Mary is 20 years old and thinking about her finances and she wants to make some investments towards a couple of goals to achieve after retirement. First, she wants to be able to withdraw $100,000 each month for 20 years when she retires at the age of 50. Second, she would like to donate $50,000,000 at the age of 70. Lastly, the year she retires, she wants to buy a house that costs $10,000,000 today, with the price being estimated to increase by 2% each year. a. If she can earn 18% compounded monthly on her retirement account, how much does she need to deposit into her account each month, starting next month, until retirement to achieve her goals? b. If she decides to save and deposit $5,000 each month for the first 5 years only and then not to make any further deposits, what is the most she can offer on the house using her savings without having to give up the other two goals?