If you purchase this Treasury security on May 14, 2014, what are the clean price, accrued interest, and dirty price?

The clean price of a Treasury security purchased on May 14th, 2014 is the purchase price without any accrued interest. Accrued interest refers to the amount of interest that has accumulated since the last coupon payment date and it is calculated based on the days passed since then. The dirty price is calculated by adding the accrued interest to the clean price. So for a Treasury security purchased on May 14th, 2014,
the clean price would be equal to what was paid for the security, while its dirty price would be equal to that same amount plus any accrued interest associated with holding it past its most recent coupon payment date (which may have been in April).

To calculate accrued interest, you must first determine how many days have passed since its last coupon payment date. This can usually be found on your monthly statement or from your investment advisor/banker. Next, divide this number by 365 (or 360 if using an alternate calendar method) and multiply it by the annualized yield rate on your note (also known as APY or Annual Percentage Yield). Finally, take this number and multiply it by either par value or face value of your Treasury security as indicated in your contract; this will give you an accurate calculation of how much accrued interest there is associated with it.

For example: Let’s say you bought a one year $1 million par value Treasury note at 5% annualized yield rate (APY) two months after its most recent coupon payment date – which was 30-April-2014.. Its Clean Price would remain unchanged at$1 million but its Accrued Interest would increase to about $4167 ($1million x 5% / 12 months x 2 months), meaning Dirty Price for that note = $1million + $4167 = $1004167