You just won the lottery, which promises you $$440,000$ per year for the next $20$ years. You receive the first payment today $($hint: annuity due$).$ If your discount rate is $9\mathrm{.}00\%,$ what is the present value of your winnings?

$$4,378,050$

$$4,263,810$

$$4,592,674$

$$4,111,618$

$$4,016,560$