Question

The bond has a coupon rate of 5.57 percent, it makes semiannual payments, and there are 5 months to the next coupon payment. A clean price of $923 and the par value is $1,000. What is the invoice price?

Answer 1

The invoice price of the bond can be calculated by adding the clean price and the accrued interest. In this case, the invoice price is $923,023.22.

Step-by-step explanation:

The invoice price of a bond refers to the price at which the bond is bought or sold, including any accrued interest. To calculate the invoice price, we need to take into account the clean price, which is the price of the bond without accrued interest. In this case, the clean price is $923 and the par value is $1,000.

First, we need to calculate the accrued interest. The bond makes semiannual payments, so the next coupon payment is 5 months away. Since each coupon payment is for half of the annual coupon rate, the accrued interest can be calculated as follows:

Accrued Interest = (Coupon Rate / 2) x (Time since last coupon payment / Time between coupon payments)

Accrued Interest = (5.57% / 2) x (5 months / 6 months)

Accrued Interest = 0.02785 x 0.83333 = 0.02322

Next, we calculate the dirty price, which is the clean price plus the accrued interest:

Dirty Price = Clean Price + Accrued Interest

Dirty Price = $923 + $0.02322

Dirty Price = $923.02322

Finally, we can calculate the invoice price, which is the dirty price multiplied by the par value:

Invoice Price = Dirty Price x Par Value

Invoice Price = $923.02322 x $1,000

Invoice Price = $923,023.22