Dave is beginning to plan for his retirement. Beginning one year from now, Dave will begin depositing a fixed amount in a retirement account each year for the next $30$ years. The retirement account will pay $9\%$ interest compounded monthly. One year after his last deposit, Dave wants to be able to withdraw $$75,000$ a year for $20$ years. Dave's retirement account will continue to earn $9\%$ compounded monthly. How much will Dave have to deposit in his retirement account each year for his plan to work?