The winner of this Saturday's $$550,000,000$ drawing will have the option to take the payments over time, but it's not in equal payments. In other words this is a graduated annuity. There will be $30$ payments over $29$ years, the first payment will be immediate & the payments will increase $5\%$ each year. The estimated cash option is $$277,500,000.$ Assuming combined federal and state income tax of $35\%.$ Assume your Uncle Jimmy won the lottery & has no idea what option to take. Your task is to prepare a detailed analysis, including identifying what the annual payments will be$,$ and explanation to help Jimmy decide what to do$.$ From a financial standpoint which option is the best for him and why?