How to apply the "Act/365", or "Actual/365" Day Count Convention to Monthly, Quarterly, Semiannually or Annually Compound Interest method?

It is not common that banks offer term deposits (or CD - Certificate of Deposit) with Monthly, Quarterly, Semiannually or Annually Compound Interest method using the Act/365 Day Count Convention.

But if they do, the Accrued Interest on an Accrual Range that crosses Compound Period boundaries must be split into multiple smaller parts along the boundaries. This allows us to calculate compounded Principal at the end of each part with a recursive formula:

[T1,T2) = R(1)+R(2)+...+R(i)+...

Principal(i) 
  = Principal(i-1) × (1 + Interest_Rate × Calendar_Days(R(i))/365)
  = Principal(i-1) × (1 + Daily_Interest_Rate × Calendar_Days(R(i)))

Since the Calendar_Days() may vary from part to part (number of days in each month varies), We can not express the compounded Principal in an exponential form as the case of daily Compound Interest.

The Accrued Interest can then be calculated as the Principal difference between T1 and T2:

Accrued_Interest(T1,T2) = Principal(T2) - Principal(T1 

⇒ Day Count Convention - "Act/Act Bond"

⇐ "Act/365" - Daily Compound Interest

⇑ Day Count Convention - "Act/365"

⇑⇑ Day Count Conventions