You have just won the lottery. The state offers you an amortized payout of $$200,000$ at

the end of each year for $30$ years. The payout is taxable and the tax rate is $60\%.$ You do

not expect the government $($who pays the payout$)$ to go bankrupt. The risk$-$free rate is

$13\%$ per year and the total expected market return is $17\%.$

What is the value of the lump$-$sum payment that would cause you to be indifferent

between taking the lump$-$sum or the amortized payout?