Twelve years ago, Jordan invested a sum of $$4,500.$ The interest rate he earned changed over time: During the first four years, he earned $4$ percent annually compounded, during the following three years he earned $6\mathrm{.}5$ percent compounded quarterly, and during the final five years, he earned $9$ percent continuously compounded. Find the value of this investment at the end of the $12$th year.