Suppose the Winner of a $4,000,000 Sweepstakes Will Be Paid $\sum _ { n = 1 } ^ { 40 } 100,000 \left( \frac { 1 } { 1.05 } \right) ^ { n }$

Suppose the winner of a $4,000,000 sweepstakes will be paid $100,000 per year for 40 years, starting a year from now. The money earns 5% interest per year. The present value of the winnings is $\sum _ { n = 1 } ^ { 40 } 100,000 \left( \frac { 1 } { 1.05 } \right) ^ { n }$ . Compute the present value using the formula for the $n$ th partial sum of a geometric series. Round your answer to two decimal places.

A) $\$ 6,852,274.09$
B) $\$ 1,959,646.05$
C) $\$ 4,568,182.73$
D) $\$ 1,246,221.03$
E) $\$ 1,715,908.64$