Question

Suppose that a 30-year government bond has a maturity value of $1000 and a coupon rate of 5%, with coupons paid semiannually. Find the market price of the bond if the yield rate is 4% compounded semiannually. (Round your answer to the nearest cent.)
$  

Is this bond selling at a discount or at a premium?

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 5% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 25

The YTM will be as follows:

= 4% / 2 (Since the payments are semi annually, hence divided by 2)

= 2%

N will be as follows:

= 30 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 60

So, the price of the bond will be computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 25 x [ [ (1 - 1 / (1 + 0.02)⁶⁰ ] / 0.02 ] + $ 1,000 / 1.02⁶⁰

= $ 25 x 34.76088668 + $ 304.7822665

= $ 1,173.80 Approximately

Since the bonds value is greater than $ 1,000, hence the bond is selling at a premium