How to calculate Accrued Interest on EOM periods using the "30/360 US" Day Count Rules?

Let's use the following Jefferies bond security to show you how to calculate Accrued Interests on Accrual Periods scheduled on EOM (End of Month) using the 30/360 US Day Count Convention.

CUSIP:                  47233JCD8
Issuer:                 Jefferies
Interest rate:          4.4%
Interest frequency:     Semiannually, Paid on EOM
Day Count Convention:   30/360 US
Term:                   10 Years
  Start Date:           2019-08-30
  Maturity Date:        2034-08-31

If you bought $1,000.00 of this Citigroup bond, here is how you can calculate Accrued Interest in an Accrual Period that starts on the last day of February: [T1,T2) = [2024-02-29, 2024-08-31):

T1 = 2024-02-29: Starting date (inclusive)
T2 = 2024-08-31: Ending date (exclusive) of the Accrual Range 
T3 = 2024-08-31: Ending date (exclusive) of the Accrual Period  
T4 = 2025-02-28: Ending date (exclusive) of the Accrual Year

Apply the following adjustments sequentially:
  If interest scheduled to be paid on EOM: 
    If T1 is EOM of February:
      Set D1 to 30
      If T2 is EOM of February, set D2 to 30
  If D1 = 31, set D1 = 30;
  If D2 = 31 and D1 > 29, set D2 = 30.

We have:
  D1 = 30, because T1 is EOM of February 
  D2 = 30, because D2 = 31 and D1 > 29

DiR(Y1,M1,D1,Y2,M2,D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  = 360×(2024-2024) + 30×(8-2) + (30-30)
  = 180 

DiY(Y1,M1,D1,Y2,M2,D2) = 360

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
  = 180 / 360 
  = 0.5

Accrued_Interest = Principal × Interest_Rate × Day_Count_Factor
  = $1,000.00 × 4.4% × 0.5
  = $22.00

So you get paid exactly half year interest for the period that starts on the EOM of February.

Now let's look at an Accrual Period that ends on the EOM of February: [T1,T2) = [2023-08-31, 2024-02-29):

T1 = 2023-08-31: Starting date (inclusive)
T2 = 2024-02-29: Ending date (exclusive) of the Accrual Range 
T3 = 2024-02-29: Ending date (exclusive) of the Accrual Period  
T4 = 2023-08-31: Ending date (exclusive) of the Accrual Year

Apply the following adjustments sequentially:
  If interest scheduled to be paid on EOM: 
    If T1 is EOM of February:
      Set D1 to 30
      If T2 is EOM of February, set D2 to 30
  If D1 = 31, set D1 = 30;
  If D2 = 31 and D1 > 29, set D2 = 30.

We have:  
  D1 = 30, because D1 = 31
  D2 = 29, no adjustment 

DiR(Y1,M1,D1,Y2,M2,D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  = 360×(2024-2023) + 30×(2-8) + (29-30)
  = 179 

DiY(Y1,M1,D1,Y2,M2,D2) = 360

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
  = 179 / 360 
  = 0.49722222222222

Accrued_Interest = Principal × Interest_Rate × Day_Count_Factor
  = $1,000.00 × 4.4% × 0.5
  = $21.877777777778
  = $21.88

So we are getting paid 1 day less than year interest. There seems be a mistake in the 30/360 US Day Count Convention rules.

References:

• JEF 4.4% 08/31/2034, public.com.

⇒ "30/360 US" - Monthly Interest Frequency

⇐ "30/360 US" - Rules Expressed Differently

⇑ Day Count Convention - "30/360 US"

⇑⇑ Day Count Conventions