Suppose your $15-$year old cousin earned $$11,500$ one year by pressure$-$washing houses. Because she lives with her parents, she decided to save all of her earnings. If she invested all $$11,500$ in an account that earns $9\mathrm{.}5\%$ interest per year, how much will the account be worth in $50$ years when she is at the traditional retirement age? $($to be clear: not when she is $50,$ but rather $50$ years from now$)$