How to apply the "Act/Act Bond", or "Actual/Actual Bond" Day Count Convention to Monthly, Quarterly, Semiannually or Annually Compound Interest method?

Monthly, Quarterly, Semiannually or Annually Compound Interest do not normally using the Act/Act Bond convention. But if it happens, the Day Count Factor formula is still valid if the Accrual Range is inside a single Accrual Period:

Accrual_Range = [T1, T2) 
Accrual_Period = [T1, T3), where T3 > T2 

DiR(T1,T2) = Calendar_Days(T1,T2) 

DiY(T1,T2) 
  = Accrual_Frequency × Calendar_Days(T1,T3)

Day_Count_Factor(T1,T2) 
  = Calendar_Days(T1,T2)
    / Accrual_Frequency × Calendar_Days(T1,T3)

Accrued_Interest(T1,T2) 
  = Principal × Interest_Rate × Day_Count_Factor(T1,T2)

For Accrual Range that crosses Accrual Period boundaries must be split into multiple smaller parts along the boundaries.

[T1,T2) = R1+R2+... 
  R1 in Accrual Period 1 
  R2 in Accrual Period 2
  ... 

Accrual_Frequency(R1) = Calendar_Days(Accrual_Period_1)
Accrual_Frequency(R2) = Calendar_Days(Accrual_Period_2)
...

⇒ Day Count Conventions

⇐ "Act/Act Bond" - Daily Compound Interest

⇑ Day Count Convention - "Act/Act Bond"

⇑⇑ Day Count Conventions