Depending on how much of the work you really need to do yourself, File::Basename is a option.

use File::Basename;
use strict;

my %exts;

open FILE , '/some/big/file' or die "Screaming $!";
while ( <FILE> ) {
 chomp;
 my $file = $_;
 my ($name, $path, $suffix) = fileparse( $file , '\..*' );
 $exts{$suffix}++;
}

# Dump your hash here.
[download]

Update: Totally untested , looks OK to me.