Gertie Minzenberger is putting away money in a vacation fund to travel in $13$ years and currently has an amount of $$281,720\mathrm{.}00.$ Given an interest rate of $8\mathrm{.}00\%$ compounded tri$-$annually, how much will they have in $13$ years?

a$.$ $$354,886\mathrm{.}06$

b$.$ $$766,172\mathrm{.}40$

c$.$ $$786,260\mathrm{.}92$

d$.$ $$315,751\mathrm{.}45$