Accrued interest and clean price

The buyer must compensate the seller for the fraction of the next coupon payment the seller is due but will not receive.

This amount is called accrued interest.

While different markets may differ slightly in their exact methods of calculating accrued interest, all major bond markets follow the practice of quoting clean prices (as opposed to full or dirty prices, which include accrued interest).

It is important that you check the precise method used for calculating accrued interest in the particular market being used, but two typical systems are represented by US government bonds and eurobonds.

The US Treasury market uses an "actual/actual, semi-annual" method, i.e. the actual number of days divided by the actual number of days in the interest period, all on a six-monthly basis. Thus:

So, the clean price of an 8% US Treasury with a dirty price of  98.55 sold after the last coupon payment (and where we assume that there are 184 days in the coupon period) would be calculated as follows:

clean price = 98.55 - (8/2 x 6/184) = 98.42

For eurobonds, the system is "30/360, annual", meaning 12 months of 30 days, divided by 360 (not 365).

Thus:

So, the clean price of an 8% eurobond with a dirty price of 98.55 sold 3 months and 4 days after the last coupon payment is calculated as follows:

clean price = 98.55 - { 8 x  ( 94/360 ) } = 96.46

The eurobond method is conceptually simple, but gets a little complicated on the 31st day of a month or at the end of February !