My wife of 20 years and myself were both granted annulments prior to us being married. There was a charge at the time. It was $600.00 for each of us. We were granted the annulment in the Archdiocese of Milwaukee.
There is usually some charge for annulments, simply because of the administrative costs of the process. If, for some reason, the party requesting the annulment cannot afford to pay, that is not an impediment to the process.