This is a challenging question and will take significantly more time to solve than the average problem. Please spend your time wisely and attempt it in the end.

Ms. Ieda Silva plans to retire in 28 years and expects to live for 25 years after retirement. She is preparing a savings plan to meet the following 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 son an inheritance of $500,000 when she passes on. Finally, she would like to set up a fund that will pay $15,000 per month forever to her favorite charity after she passes on. These payments to the charity will start one month after she passes on. All monies can earn 10 percent annual rate compounded monthly. How much will she have to save per month to meet these objectives? She wishes to make the first deposit a month from now and the last deposit on the day she retires. (Hint: Calculate separately the present value of each objective today and add them together.)