How does "Act/365" convention works on an Accrual Range that crosses one or more Accrual Period boundaries?

When an Accrual Range crosses one or more Accrual Period boundaries, there is no need to split it into multiple parts, since Act/365 Day Count Factor is additive.

Here is an example of a 5-year term deposit:

Principal:             $1,000.00 
Interest Method:       Simple Interest 
Interest Frequency:    12 (Monthly) 
Interest Rate:         5.00%
Day Count Convention:  Act/365
Term:                  5 Years 
  Start date:          2023-01-01 
  Maturity date:       2028-01-01

Here is how you can calculate the Accrued Interest in the date range of [2023-01-01, 2023-03-01), which spans 2 Accrual Periods:

T1 = 2023-01-01: Starting date (inclusive)
T2 = 2023-03-01: Ending date (exclusive) of the Accrual Range 
T3 = 2023-02-01: Ending date (exclusive) of the Accrual Period  
T4 = 2024-01-01: Ending date (exclusive) of the Accrual Year

DiR(T1,T2) = DiR(T1,T2) 
  = Calendar_Days(T1,T2) 
  = 59

DiY(T1,T2) = 365 

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
  = 59 / 365 
  = 0.16164383561644

Accrued_Interest = Principal × Interest_Rate × Day_Count_Factor
  = $1,000.00 × 5.0% × 0.16164383561644
  = $8.0821917808219
  = $8.08 

You will get the same result, if you split the Accrual Range into 2 parts:

R1 = [2023-01-01, 2023-02-01) within 
  P1 =[2023-01-01, 2023-02-01) Accrual Period 
R2 = [2023-01-01, 2023-03-01) within 
  P2 =[2023-01-01, 2023-03-01) Accrual Period 

Accrued_Interest 
  = Accrued_Interest(R1) + Accrued_Interest(R2)
  = Principal × Interest_Rate × Day_Count_Factor(R1) + 
    Principal × Interest_Rate × Day_Count_Factor(R2)
  = $1,000.00 × 5.0% × 31/365 + 
    $1,000.00 × 5.0% × 28/365
  = $4.2465753424658 + $3.8356164383562
  = $8.082191780822
  = $8.08

⇒ "Act/365" - Leap Years

⇐ What Is "Act/365"

⇑ Day Count Convention - "Act/365"

⇑⇑ Day Count Conventions