Several years ago, the Wall Street Journal reported that the winner of the Massachusetts State Lottery prize had the misfortune of being both bankrupt and in prison for fraud. The balance of the prize was $$9,420,713,$ to be paid in $19$ equal annual installments $($there were $20$ installments, but the winner had already received the first payment$).$ The bankruptcy court judge ruled that the prize should be sold off to the highest bidder and the proceeds were to be paid to the creditors.

If the interest rate was $8\%,$ how much would you have been prepared to bid for the prize? Explain your reasoning.