How do I get the price of a line item for the transactions which are already completed?
Yes, Commerce Module does store product amount of past order... You can retrieve using below details...

To get full details of order

$order = commerce_order_load($order_id);
$view_mode = "administrator";
print entity_view('commerce_order', array($order-&gt;order_id =&gt; $order), $view_mode, NULL, TRUE);


To be more specific

  $order = commerce_order_load($order_id);
  foreach ($order-&gt;commerce_line_items['und'] as $line) {
    $line_item = commerce_line_item_load($line['line_item_id']);
    drupal_set_message("&lt;pre&gt;" . print_r($line_item,1) . "&lt;/pre&gt;");
  }


There is no chance it gets new price instead of old price since it gets tracked in field_data_commerce_unit_price table in database ... All you need to do is divide by 100 if decimal places are 2 in order line item amount...