Suppose Jay wants to retire in exactly $12$ years from today. He needs exactly $$150000\mathrm{.}00$ when he reaches his future retirement age. In order to meet his goal retirement savings, he will make monthly contributions to his retirement account beginning one month from today. He will continue making equal monthly payments in the account until he reaches retirement age in $12$ years.

What minimum amount needs to be places in his account at the end of each month so he will reach his retirement savings goal, if the annual interest rate is $4\mathrm{.}5\%?$