An investment promises to pay you $$400$ per year starting in $5$ years. The cash flow from the investment is expected to increase by $2$ percent per year forever. If alternative investments of similar risk earn a return of $9$ percent per year, determine the maximum you would be willing to pay for the investment. $($Round answer to $2$ decimal places, e$.$g$.125\mathrm{.}12.$ Do not round your intermediate calculations.$)$