"30/360" - Cross-Period Accrual

Q

How does "30/360" convention works on an Accrual Range that crosses one or more Accrual Period boundaries?

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A

When an Accrual Range crosses one or more Accrual Period boundaries, there is no need to split it into multiple parts, as long as the Accrual Frequency is Monthly, Quarterly, Semiannually, or Annually and Accrual Period boundaries are not falling on End of Month in February.

Here is an example of US FHLB (Federal Home Loan Bank) bond security.

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 for 1.5 Accrual Periods in the date range of [T1,T2) = [2023-06-11, 2024-03-11):

T1 = 2023-06-11: Starting date (inclusive)
T2 = 2024-03-11: Ending date (exclusive) of the Accrual Range 
T3 = 2023-12-11: Ending date (exclusive) of the Accrual Period  
T4 = 2024-06-11: Ending date (exclusive) of the Accrual Year

DiR(Y1,M1,D1,Y2,M2,D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  = 360×(2024-2023) + 30×(3-6) + (11-11)
  = 270

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

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
  = 270 / 360 
  = 0.75

Accrued_Interest = Principal × Interest_Rate × Day_Count_Factor
  = $1,000.00 × 4.5% × 0.75
  = $33.75

 

"30/360" - Leap Years

"30/360" - Whole Accrual Period

Day Count Convention - "30/360"

⇑⇑ Day Count Conventions

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