For a nominal annual interest rate of 8.4% per annum, the periodic interest rate is 8.4% per period. What is the compounding frequency per year (that is, how many times per year is interest compounded)?

Introduction / Context:
This question examines the simple but important case where the periodic interest rate is equal to the nominal annual interest rate. It tests whether you understand what that implies about the number of compounding periods per year and the meaning of annual compounding.

Given Data / Assumptions:

• Nominal annual interest rate r_nom = 8.4% per annum.
• Periodic interest rate r_per = 8.4% per period.
• The nominal rate is spread evenly across m compounding periods per year.
• We assume standard financial interpretation of nominal and periodic rates.

Concept / Approach:
The core relationship is r_nom = m * r_per, where m is the compounding frequency per year. If the periodic rate equals the nominal rate, then the only way the equality can hold is when there is exactly one compounding period per year. This case describes annual compounding, where interest is added once per year at the full nominal rate.

Step-by-Step Solution:
Step 1: Nominal annual rate r_nom = 8.4%.Step 2: Periodic rate r_per = 8.4% per period.Step 3: Use the formula r_nom = m * r_per.Step 4: Substitute values: 8.4 = m * 8.4.Step 5: Divide both sides by 8.4 to get m = 1.Step 6: Therefore, the interest is compounded once per year, which is annual compounding.

Verification / Alternative check:
To verify, think about what happens in practice. If an investment promises 8.4% per year compounded annually, the full 8.4% is applied once at the end of the year. This exactly matches the idea of a periodic rate of 8.4% per year with only one period, so the calculation is consistent and intuitive.

Why Other Options Are Wrong:

• 2: If m were 2, then the nominal rate would be 2 * 8.4% = 16.8%, which is not the given 8.4%.
• 3: If m were 3, then the nominal rate would be 3 * 8.4% = 25.2%, far larger than 8.4%.
• 4: If m were 4, then the nominal rate would be 4 * 8.4% = 33.6%, again not equal to 8.4%.

Common Pitfalls:
Students sometimes misinterpret the phrase compounded annually and think there might still be more than one compounding period inside a year. In fact, annual compounding means exactly one compounding period per year. Another error is to mix up nominal and effective rates. In this question, the word nominal is present, but the mathematics relies only on the nominal and periodic rates being equal, which forces the compounding frequency to be one.

Final Answer:
The compounding frequency is 1 time per year, which corresponds to annual compounding.