How to apply the "30/360" Day Count Convention to Monthly, Quarterly, Semiannually or Annually Compound Interest method?

30/360 Day Count Convention can be used for Monthly, Quarterly, Semiannually or Annually Compound Method, as long as the Compound Period boundaries are not falling on End of Month in February.

For a single Compound Period, the Accrued Interest can be calculated as:

[T1,T3) = [Y1-M1-D1, Y3-M3-D3) is a single Accrual (Compound) Period
  After adjustments:
    D3 = D1, as long as they are not February 28 or 29
    360×(Y3-Y1) + 30×(M3-M1) = 360/Compound_Frequency 

DiR(Y1,M1,D1,Y3,M3,D3)
  = 360×(Y3-Y1) + 30×(M3-M1) + (Minimum(D3,30)-Minimum(D1,30))
  = 360/Compound_Frequency + 0 
  = 360/Compound_Frequency 

DiY(Y1,M1,D1,Y3,M3,D3) = 360 

Day_Count_Factor(Y1,M1,D1,Y3,M3,D3) 
  = DiR(Y1,M1,D1,Y3,M3,D3) / DiY(Y1,M1,D1,Y3,M3,D3)
  = (360/Compound_Frequency) / 360 
  = 1/Compound_Frequency

Accrued_Interest 
  = Principal × Interest_Rate × Day_Count_Factor(Y1,M1,D1,Y3,M3,D3) 
  = Principal × Interest_Rate/Compound_Frequency

The compounded Principal can be expressed as:

New_Principal 
  = Old_Principal + Accrued_Interest
  = Old_Principal + Old_Principal × Interest_Rate/Compound_Frequency
  = Old_Principal × (1 + Interest_Rate/Compound_Frequency)

For an Accrual Range with multiple Compound Periods, we can split the range into a sequence of Compound Periods and derive a recursive formula to calculate the compounded Principal.

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

Principal(i) 
  = Principal(i-1) × (1 + Interest_Rate/Compound_Frequency)

We can also re-write these compounded Principals in an exponential form:

Principal(1) 
  = Principal(0) + (1 + Interest_Rate/Compound_Frequency)
  = Principal(0) × (1 + Interest_Rate/Compound_Frequency) ** 1

Principal(2) =
  = Principal(1) + (1 + Interest_Rate/Compound_Frequency)
  = Principal(0) × (1 + Interest_Rate/Compound_Frequency) ** 2

Principal(3) =
  = Principal(2) + (1 + Interest_Rate/Compound_Frequency)
  = Principal(0) × (1 + Interest_Rate/Compound_Frequency) ** 3

Now we have derived the generic formula to calculate the compounded Principal for a Accrual Range of N Compound Periods:

[T1, T2) = N consecutive Compound Periods
Principal(T2) 
  = Principal(T1) × (1 + Interest_Rate/Compound_Frequency) ** N

where: 
  Principal(T1) is the Principal on date T1. 

From the compounded Principal, we can derive the generic formula to calculate the Accrued Interest of the same Accrual Range:

[T1, T2) = N consecutive Compound Periods

Principal(T2) 
  = Principal(T1) × (1 + Rate/Frequency) ** N

Accrued_Interest(T1,T2) = Principal(T2) - Principal(T1) 
  = Principal(T1) × (1 + Rate/Frequency) ** N - Principal(T1) 
  = Principal(T1) × ((1 + Rate/Frequency) ** N - 1)

where: 
  Rate = Interest_Rate 
  Frequency = Compound_Frequency

⇒ Day Count Convention - "30/360 US"

⇐ "30/360" - Daily Compound Interest

⇑ Day Count Convention - "30/360"

⇑⇑ Day Count Conventions