display dropdown values based on previous dropdown

Answer 1

You need to reference the parent in each child. Carrier:

<label for="carrier_sold">Carrier Sold: </label>
    <select name="carrier_sold" id="carrier_sold">
    <option value="" selected="selected">Select...</option>
    <option value="MetLife">Metlife</option>
    <option value="Travelers">Travelers</option>

    </select>

Travelers: store the parent for each option, for example in a data-xyz attribute.

<label for="payment_plan">Payment Plan: </label>
<select name="payment_plan" id="payment_plan">
   <option value="" selected="selected">Select...</option>
   <option data-parent="MetLife" value="bill">Bill</option>
   <option data-parent="MetLife" value="full">Full</option>
   <option data-parent="Travelers" value="eft">EFT</option>
   <option data-parent="Travelers" value="rcc">RCC</option>
</select>

The jQuery:

$('#carrier_sold').change(function() {
   var parent = $(this).val();
   $('#payment_plan').children().each(function() {
      if($(this).data('parent') != parent) {
                $(this).hide();
      } else    $(this).show();
   });
});

Repeat for the next instance. Ideally, I'd make a class-based jQuery function that works off of classes instead of IDs, and pulls the respective children from each parent via a data-child attribute or similar.

And to jazz it up even more, you could hide the child unless the parent has a value. You can also experiment with change() vs. blur().