You have just won the lottery, $500 million. There are the following two payment options:

1. Lump sum of $500 million
2. Annual payout $13.37 million that increases at 4%

a) Plot as a function of time the total amount of money assuming a 3%, 4%, 5%, and 6% before tax revenue. Assume tax is 40% and applied to revenue at the end of the year. Put the lump sum in green and the annual payout in red.

b) You decide instead of just investing you would like to have $1 million in walking around money every year. Plot as a function of time the total account balance assuming a 3%, 4%, 5%, and 6% before tax revenue. Assume tax is 40% and applied to revenue at the end of the year. Put the lump sum in green and the annual payout in red.