Tim is a $65-$year$-$old man who recently experienced what he thought were stroke$-$like symptoms and went to the emergency room at a nearby hospital. Although it turned out to be a severe case of heartburn, not a stroke, his medical bill for the hospitalization and tests totaled $$5,535.$ Tim has an insurance policy with a $$100$ hospital stay deductible and a coinsurance rate of $20\%.$ He can therefore expect a reimbursement from the insurance company of $$\_\_\_\_\_\_\_.$

$.($Note: Round your answer to the nearest dollar.$)$