You Win the Lottery, Which Pays $1 Million in 20 $\mathrm { PV } = \$ 50,000 \sum _ { T _ { - 0 } } ^ { 20 } [ 1 / ( 0.10 ) ] ^ { t }$

You win the lottery, which pays $1 million in 20 annual $50,000 payments. Your friends ask how much that would be if you received a single lump sum payment today. You do not have your calculator, but you show them the following equation to help them solve it themselves, assuming the interest rate is 10 percent:

A) $\mathrm { PV } = \$ 50,000 \sum _ { T _ { - 0 } } ^ { 20 } [ 1 / ( 0.10 ) ] ^ { t }$
B) $P V = \$ 50,000 \times \frac { 1 - [ 1 / ( 0.10 ) ] ^ { 20 } } { 1 - 1 / ( 0.10 ) }$
C) $P V = ( 50,000 \times 20 ) / ( 0.10 )$
D) $\mathrm { PV } = \$ 50,000 \sum _ { t = 0 } ^ { 20 } ( 0.10 ) ^ { t }$
E) $\mathrm { PV } = \$ 1,000,000 / .1$