Congratulations! You have just won the State Lottery. The lottery prize was advertised as an annuitized $350 million paid out in 30 equal annual payments beginning immediately. The annual payment is determined by dividing the advertised prize by the number of payments. You now have up to 60 days to determine whether to take the cash prize or the annuity.

a. If you were to choose the annuitized prize, how much would you receive each year?

b. The cash prize is the present value of the annuity payments. If interest rates are 3.5%, how much will you receive before taxes if you choose the cash option?

c. Now suppose that, as many lotteries do, the annuitized cash flows will grow by 3% per year to keep up with inflation, but they still add up to $350 million. In this case, the first payment will be $7,356,740.76 today. If you took the cash prize instead, how much would you receive (before taxes)?