What is the "30/360" Day Count Convention?

30/360 - 30/360 is a Day Count Convention used by the US agency and corporate bonds.

30/360 is also referred as 30/360 ISDA, 30/360 Bond Basis, 30/360 U.S. Municipal, 30A/360, 360/360, Bond Basis.

30/360 can be formally defined as:

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
   = DiR(Y1,M1,D1,Y2,M2,D2) / DiY(Y1,M1,D1,Y2,M2,D2)

DiR(Y1,M1,D1,Y2,M2,D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  where D1 and D2 are adjusted as below:
    If D1 = 31, set D1 = 30;
    If D2 = 31 and D1 > 29, set D2 = 30.

DiY(Y1,M1,D1,Y2,M2,D2) = 360

where: 
  T1 = (Y1,M1,D1): Starting date (inclusive)  
  T2 = (Y2,M2,D2): Ending date (exclusive) of the Accrual Range  
  T3 = (Y3,M3,D3): Ending date (exclusive) of the Accrual Period
  T4 = (Y4,M4,D4): Ending date (exclusive) of the Accrual Year 

Example:
   2026-01-01   2025-01-16   2026-02-01            2027-01-01
---T1-----------T2-----------T3-----------...------T4--- 

  [T1-----------T2): Accrual Range
  [T1------------------------T3): Accrual Period
  [T1-------------------------------------...------T4): Accrual Year

30/360 Convention always rounds 31st day back to 30th day for the starting date, and rounds 31st day back to 30th day for the ending date only if the starting date is on the 31st or 30th day. It does not adjust the month of February, which has only 28 or 29 days.

We can also re-write the 30/360 Convention rules using the Minimum() function as:

DiR(Y1,M1,D1,Y2,M2,D2) 
  = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  with the following adjustments: 
    D1 = Minimum(D1,30), 
    If D1 = 30 or 31, set D2 = Minimum(D2,30).

DiY(Y1,M1,D1,Y2,M2,D2) = 360

Here is an example of US FHLB (Federal Home Loan Bank) bond security. Note that its first Accrual Period is an irregular period, longer than 6 months.

CUSIP:                  3130ATVE4
Issuer:                 US FHLB
Interest rate:          4.5%
Interest frequency:     Semiannually (2 times in a year)
First interest Payment: 2023-06-11
Day Count Convention:   30/360
Term:                   4 Years 
  Start Date:           2022-11-07
  Maturity Date:        2026-12-11

If you bought $1,000.00 of this FHLB bond, here is how you can calculate Accrued Interest in the date range of [T1,T2) = [2022-11-07, 2023-06-11):

T1 = 2022-11-07: Starting date (inclusive)
T2 = 2023-06-11: Ending date (exclusive) of the Accrual Range 
T3 = 2023-06-11: Ending date (exclusive) of the Accrual Period  
T4 = 2024-12-11: Ending date (exclusive) of the Accrual Year

DiR(Y1,M1,D1,Y2,M2,D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  = 360×(2023-2022) + 30×(6-11) + (11-7)
  = 214 

DiY(Y1,M1,D1,Y2,M2,D2) = 360

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
  = 214 / 360 
  = 0.59444444444444

Accrued_Interest = Principal × Interest_Rate × Day_Count_Factor
  = $1,000.00 × 4.5% × 0.59444444444444
  = $26.75

30/360 convention has several main properties. See next tutorials for more details.

• The Day Count Factor for a whole regular Accrual Period is a constant.
• A fixed amount of Accrued Interest is paid out for each Accrual Period:
• Daily Interest Rate is a fixed value independent of Accrual Periods.
• If End of Month (EOM) is on 31th, no Accrued Interest is given on the 30th.
• If End of Month (EOM) is in February, 2-day or 3-day Accrued Interest is given on EOM.
• Not applicable for daily Compound Interest.
• Day Count Factor is additive for consecutive and non-overlapping Accrual Ranges, if no range boundary falls on any End of Month in February, or any 31-day months.
• Day Count Factor is not additive for consecutive and non-overlapping Accrual Ranges, if a range boundary falls on any End of Month in February, or any 31-day months.

References:

• Offering Notices/Pricing Supplements - FHLB Search Tool, US FHLB.
• MSRB Rule Book for the Municipal Market, msrb.org.

⇒ "30/360" - Rules Expressed Differently

⇐ Day Count Convention - "30/360"

⇑ Day Count Convention - "30/360"

⇑⇑ Day Count Conventions