How to apply the "Act/Act Bond", or "Actual/Actual Bond" Day Count Convention to Daily Compound Interest?

Daily Compound Interest do not normally using the Act/Act Bond convention. But if it happens, the Day Count Factor formula is still valid for the Daily Interest calculation:

T1 = (Y1,M1,D1)
T2 = (Y2,M2,D2) = T1 + 1 day
T3 = (Y3,M3,D3) = T1 + 1 day

DiR(T1,T2) = Calendar_Days(T1,T2) 
  = 1

DiY(T1,T2) 
  = Accrual_Frequency × Calendar_Days(T1,T2)
  = Accrual_Frequency × 1
  = Accrual_Frequency

Day_Count_Factor(T1,T2) 
  = DiR(T1,T2) / DiY(T1,T2)
  = 1 / Accrual_Frequency

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

But the Accrual Frequency is no longer a constant. It varies between 365 and 366 because of leap days. The Act/Act Bond does not specify any rules to determine the Accrual Frequency. But we can think of 2 options:

1. Count calendar days in anniversary years - Using the first day of your investment as the starting point, count days in Accrual Years that end on the anniversary dates.

[T1,T2) = R1+R2+... 
  R1 = [T1,T1+1 year)
  R2 = [T1,T1+2 years) 
  ... 

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

2. Count calendar days in calendar years - Splitting the Accrual Range into smaller parts by the calendar year boundaries, count days in the calendar years.

[T1,T2) = R1+R2+... 
  R1 = Intersection of [T1,T2) in year 1
  R2 = Intersection of [T1,T2) in year 2
  ...

Accrual_Frequency(R1) = Calendar_Days(Year 1)
Accrual_Frequency(R2) = Calendar_Days(Year 2)
... 

Since there is no rules specified for DiY(T1,T2), Act/Act Bond convention is not applicable for daily Compound Interest.

⇒ "Act/Act Bond" - Monthly Compound Interest

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

⇑ Day Count Convention - "Act/Act Bond"

⇑⇑ Day Count Conventions