Question

# 1. A 30-year bond has a face value of \$1,000 and a 9% coupon rate, paid...

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.

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

Feel free to ask in case of any query relating to this question

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