As an employee in the Lottery Commission, your job is to design a new prize. Your idea is to create two grand prize choices: $(1)$ receiving $$50,000$ at the end of each year beginning in one year for $20$ consecutive years, or $(2)$ receiving $$500,000$ today followed by a one$-$time payment at the end of $20$ years. Using an interest rate of $6\%$ which of the following comes closest to the amount prize $(2)$ needs to pay at the end of year $20$ in order that both prizes have the same present value?

$$500,000$

$$440,463$

$$326,649$

$$235,712$

$$114,932$