A professor is trying to save for his two daughters future weddings. He makes an assumption that they will both get married on the same day in exactly $24\mathrm{.}00$ years from today. The cost today of a wedding is $$31,898\mathrm{.}00,$ and the cost grows annual at a rate of $4\mathrm{.}00\%$ per year. The professor will make monthly contributions at the end of each month to a mutual fund that pays $3\mathrm{.}96\%$ APR $($with monthly compounding$).$ The professor will make the last contribution the day of the wedding. The professor has already set aside $$3,000\mathrm{.}00$ in an account. To pay for BOTH weddings, how much will he have to contribute each month to fully pay for the weddings in cash?