Actual / 365
The basic equation for calculating the accrued interest to a settlement day is:
(1)\begin{align} Accrued\ interest=\frac{elapsed\ days}{365}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
(2)\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
page revision: 0, last edited: 02 Feb 2009 22:17