Question

1. A 30-year bond has a face value of $1,000 and a 9% coupon rate, paid semi-annually. a. You buy the bond today when it has a yield to maturity of 7%. Compute the price of the bond today.

Answer 1

The price of the bond is computed as shown below:

The coupon payment is computed as follows:

= 9% / 2 x $ 1,000 (Since the coupon payments are semi annual, hence divided by 2)

= $ 45

The YTM is computed as follows:

= 7% / 2 (Since the coupon payments are semi annual, hence divided by 2)

= 3.5% or 0.035

N is computed as follows:

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

= 60

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

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

= $ 45 x [ [ ( 1 - 1 / (1 + 0.035)⁶⁰ ] / 0.035 ] + $ 1,000 / 1.035⁶⁰

= $ 45 x 24.94473412 + $ 126.9343059

= $ 1,249.45 Approximately

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