Question

A government bond with a coupon rate of 8% makes semiannual coupon payments on January 14 and July 14 of each year. The Wall Street Journal reports the asked price for the bond on January 29 at $1,000.625. What is the invoice price of the bond? The coupon period has 182 days. (Round your answer to 2 decimal places.)

Answer 1

$1,003.92

Step-by-step explanation:

the invoice price (or dirty price) of the bond = bond's market price + accrued interest:

• bond market price = $1,000.625 (given by WSJ)
• accrued interest = (coupon* / days within the period) x days passed since last coupon paid = ($40/182 days) x 15 days = $0.21978 x 15 days = $3.2967

dirty price = $1,000.625 + $3.2967 = $1,003.92

*semiannual coupon = $1,000 x 8% x 1/2 = $40

Answer 2

$1003.92

Step-by-step explanation:

The invoice price is calculated as the reported price plus the accrued interest. Therefore, the formula for accrued interest is shown below:

`Accrued Interest = (Annual coupon payment)/(2) * (days since last coupon payment)/(days separating coupon payments)`

Given that the coupon rate is 8%, therefore the bond pays $80 of coupon payments every year.

January 14 was the day that the last coupon was paid, so it has been 14 days since the last payment.

The coupon period is 182 days.

Therefore, the accrued interest is

`= (80)/(2) * (14)/(182) \\= 3.297`

The invoice price is calculated as:

$1000.625 + $3.297

= $1003.922.

Therefore the invoice price of the bond is $1003.92