What is the behavior of Act/Act Bond convention on whole Accrual Periods?

One important property of the Act/Act Bond convention is that the Day Count Factor for a whole Accrual Period is a constant.

This allows US 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 

Day_Count_Factor(T1,T3) = DiR(T1,T3) / DiY(T1,T3)

               Calendar_Days(T1,T3)
  = ----------------------------------------
    Accrual_Frequency × Calendar_Days(T1,T3)

           1 
  = -----------------
    Accrual_Frequency

The Accrued Interest of a whole Accrual Period is:

Accrued_Interest(T1,T3) 
  = Principal × Interest_Rate × Day_Count_Factor(T1,T3)
  = Principal × Interest_Rate / Accrual_Frequency

For US Bonds, the Interest Frequency (Accrual Frequency) is always semiannually (2 times in year), the Day Count Factor and Accrued Interest for a whole Accrual Period can simplified as:

Day_Count_Factor(T1,T3) 
  = 1 / Accrual_Frequency
  = 1 / 2
  = 0.5 

Accrued_Interest(T1,T3) 
  = Principal × Interest_Rate / Accrual_Frequency
  = Principal × Interest_Rate / 2
  = 0.5 × Principal × Interest_Rate

This convention also allows US 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 splitting the Accrual Year into 2 Accrual Periods:

Accrued_Interest(T1,T4) 
  = Accrued_Interest(T1,T3) + Accrued_Interest(T3,T4)
  = Principal × Interest_Rate / 2 + Principal × Interest_Rate / 2
  = Principal × Interest_Rate

⇒ "Act/Act Bond" - Cross-Period Accrual

⇐ What Is "Act/Act Bond"

⇑ Day Count Convention - "Act/Act Bond"

⇑⇑ Day Count Conventions