Question 1 (21 Marks) Natalie celebrates her 20th Birthday today. She plans to deposit a constant amount of money in her savings account each year until she retires 45 years later at age 65 to support her retirement spending. The interest rate on her savings account is 10% per year. Natalie will start making these deposits on her 21st birthday and continues to make deposit each year until the last deposit on her 65th birthday. Natalie wants to be able to withdraw $40,000 from her savings account on each birthday for 35 years following her retirement until she is 100; the first withdrawal from her retirement savings will be on her 66th birthday. (a) How much does Natalie have to accumulate in her saving account at the time she retires to support her retirement spending? (5 Marks) (b) How much does Natalie need to deposit in her savings account each year until she retires 45 years later at age 65 to fund her retirement if Natalie decides to increase withdraw amount from $40,000 to $50,000 from her saving account on each birthday for 35 years following her retirement? (6 Marks)