The bike you have been saving for is discounted $15\%.$ You have $$500$ saved to purchase it$.$ The original, non$-$discounted price of the bike is $$550.$ There is a $5\mathrm{.}02\%$ sales tax added to the price of the bike. After you purchase the bike with the discount and sales tax, how much money will you have left over? Round your answer to the nearest dollar.