Please show your work and formulas.

Question 1: Your boyfriend just won the Florida lottery. He has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity?

Question 2: After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift which you will deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?

Question 3: Erika and Kitty, who are twins, just received $30,000 each for their 25th birthday. They both have aspirations to become millionaires. Each plans to make a $5,000 annual contribution to her early retirement fund on her birthday, beginning a year from today. Erika opened an account with the Safety First Bond Fund, a mutual fund that invests in high-quality bonds whose investors have earned 6% per year in the past. Kitty invested in the new Issue Bio-Tech Fund, which invests in small, newly issued biotech stocks and whose investors have earned an average of 20% per year in the fund's relatively short history. (a) If the two women's funds earn the same returns in the future as in the past, how old will each be when she becomes millionaire? (b) How large would Erika's annual contributions have to be for her to become millionaire at the same age as Kitty, assuming that the expected returns are realized? (c) Is it rational or irrational for Erika to invest in the bond fund rather than in stocks?