Bond X is noncallable and has $20$ years to maturity, an $8\%$ annual coupon, and a $$1,000$ par value. Your required return on Bond X is $9\%$; if you buy it$,$ you plan to hold it for $5$ years. You $($and the market$)$ have expectations that in $5$ years, the yield to maturity on a $15-$year bond with similar risk will be $7\mathrm{.}5\%.$ How much should you be willing to pay for Bond X today? $($Hint: You will need to know how much the bond will be worth at the end of $5$ years.$)$ Do not round intermediate calculations. Round your answer to the nearest cent.

$