Unpaid Assessments.  The interest rate for late payments of assessments is usually set by the CC&Rs (or bylaws), but if there is no such provision in the CC&Rs, the interest rate can be set by rule.  Finally, if the governing documents do not authorize the association to charge interest, Utah law says unpaid assessments and fines accrue interest at the rate set in Utah Code Section 15-1-1(2), which is 10% per annum.

If interest is imposed merely by a rule and not by the CC&Rs, the amount is capped at 1.5% per month (18% per annum) 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. 

If the CC&Rs set an interest rate, a board may not simply pick a different interest rate out of thin air.  So, if the CC&Rs say the interest rate is 12% per annum, the interest that is charged to owners must be 12%, or possibly lower but it cannot be higher.

Contracts.  For a contract between the HOA and third parties, if the contract doesn't specify an interest rate, the law allows interest to be charged at the rate of 10% per annum.  The law applies to "any lawful written, verbal, or implied contract, including a contract for services, a loan or forbearance of any money, goods, or a claim for breach of contract."  Utah Code Section 15-1-1 (link below).

No Time Period Stated?  Whenever an interest rate is mentioned in any law or contract (including CC&Rs) and no period of time is stated, such as "per annum" (per year) or "monthly," the rate is per year.  So, if CC&Rs simply said "interest accrues at the rate of 12%," then interest accrues at 12% per year.  Utah Code Section 15-1-3 (link below).