Calculate the periodic interest rate (per quarter) corresponding to a nominal annual rate of 9.0% compounded quarterly.

Introduction / Context: This conceptual question checks whether you can convert a nominal annual interest rate with a specified compounding frequency into a periodic rate. Such conversions are common when working with loans, investments, and annuities.

Given Data / Assumptions:

• Nominal annual interest rate = 9.0% per year.
• Compounding frequency = quarterly (4 times per year).
• We need the interest rate per quarter.

Concept / Approach: When a nominal annual rate r_nom is compounded m times per year, the periodic rate i is: i = r_nom / m Where r_nom is expressed as a percentage or as a decimal consistently. Here quarterly compounding means m = 4.

Step-by-Step Solution: Step 1: Take the nominal rate r_nom = 9.0%. Step 2: Determine the number of compounding periods per year, m = 4. Step 3: Compute i = 9.0% / 4. Step 4: i = 2.25% per quarter. Therefore the periodic interest rate that applies each quarter is 2.25%.

Verification / Alternative Check: You can verify by multiplying the periodic rate by the number of periods: 2.25% * 4 = 9.0%, which matches the original nominal annual rate. This confirms the calculation is consistent.

Why Other Options Are Wrong: Option A (3.45% per quarter) and option C (5.25% per quarter) would produce effective annual rates much higher than 9% when compounded. Option D (6.25% per quarter) is even larger and clearly inconsistent.
Option E (1.25% per quarter) is too small because four such periods would only yield a nominal rate of 5% per year.

Common Pitfalls: Learners sometimes confuse nominal and effective rates and attempt to use exponentiation when only a simple division is required. Another error is misreading quarterly as meaning every four years rather than four times a year.

Final Answer: The periodic interest rate is 2.25% per quarter.