You have a goal of saving money to do some home renovation in $6$ years. You expect the renovation to cost $$46,724.$ You plan on putting money $($today$)$ in a savings account that offers you a $4\mathrm{.}5\%$ APR $($with monthly compounding$).$ How much do you need to invest $($today$)?$

To nearest $$0\mathrm{.}01$