After graduating from college with a bachelor of business administration, you begin an ambitious plan to retire in $26\mathrm{.}76$ years. To build up your retirement fund, you will make quarterly payments into a mutual fund that on average will pay $11\mathrm{.}44\%$ APR compounded quarterly. To get you started, a relative gives you a graduation gift of $$3,487\mathrm{.}23.$

Once retired, you plan on moving your investment to a money market fund that will pay $4\mathrm{.}92\%$ APR with monthly compounding. As a young retiree, you believe you will live for $32\mathrm{.}61$ more years and will make monthly withdrawals of $$10,351\mathrm{.}14.($YOUR WITHDRAWALS ARE AT THE BEGINNING OF THE MONTH!!!!$)$ To meet your retirement needs, what quarterly payment should you make?