You are planning for your retirement. You believe that you could live comfortably in retirement with the equivalent of $$100,000$ per year in today's dollars $($for simplicity, assume this is as of your $22$nd birthday$).$ Further, you plan to start saving when you turn $22$ and retire when you turn $67.$ You anticipate living approximately another $30$ years past that point. Assume that inflation is $3\%$ per year on average until then, and that the market will earn a $12\%$ return. Assuming that you will make monthly contributions to and withdrawals from your retirement account, how much money will you need to save each month to reach your goal?