What is the behavior of 30E/360 convention on whole Accrual Periods?

One important property of the 30E/360 convention is that the Day Count Factor for a whole Accrual Period is a constant, 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.

This allows Bond investors to receive a fixed amount of Accrued Interest after each Accrual Period.

In order to calculate the Day Count Factor of a whole Accrual Period, we need to set T2 = T3 and apply the Day Count Convention rules:

T1 = (Y1,M1,D1):      Starting date (inclusive)  
T2 = T3 = (Y3,M3,D3): Ending date (exclusive) of the Accrual Period 
  where: Minimum(D3,30) = Minimum(D1,30), 
    because Accrual Period boundaries fall on the same day.

DiR(Y1,M1,D1,Y3,M3,D3)
  = 360×(Y3-Y1) + 30×(M3-M1) + (Minimum(D3,30)-Minimum(D1,30))
  = 360×(Y3-Y1) + 30×(M3-M1) + 0 

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
  = DiR(Y1,M1,D1,Y2,M2,D2) / 360
  = 360×(Y3-Y1) + 30×(M3-M1) / 360 
  = Constant, because the # of months in each Accrual Period is fixed

This convention also allows Bond investors to receive a fixed amount of Accrued Interest after each Accrual Year on the anniversary dates of the bond's issue date. This can be calculated by setting T2 = T3 and apply the Day Count Convention rules:

T1 = (Y1,M1,D1):      Starting date (inclusive)  
T2 = T4 = (Y4,M4,D4): Ending date (exclusive) of the Accrual Year 
  where: 
    Minimum(D4,30) = Minimum(D1,30)
      because Accrual Year boundaries fall on the same day.
    M4 = M1
      because Accrual Year boundaries fall on the same month.
    Y4 = Y1 + 1
      because Accrual Year is 1 year long 

DiR(Y1,M1,D1,Y4,M4,D4)
  = 360×(Y4-Y1) + 30×(M4-M1) + (Minimum(D4,30)-Minimum(D1,30))
  = 360×1 + 30×0 + 0 
  = 360 

Day_Count_Factor(Y1,M1,D1,Y4,M4,D4)
  = DiR(Y1,M1,D1,Y4,M4,D4) / 360
  = 360 / 360 
  = 1 

Accrued_Interest(T1,T4) 
  = Principal × Interest_Rate × Day_Count_Factor(Y1,M1,D1,Y4,M4,D4)
  = Principal × Interest_Rate × 1
  = Principal × Interest_Rate

⇒ "30E/360" - Cross-Period Accrual

⇐ "30E/360" - DAYS360() Excel Function

⇑ Day Count Convention - "30E/360"

⇑⇑ Day Count Conventions