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 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? (20 marks)

2. (b) How much can Cassie withdraw each month after retirement? (10 marks)

please use the formula about PVFVPVA

and please list the formula and write the steps clearly very thanks