Instructions: Please make sure that you show all your work when solving the problems. Feel free to make any assumptions whenever you feel necessary. Just make sure that you clearly state your assumptions.
1) Lady Gaga is 30 and already worried about her future. She wants to make sure that she’ll be able to keep up with the life standard she got used to – at the end of the day, she was born this way and wants to die this way, too. She has couple of goals that she wants to achieve after she retires. First, she wants to be able to withdraw $150,000 each month to cover her clothing and make-up expenses for 15 years after she stops singing and retires at the age of 65. Second, she wants to be able to donate $3,000,000 to St. Jude Children’s Hospital at the age of 75. Lastly, the year she retires, she also wants to buy a house in Honolulu, HI that costs $7,500,000 today, with the price being estimated to increase by 1% each year.
a. If she can earn 15% compounded monthly on her retirement account, how much does she need to deposit into her account each month until retirement to achieve her goals?
b. What if she decides to save $40,000 each month for the first 10 years, then not to save for 15 years, and to go back to saving and investing for the last 10 years before retirement – how much would she then need to save every month for the last 10 years to achieve the same goals?