Actual / Actual

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

(1)\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

(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: 3, last edited: 02 Feb 2009 22:09