You have won the lottery. $$750$ million was the prize which will be paid in equal installments over the next $25$ years $($so $25$ payments of $$30$ million per year, starting today$).$ You also have the option to take a lump sum immediately which will be calculated based on the above payout using a dsicount rate of $6\%.$ Assume that you have to pay a $50\%$ tax on your prize, what is the resulting payout $($after tax$)?$ Hint: a $6\%$ discount does not mean the prize is $6\%$ less $--$ this is obviously a time value of money problem so think about what is given here and construct a timeline to properly account for the cash flows.