After graduating from college with a bachelor of business administration, you begin an ambitious plan to retire in $23\mathrm{.}00$ years. To build up your retirement fund, you will make quarterly payments into a mutual fund that on average will pay $12\mathrm{.}08\%$ APR compounded quarterly. To get you started, a relative gives you a graduation gift of $$2,034\mathrm{.}00.$

Once retired, you plan on moving your investment to a money market fund that will pay $5\mathrm{.}64\%$ APR with monthly compounding. As a young retiree, you believe you will live for $28\mathrm{.}00$ more years and will make monthly withdrawals of $$10,129\mathrm{.}00.($YOUR WITHDRAWALS ARE AT THE BEGINNING OF THE MONTH!!!!$)$ To meet your retirement needs, what quarterly payment should you make?