One day, your friend Cassie Kwok calls you and seeks your advice on some financial matters. Cassie is a lawyer with three children. She is planning for retirement in 30 years. Currently, she has $150,000 in a savings account and $250,000 in a mutual fund. Moreover, she plans to add to her savings by depositing $1,000 per month in her savings account at the end of each month of next 10 years and then $2,000 per month at the end of each month(of subsequent 20 years) until retirement. The savings account will return 6% APR compounded monthly and the investment in the mutual fund will return 8% APR compounded annually. Cassie expects to live for 20 years after she retires and at retirement she will deposit all of her savings in a bank account paying 3% APR compounded monthly. In addition, she would like to have a total of $2,000,000 to leave to her children when she passes away.

Required:

1. (a) How much will Cassie have at retirement?

2. (b) How much can Cassie withdraw each month after retirement?