Assume that you are considering the purchase of a $25-$year, noncallable bond with an annual coupon rate of $9\mathrm{.}3\%.$ The bond has a face value of $$1,000,$ and it makes semiannual interest payments. If you require a $9\mathrm{.}8\%$ nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

a$.$ $$964\mathrm{.}41$

b$.$ $$949\mathrm{.}46$

c$.$ $$995\mathrm{.}89$

d$.$ $$525\mathrm{.}25$

e$.$ $$953\mathrm{.}65$