b) "Actual/360" and (g) "Actual/Fixed 365," page 3. ↩ ↩2

  6. The same document, Section 4(7), item (f), "Actual/365 or Actual/Actual," page 3. ↩

  7. Municipal Securities Rulemaking Board, "Rule G-33: Calculations," section (e)(ii), "Day Count Formula." The same section says periods are counted including the first day and excluding the last day. ↩ ↩2

  8. European Investment Bank, "Offering Circular, European Investment Bank Debt Issuance Programme" (November 28, 2025), "Day Count Fraction," pages 28–29. ↩

  9. International Bank for Reconstruction and Development, "Prospectus (Global Debt Issuance Facility)" (September 24, 2021), Condition 5(l), item (vi), page 26. ↩

  10. Federal Reserve Bank of New York, "Additional Information about Reference Rates," explanation of how the SOFR Averages and Index are calculated. It uses the actual number of calendar days and assumes a 360-day year. ↩ ↩2

  11. Japan Securities Clearing Corporation, "清算対象取引（金利スワップ）" (Transactions eligible for clearing: interest rate swaps, in Japanese), "11．日数計算式" (Day count fraction). The page writes the convention for the floating rate side (OIS and yen TIBOR) as "Actual/365(Fixed)," and the floating rate types are in "4．変動金利の種類" (Types of floating rate) on the same page. ↩ ↩2

  12. Municipal Securities Rulemaking Board, "Rule G-33: Calculations," section (e)(i), "Day Count Basis." Securities paying interest solely at redemption use the day count basis selected by the issuer. ↩

  13. The study group document, "金利の計算例" (Example of interest calculation), page 6. ↩

  14. This takes the difference between the values in the worked example. The text gives 9,360 yen, the difference between the rounded amounts of interest (916,667 yen and 926,027 yen). ↩

  15. Japan Securities Clearing Corporation, "清算対象取引（金利スワップ）" (Transactions eligible for clearing: interest rate swaps, in Japanese), "12．営業日調整" (Business day adjustment). ↩

  16. EBF, the Supplement, Section 4(7), items (c) "30E/360" and (d) "30/360," page 3. European Investment Bank, "Offering Circular," "Day Count Fraction," pages 28–29, also has a rule on the end of February. ↩

  17. The study group document, "２．OIS とは何か" (What is OIS), page 3. ↩