What is the compounding frequency for an effective interest rate of 4.55% for an $82,000 loan?

To determine the compounding frequency for an effective interest rate of 4.55% on an $82,000 loan, it's essential to recognize how effective interest rates relate to the nominal interest rate and compounding frequency. The effective interest rate reflects the actual cost of borrowing, taking into account how often interest is compounded.

When a loan has a semi-annual compounding frequency, the nominal interest rate is divided by two to reflect the two compounding periods in a year. This typically results in a lower effective interest rate compared to monthly compounding, since interest is calculated and added to the principal less frequently.

In this scenario, an effective interest rate of 4.55% suggests that the frequency of compounding is less frequent than monthly or quarterly, as those would typically produce a higher effective rate given the same nominal rate. Therefore, semi-annual compounding is a likely fit because it typically results in a closer effective rate approximation, such as 4.55%.

The semi-annual compounding frequency is, therefore, the correct choice because it aligns with the expected effective interest rate under typical market conditions, reflecting the practice commonly observed in mortgage calculations.