Question

Suppose that a 25-year government bond has a maturity value of $1000 and a coupon rate of 3%, with coupons paid semiannually. Find the market price of the bond if the yield rate is 2% compounded semiannually. (Round your answer to the nearest cent.)

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 3% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 15

The YTM will be as follows:

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

= 1% or 0.01

N will be as follows:

= 25 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 50

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

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

= $ 15 x [ [ (1 - 1 / (1 + 0.01)50 ] / 0.01 ] + $ 1,000 / 1.0150

= $ 15 x 39.19611753 + $ 608.0388247

= $ 1,195.98 Approximately