The interest rate for late payments of assessments is set by the CC&Rs (or bylaws). If the CC&Rs do not mention interest on late payments, the law allows interest to be charged at the rate of 10% per annum, as long as the CC&Rs were recorded after May 13, 1981. See Utah Code Section 15-1-1. For CC&Rs recorded before that, the law does not allow for interest other than what the CC&Rs say.
A board may not simply pick an interest rate out of thin air. If the CC&Rs say the interest rate is 12% per annum, the interest that is charged to owners must be 12% or lower, it cannot be higher. If the CC&Rs do not mention charging interest, the interest that is charged to owners must be 10% or lower, it cannot be higher.
For 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).
(For reference: 57-8 is the Condo Act, 57-8a is the Community Association Act, 16-6a is the Nonprofit Act)