The Howe family recently bought a house. The house has a $30-$year, $$241,644\mathrm{.}00$ mortgage with monthly payments and a nominal interest rate of $4\mathrm{.}9$ percent. What is the total dollar amount of principal the family will pay during the first $4$ years of their mortgage? $($Assume that all payments are made at the end of the month.$)$

$$16,647\mathrm{.}91$

$$17,647\mathrm{.}91$

$$19,647\mathrm{.}91$

$$15,647\mathrm{.}91$

$$18,647\mathrm{.}91$