A $1,000 corporate bond with 10 years to maturity pays a coupon of 8% (semi-annual) and the market required rate of return is a) 7.2% and b) 10%. What is the current selling price for a) and b)?
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+118609 A $1,000 corporate bond with 10 years to maturity pays a coupon of 8% (semi-annual) and the market required rate of return is a) 7.2%
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First lets think about this a bit.
You will be happy with at return of 7.2%. This is less than the coupon rate of 8% so that means you will be prepared to pay more than $1000 for the bond. You will use this logic when you check the reasonableness of the answer that we will get.
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r=0.08/2=0.04 every 6 months
i=0.072/2=0.036 every 6 months
C=1000
$$P=C+[(I-Ci)a_{n|i}]$$
Where
n=20 (lots fo 6 months) and
$$a_{n|i}\\\\
=\frac{1-(1+i)^{-n}}{i}\\
=\frac{1-(1+0.036)^{-20}}{0.036}\\
=\frac{1-(1.036)^{-20}}{0.036}\\$$
$$\left({\frac{\left({\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{1.036}}}^{\left(-{\mathtt{20}}\right)}\right)}{{\mathtt{0.036}}}}\right) = {\mathtt{14.084\: \!658\: \!505\: \!338\: \!905\: \!8}}$$
near enough to 14.08466
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$$\\P=C+[(I-Ci)a_{n|i}]\\\\
P=1000+[(40-1000*0.036)*14.08466]\\
P=1000+[(40-36)*14.08466]\\
P=1000+[4*14.08466]\\$$
$${\mathtt{1\,000}}{\mathtt{\,\small\textbf+\,}}\left[{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{14.084\: \!66}}\right] = {\mathtt{1\,056.338\: \!64}}$$
this is more than $1000 so it fits with the reasonableness check 
