A state lottery commission pays the winner of the Million Dollar lottery $20$ installments of $$50,000/$year$.$ The commission makes the first payment of $$50,000$ immediately and the other n $=19$ payments at the end of each of the next $19$ years. Determine how much money the commission should have in the bank initially to guarantee the payments, assuming that the balance on deposit with the bank earns interest at the rate of $5\%/$year compounded yearly.