Dynamically changing available select options
This is a classic example of counting on the UI to keep track of state and model.

Because you know there are only 2 options, and you know how to go from one option to another, you simply hide and add options. Nowhere in your code is explicitly declared what durations are linked to which option.

If you dont care about that, you could optimize the code doing something like this:

$(document).ready(function() {
  var monthsDifference = $("#term option[value='48'], #term option[value='42']");

    $("input.radio-button-selector").change(function(){ 
        if ( $(this).val() == "opt2" ) {
            monthsDifference.hide();
        }
        else if ( $(this).val() == "opt1" ) {
            monthsDifference.show();
        }
        });
    });


I would advise you to care though, and have the code know what the months are and build selectors for each option. Something like this (untested):

$(document).ready(function() {
  var optionMonths = {
      opt1: [6,9,10,12,18,24,30,36,42,48],
      opt2: [6,9,10,12,18,24,30,36]
  }
  //Cache all options
  var $options =  $("#term option");

    $("input.radio-button-selector").change(function(){ 
        //Hide all options first
        $options.hide();    
        //Then show relevant options
        showOptionMonths( optionMonths[ $(this).val()] );
    });
});

function showOptionMonths( months ){
    months.forEach( function( month ){
       $("#term option[value='" + month + "']").show();
    });
}


Of course, I would try to find a better name than opt1 or opt2, but I dont have enough knowledge of what you are trying to achieve to suggest something more meaningful.

Finally, you could cache the selectors for each option, I leave that as an exercise for the reader.