Answer:
b. 1,062.81
Explanation:
the key to answer this question is to remember that valuation of a bond depends basically of calculating the present value of a series of cash flows, so let´s think about a bond as if you were a lender so you will get interest by the money you lend (coupon) and at the end of n years you will get back the money you lend at the beginnin (principal), so applying math we have the bond value given by:
[tex]price=\frac{principal*coupon}{(1+i)^{1} }+ \frac{principal*coupon}{(1+i)^{2} } \frac{principal*coupon}{(1+i)^{3} }+...+\frac{principal+principal*coupon}{(1+i)^{n} }[/tex]
where: principal as said before is the value lended, coupon is the rate of interest paid, i is the interest rate and n is the number of periods
so applying to this particular exercise, as it is not said we will assume that 6% and 7% are interest rate convertible seminually, so the price of the bond will be:
[tex]price=\frac{1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{1} } +\frac{1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{2} }+\frac{1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{3} }+...+\frac{1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{15} }+\frac{1,000+1,000*\frac{0.07}{2} }{(1+\frac{0.06}{2}) ^{16} }[/tex]
price=1,062.81
take into account that here we are asked about semianually payments, so in 8 years there are 16 semesters.
