Your Council Tax bill assumes that there are at least two adults over 18 living in the property (as their main home). More than two people make no difference to the charge. One person or no one at all in a property may qualify for discount.
Discounts aren't based on income. It doesn't matter about how much you have or the savings you have. A discount is given if your circumstances meet certain conditions.
From time to time we carry out a review of single persons discounts claimed, so we may ask you to confirm you're you remain the only adult living at the address.