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I am trying to calculate the accrued interest for a set of Treasury Bonds. I am comparing the answer from the code below with that for the 1st Bond(row) over here. In the link the AI is 0.061 whereas from the Python code I get 0.125 and am therefore trying to understand where I'm going wrong. I use the formula for AI available here.

#l contains the months to maturity 
accrued_interest = 0
d_ordered = {}
l = [0]*59 # My set of Bonds (not included here) includes a 30 year to maturity Semi-Annual coupon bearing bond and hence l will have 59 periods
l[0] = 3 # I have a function (not included here) which calculates the difference in months between each of the coupon payments (and the settlement date and first coupon payment)
d_ordered[0] = l
coupon = 0.250
days_in_coupon_period = 180 #The Link contains half-yearly bonds
for i in range(0,1,1):
    months_to_maturity_array = numpy.array(d_ordered[i])
    for k in range(0,59,1):
        # Adding the AI associated with each period k
        accrued_interest = accrued_interest + ((coupon) * ((30*months_to_maturity_array[k]) /days_in_coupon_period))
    print('AI', accrued_interest)

Thank You

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  • $\begingroup$ @haginile I kindly request your help in this question as you provided the document against which I am comparing the Accrued Interest. $\endgroup$
    – Jojo
    Aug 5, 2015 at 15:38

1 Answer 1

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US Treasuries follow the Actual/Actual day count convention, so you can't make the assumption that there are 180 days in a coupon period.

Let's assume that the settlement date (T + 1 for US Treasuries) is 8/6/2015, the previous coupon date for a bond is 7/31/2015, and the next coupon date is 1/31/2016. Then the number of days in the coupon period is 184 days, and the accrual period is 4 days. The accrued interest, assuming a 5% coupon rate, must be $4/184 \times 5/2 = 0.054347826$.

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  • $\begingroup$ Thank you once again. One thing I'm unsure of is how to set the settlement dates for each coupon payment. I've previously assumed its just 1 day after the coupon payment is due. And hence, if I were to have a 30 year to maturity bond, then the formula would be : $accrued interest = accrued interest from last period + (1/coupon period × coupon/2)$. Is this correct? $\endgroup$
    – Jojo
    Aug 5, 2015 at 16:21
  • $\begingroup$ @Jojo There should be one settlement for all cash flows. If the pricing date is today, the settlement date is just the next business day after the pricing date. $\endgroup$
    – Helin
    Aug 5, 2015 at 16:26
  • $\begingroup$ Thanks. So, if there is a bond with 12 months to maturity and it has settlement date 8/6/2015 and has the same description as you described in you answer, and a coupon date on 7/31/2016, would the Accrued Interest for this bond be $0.054347826 + 4/184×5/2$? I'm sort of confused how to calculate the Accrued Interest for the next period. $\endgroup$
    – Jojo
    Aug 5, 2015 at 16:34
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    $\begingroup$ @Jojo, sorry i'm quite confused... there's one accrued interest for each bond and for each settlement date. 0.054 IS the accrued interest. Why are you adding the other term? $\endgroup$
    – Helin
    Aug 5, 2015 at 16:40
  • $\begingroup$ Thank You. I have further questions about this calculation and have asked a separate question here to try and address these. $\endgroup$
    – Jojo
    Aug 5, 2015 at 17:37

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