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 $8\mathrm{.}4\%$ nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?