What is the formula for calculating the effective annual rate (EAR)?

The formula for calculating the effective annual rate (EAR) is crucial for understanding how interest compounds over time, particularly when dealing with loans or investments that have different compounding periods.

The correct formula, as provided in the selected choice, incorporates the concept of compounding frequency. By taking the quoted interest rate and dividing it by the number of compounding periods per year (represented as "m"), this portion reflects the periodic interest rate. Raising this value to the power of "m" accounts for the effect of compounding throughout the year. Subtracting 1 at the end of the calculation provides the actual effective rate, as it removes the initial principal from the compounded amount.

This formula effectively allows one to determine what the actual interest earned or paid would be over a year, taking into account how often the interest is compounded, which is essential for accurate financial planning and decision-making. Understanding EAR helps investors and borrowers compare different financial products that may have varying rates and compounding schedules.