You have won the lottery! $$500$ million was the grand prize which will be paid in equal installments over the next $25$ years $($so $25$ payments of $$20$ 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 discount rate of $6\%.$ Assume that you have to pay a $50\%$ tax on your prize, what is your resulting payout $($after tax$)?$ HINT $-$ you are calculating the PV of the annuity due. $*******$Using $4$ Equations: PV of ordinary annuity$=$ PMT$*((1/$I$)-(1/(($I$*(1+$I$))^$N$)))$ & PV of annuity due$=$ PV ordinary annuity $*(1+$I$)$ & Taxes $=$ PV of annuty due $*$ Tax$\%$ & Payout $=$PV annuity due $-$ Taxes