Paul and Donna Kelsch are planning a Mediterranean cruise in $3$ years and will need $$5,500$ for the trip. They decide to set up a "sinking fund" savings account for the vacation. They intend to make regular payments at the end of each $3$ month period into the account that pays $6\%$ interest compounded quarterly. What periodic sinking fund payment $($in $$)$ will allow them to achieve their vacation goal? $($Round your answer to the nearest cent.$)$