Billie Eilish is 20 and already worried about her future finances. She is currently happy but wants to be happier than ever by the time she retires. Hence, she wants to make some investments towards a couple of goals that she wants to achieve after retirement. First, she wants to be able to withdraw $100,000 each month to cover her clothing and make-up expenses for 20 years after she stops singing and retires at the age of 50. Second, she would like to donate $50,000,000 to NRDC at the age of 70. Lastly, the year she retires, she wants to buy a house in Hawaii 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 in Hawaii using her savings without having to give up the other two goals?
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