A bond makes annual coupon payments, is currently worth $$997,$ and has a duration of $4\mathrm{.}74$ years. The bond's yield$-$to$-$maturity is currently $9\%.$ If the rate on same$-$risk bonds suddenly changes to $9\mathrm{.}01\%,$ then what does duration predict the new price of the bond to be$?$ Round your answer to the nearest penny.