The law does not limit the amount of a late fee authorized in the CC&Rs.  But, a late fee should only be charged once per late payment, and not, for example, monthly or quarterly for the same late payment.

In the event a late fee is not authorized in a declaration, both the Condo Act and the Community Association Act authorize associations to adopt a rule imposing a charge for a late payment of an assessment.  However, if a late fee is imposed merely by a rule and not by the CC&Rs, the amount is capped at $50 and the board must first formally adopt the fee and the fee amount by rule (and follow any required procedures to adopt a rule) and provide a copy to each owner.  See Utah Code Subsections 57-8-8.1 and 57-8a-201.   

An association has a lien on a unit or lot for late fees, as well.  See Utah Code Subsections 57-8-44(1)(a)(ii)(B) and 57-8a-301(1)(a)(ii)(B).