Actual / Actual

The basic equation for calculating the accrued interest to a settlement day is:

\begin{align} Accrued\ interest=\frac{elapsed\ days}{days\ in\ current\ year}x\ coupon \end{align}

For example, a Treasury bond maturing on August 15, 2020 pays a coupon of 8.750%. If you purchase this bond on Friday, January 30 to settle on Monday, February 2 of 2009; what will be the accrued interest and total price if you pay an ask price of 148:25?

First calculate the quoted price for $100 worth of this bond. The 25 after the colon implies 25/32 which in decimal form is 0.78125. Adding this to the quoted 148 produces, 148.78125.

Next calculate the accrued interest for the days since interest was last paid (August 15).

Month Days
August 17
September 30
October 31
November 30
December 31
January 31
February 1
Total 171

Apply this to the formula

\begin{align} Accrued\ interest=\frac{171}{365}x\ 8.75=4.099315 \end{align}

So the total price is 148.78125 + 4.099315 = 152.88156