Edit in JSFiddle

$(document).ready(function() {

  $("#getRate").on("click", function(event) {

    // Download the xml rates file
    var date = $("#kurs_data_rok").val() + '-' + $("#kurs_data_miesiac").val() + '-' + $("#kurs_data_dzien").val();

    $("#kurs-result").html('<img src="./images/site/ajax-loader.gif" width="50" />');
    $("#kurs_euro1").val('');
    $("#kurs_euro2").val('');
    $("#tabela_nbp").val('');

    $.post('./ajax/api_nbp_tab_A_xml.php', {
      'data': date
    }, function(data) {

      $("#kurs-result").html(data);

      var xhttp = new XMLHttpRequest();

      xhttp.onreadystatechange = function() {
        if (xhttp.readyState == 4 && xhttp.status == 200) {
          getRates(xhttp);
        }
      }

      xhttp.open("GET", "xml/" + date + ".xml", true);
      xhttp.send();

    });

    function getRates(xml) {
      var xmlDoc = xml.responseXML;

      var tab = xmlDoc.getElementsByTagName("ExchangeRatesSeries")[0].getElementsByTagName("Rates")[0].getElementsByTagName("Rate")[0].getElementsByTagName("No")[0].childNodes[0].nodeValue;
      var rate = xmlDoc.getElementsByTagName("ExchangeRatesSeries")[0].getElementsByTagName("Rates")[0].getElementsByTagName("Rate")[0].getElementsByTagName("Mid")[0].childNodes[0].nodeValue;

      var point = rate.indexOf(".");
      var rateInt = rate.substr(0, point);
      var rateDec = rate.substr(point + 1);

      $("#kurs_euro1").val(rateInt);
      $("#kurs_euro2").val(rateDec);
      $("#kurs-result").html(tab);
      $("#tabela_nbp").val(tab);

    }

  });

});