Suzy wants to retire in $30$ years. She expects to live $25$ years after retirement. She prepares a savings plan to meet the objectives: First, after retirement she would like to be able to withdraw $$20,000$ per month. The first withdrawal will occur at the end of the first month after retirement. Second, she would like to leave her daughter a $$500,000$ inheritance. Lastly, she wants to set up a fund that will pay $$5000$ per month forever to her favorite charity after she dies. These payments will begin one month after she dies. All the monies earn $10\%$ annual rate compounded monthly. How much will she have to save per month to meet these objectives? She wishes to make her first deposit from now and the last deposit on the day she retires.