Congratulations! You have just won a $$20$ million Powerball Lottery. You have a choice of payouts. You can either take a $$14$ million lump$-$sum today or you can receive an annuity of $$1$ million for the next $20$ years

$($starting at t$1).$ Assuming a discount rate of $4\%$ which one should you choose? What if the annuity grows at $1\%$ per year? Please show all calculations.