Assume that you are considering the purchase of a 20year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of $1,000, and it makes semiannual interest payments. If you require an 12.7% nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?
a. 
$901.80 

b. 
$674.76 

c. 
$1243.46 

d. 
$833.43 

e. 
$769.5 
The value of the bond is computed as shown below:
The coupon payment is computed as follows:
= 9.5% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)
= $ 47.50
The YTM will be as follows:
= 12.7% / 2 (Since the payments are semi annually, hence divided by 2)
= 6.35% or 0.0635
N will be as follows:
= 20 x 2 (Since the payments are semi annually, hence multiplied by 2)
= 40
So, the price of the bond will be computed as follows:
= Coupon payment x [ [ (1  1 / (1 + r)^{n} ] / r ] + Par value / (1 + r)^{n}
= $ 47.50 x [ [ (1  1 / (1 + 0.0635)^{40} ] / 0.0635 ] + $ 1,000 / 1.0635^{40}
= $ 47.50 x 14.40611187 + $ 85.21189635
= $ 769.50 Approximately
So, the correct answer is option e.
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