Collectors Problem

What is the total amount of money in everyone's bank account if the collector chooses the $i^{th}$ package?

$P_i × N$

Let $total$ is equivalent to everyone’s current bank balance summation.
For each $i$ from $1$ to $M$ calculate the collector’s outcome with,
$total - P_i × N - S_i$.
Here $S_i$ is the amount of money the collector has to pay to the Bat club. Take the maximum outcome as the answer.