One year from today, your brother will go to a college and pay a tuition of $$17,078,$ which remains the same for his four$-$year college life. Thus, he needs to pay $$17,078$ at the beginning of each school year for four years and the first payment of $$17,078$ will be one$-$year from today. Your uncle promised to pay $50\%$ of your brother's total tuition, and he has already saved $$9,839$ for your brother in a $593$ Educational account, which earns $11\mathrm{.}2\%$ annually. How much additional money does your uncle need to save in the $593$ account today so that it will have enough money to pay $50\%$for your brother's four$-$year tuition?