# Understanding how to calculate Accrued Interest of Bonds

When calculating the accrued Interest of Treasury Bonds, how does one set the settlement date? And, is it possible for certain bonds that there are no coupon payments before the settlement date and hence there will be no accrued interest (i.e. the case when the bond is bought before the first coupon payment and after the issue date)?

Although I asked a very similar question here, I am still unclear about these particular details.

Thank You

Conceptually, let's say you sell a bond three months after the previous coupon date. Because you've sold the bond, you won't receive the next coupon payment, which happens in three months' time. But you deserve half of the next coupon payment, because you've held onto it for half the coupon period. That's what accrued interest is.

Accrued interest, in general, is calculated as $$\text{AI} = \text{AIF} \times \frac{c}{f},$$ where AIF is the accrued interest fraction, and $c$ is the annual coupon rate, and $f$ is the coupon frequency.

AIF is simply the day count fraction between the previous coupon date and the settlement date. For US Treasuries, which follows the Actual/Actual convention, it is calculated as $$\text{AIF} = \frac{\text{settlement date} - \text{previous coupon date}}{\text{next coupon date} - \text{previous coupon date}}.$$

As mentioned, US Treasuries follows $T+1$ settlement convention, which means the settlement date is always the next business day following the trade date. More specifically, if you bought the Treasury today, then it settles tomorrow. (An exception is made for Treasuries trading in the when-issued market, in which case the settlement date is the issue date.)

Accrued interest is zero on all coupon dates. On any other date, it would be non-zero. So if a bond settlement before the first coupon date and after the first interest accrual date, it would have a non-zero AI.

P.S. I think the preference is for you to edit your old question, and we can update the answers accordingly (the questions are so similar...).

• I will delete this question then. I'm just waiting on you to give the go ahead, as I can't delete a question thats been answered already.
– Jojo
Aug 5 '15 at 19:53
• @Jojo oh i don't really mind, lol. Hope this is helpful. Aug 5 '15 at 19:59
• Thanks. Got a couple more questions. So, for a bond which has been bought between its issue date and its first coupon date would the equation be $$\text{AIF} = \frac{\text{settlement date}}{\text{next coupon date}}.$$ as there is no previous coupon date? And in this sheet which you uploaded previously, did you arbitrarily set the pricing date, as of course we are not actually buying the bond?
– Jojo
Aug 5 '15 at 20:08
• No, in this case, the "previous coupon date" would be the "first accrual date", which for US Treasuries is just six months before the first coupon date. The pricing date I used was the date which those prices on the sheet are as of. Aug 5 '15 at 20:17