Maggie wins the lottery and is awarded 500,000 at the beginning of each quarter for the next 20 years. The government takes 40% of her winnings and she spends 90% of what is left. The remainder is put into a special account with an insurance company that guarantees 7% compounded monthly for the first 10 years and 4% compounded 6 times a year for the following 10 years. At the end of 20 years the accumulated value in the account is used to purchase a perpetuity-immediate with semi-annual payments of X