One day, your aunt Mary calls you and seeks your advice on some financial matters. Mary is a designer with two children. She is planning for retirement in 20 years. Currently, she has $200,000 in a savings account and $400,000 in a mutual fund. Moreover, she plans to add to her savings by depositing $5,000 per month in her savings account at the end of each month until retirement. The investment in the savings account will return 12% APR compounded monthly and the investment in the mutual fund will return 10% APR compounded annually. Mary expects to live for 30 years after she retires and at retirement she will deposit all of her investments in a bank account paying 6% APR compounded monthly. In addition, she would like to have a total of $3,000,000 to leave to her children when she passes away.

Required:

(a) How much will Mary have when she retires? (8 marks)

(b) How much can Mary withdraw each month after retirement? (4 marks)

(c) Without doing any calculation, critically discuss how an increase in (8 marks) retirement age may affect the amount that Mary can withdraw each month

after retirement. (word limit: 150 words)