Final answer:
The clean price of the bond is calculated by deducting the accrued interest from the purchase price of $1,065. With a coupon rate of 8%, the accrued interest for 5 months is approximately $33.33, therefore the clean price is roughly $1,031.67.
Step-by-step explanation:
When calculating the clean price of a bond, you must consider the accrued interest since the last coupon payment. The bond mentioned has an 8% coupon rate, $1,000 face value, pays interest semi-annually, and the next payment is one month away.
As you've purchased the bond for $1,065, this price includes both the clean price and the accrued interest for the 5 months since the last coupon payment.
To find the clean price, we deduct the accrued interest from the purchase price.
The accrued interest is calculated based on the coupon rate times the face value times the fraction of the semi-annual period that has passed. With a coupon rate of 8%, semi-annual payments are $40 (8% of $1,000 divided by
2). For 5 out of 6 months' worth of a semi-annual period, this is approximately $33.33 ($40 x (5/6)). Therefore, the clean price of the bond would be the purchase price minus the accrued interest, or $1,065 - $33.33, which equals approximately $1,031.67.