If you want only numbers, you have to check for numbers. One way to do that:

print"Enter the starting amount: ";
while( $startAmount !~ /^\d+/ ) {
    $startAmount = <STDIN>;
    chomp( $startAmount );
    if ( $startAmount !~ /^\d+$/ ) {
        print"Numbers only! Try again: ";
    } else {
        last;
    }
}
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The above checks $startAmount twice. We can avoid that with a bare block and redo:

print"Enter the starting amount: ";
{
    chomp( $startAmount = <STDIN> );
    unless ( $startAmount =~ /^\d+$/ ) {
        print"Numbers only! Try again: ";
        redo;
    }
    # this line is reached if $startAmount is a number
    print "ok, \$startAmount is $startAmount\n";
}
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There are many more ways to do that...