Assume that you are considering the purchase of a $20-$year, noncallable bond with an annual coupon rate of $9\mathrm{.}5\%.$ The bond has a face value of $$1,000,$ and it makes semiannual interest payments. If you require an $10\mathrm{.}7\%$ nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

$$721\mathrm{.}44$

$$910\mathrm{.}81$

$$901\mathrm{.}80$

$$874\mathrm{.}74$

$$1,000\mathrm{.}99$