Avigail wishes to save money to provide for Avigail's retirement. Beginning one month from now, Avigail will begin depositing a fixed amount into a retirement savings account that will earn $12\mathrm{.}00\%$ compounded monthly. Avigail will make $264$ such deposits. Then, one year after making Avigail's final deposit, Avigail will begin withdrawing $$118,000$ annually for $20$ years. The fund will continue to earn $12\mathrm{.}00\%$ compounded monthly during the $20$ years money is being withdrawn from the account. How much should the monthly deposits be to fund Avigail's retirement plan? $(15$ marks$)$