The Howe family recently bought a house. The house has a $30-$year, $$276,957\mathrm{.}00$ mortgage with monthly payments and a nominal interest rate of $3\mathrm{.}5$ percent. What is the total dollar amount of interest the family will pay during the first $4$ years of their mortgage? $($Assume that all payments are made at the end of the month.$)$

$$38,273\mathrm{.}68$

$$34,273\mathrm{.}68$

$$37,273\mathrm{.}68$

$$35,273\mathrm{.}68$

$$36,273\mathrm{.}68$