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Most of the time, an investor buys a bond between coupon payments. In such transaction, the buyer must compensate the seller of the bond for the coupon interest earned from the time of the last coupon payment to the settlement date of the bond. This amount is called accrued interest. So the buyer pays the seller the agreed price plus the accrued interest. This is known as full price. The price of the bond without the accrued interest is known as clean price. The buyer recovers the accrued interest when the next coupon payment is received.
Now we will explain how to change the PV formula to calculate the full price of a bond when it is purchased between coupon payments.
In some market it is known as a dirty price.
Assume that an investor invests $X in a 3-year zero coupon Treasury security. Three years from now, the total return received would be:
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