Question

Suppose that a 25-year government bond has a maturity value of $1000 and a coupon rate of 7%, with coupons paid semiannually. Find the market price of the bond if the yield rate is 6% compounded semiannually. (Round your answer to the nearest cent.)


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

Answer 1

The market price of the bond is computed as shown below:

The coupon payment is computed as follows:

= 7% / 2 x $ 1,000 (Since the payments are semi annual, hence divided by 2)

= $ 35

The YTM is computed as follows:

= 6% / 2 (Since the payments are semi annual, hence divided by 2)

= 3% or 0.03

N is computed as follows:

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

= 50

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

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

= $ 35 x [ [ (1 - 1 / (1 + 0.03)⁵⁰ ] / 0.03] + $ 1,000 / 1.03⁵⁰

= $ 35 x 25.72976401 + $ 228.1070798

= $ 1,128.65 Approximately

Since the bond's value is greater than $ 1,000, hence it is selling at a premium.

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