Question

You purchase a bond with an invoice price of $1,022 and a par value of $1,000. The bond has a coupon rate of 6.9 percent, and there are four months to the next semiannual coupon date. Assume a par value of $1,000. What is the clean price of the bond? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The clean price of the bond is calculated by subtracting the accrued interest from the invoice price, resulting in a clean price of $1,010.50.

Step-by-step explanation:

To calculate the clean price of the bond, we first need to understand that the invoice price (also known as the dirty price) includes accrued interest, while the clean price does not. The bond has a semiannual coupon rate, which means it pays interest twice a year. At a 6.9% annual coupon rate, each payment is 3.45% of the par value ($1,000), leading to a $34.50 coupon payment every six months.

Since there are four months to the next coupon date, two months of interest have been earned since the last coupon. As a six-month period would earn $34.50, two months would earn approximately $11.50 (34.50 * 2/6).

Therefore, to find the clean price, we subtract the accrued interest from the invoice price: $1,022 - $11.50 = $1,010.50. So, the clean price of the bond is $1,010.50.

Answer 2

the clean price of the bond is $999.98.

Step-by-step explanation:

First, we need to calculate the accrued interest, which is the interest that has accumulated on the bond since the last coupon payment. The bond pays a semi-annual coupon, so there are 6 months between coupon payments. Since there are 4 months to the next coupon payment, the accrued interest is:

accrued interest = coupon rate * (time since last coupon payment / time between coupon payments)

accrued interest = 0.069 * (2 / 6)

accrued interest = 0.023

Next, we can calculate the clean price of the bond by subtracting the accrued interest from the invoice price:

clean price = invoice price - accrued interest

clean price = 1022 - 0.023

clean price = 999.98

Therefore, the clean price of the bond is $999.98.