Company A$\text{'}$s $25-$year bonds have an annual coupon rate of $9\mathrm{.}4\%.$ Each bond has a face value of $$1,000$ and makes semiannual interest payments. If you require an $8\mathrm{.}7\%$ nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

a$.$ $$1,052\mathrm{.}71$

b$.$ $$597\mathrm{.}35$

c$.$ $$1,070\mathrm{.}89$

d$.$ $$1,079\mathrm{.}22$

e$.$ $$1,112\mathrm{.}30$