A nominal annual interest rate of 9.5% is compounded monthly. What is the corresponding periodic interest rate per month, expressed as a percentage rounded to four decimal places?

Introduction / Context:
This question checks understanding of the relationship between a nominal annual interest rate and the corresponding periodic interest rate when interest is compounded more than once per year. Being able to convert between nominal and periodic rates is very important in topics like compound interest, loans, and investments, because most formulas use the periodic rate, not the nominal annual figure.

Given Data / Assumptions:

• Nominal annual interest rate = 9.5% per annum.
• Compounding frequency = monthly.
• Number of compounding periods in one year, m = 12.
• We assume standard financial convention where the nominal rate is divided equally among all periods.

Concept / Approach:
The periodic interest rate is the rate applied each compounding period. For a nominal annual rate r_nom with m compounding periods per year, the periodic rate r_per is calculated using the simple relationship:
r_per = r_nom / m.
Here r_nom is 9.5% and m is 12, so we divide 9.5 by 12 and then round the result to four decimal places. The answer should be expressed as a percentage per month.

Step-by-Step Solution:
Step 1: Write the nominal annual rate as r_nom = 9.5%.Step 2: Identify the compounding frequency per year as m = 12 for monthly compounding.Step 3: Use the formula r_per = r_nom / m.Step 4: Compute r_per = 9.5 / 12.Step 5: 9.5 / 12 = 0.791666..., which is approximately 0.7916 when rounded to four decimal places.Step 6: Attach the percent sign to express the answer as 0.7916% per month.

Verification / Alternative check:
As a quick check, multiply the periodic rate back by 12. That is 0.791666... * 12 which gives 9.5% again. This confirms that the periodic rate is consistent with the original nominal annual rate. Any large deviation from 9.5% when multiplying back would indicate a calculation error, such as dividing by the wrong number of periods or misplacing the decimal point.

Why Other Options Are Wrong:

• 0.8916%: This would correspond to a nominal rate of about 10.7% if multiplied by 12, which is higher than the given 9.5%.
• 0.9916%: Multiplying by 12 gives almost 11.9%, which is far from 9.5%, so it does not match the given nominal rate.
• 0.6916%: Multiplying by 12 gives about 8.3%, which is lower than the required 9.5% nominal rate.

Common Pitfalls:
Students often confuse effective rates with nominal rates and sometimes try to use complex formulas unnecessarily. Here, the question only asks for the periodic rate for a nominal rate with simple equal division among periods. Another common mistake is to forget to convert the result into percentage form or to round incorrectly. Some learners also divide by the wrong number of periods, for example by 4 for quarterly compounding even though the question clearly states monthly compounding, which uses 12 periods per year.

Final Answer:
The periodic interest rate corresponding to a nominal annual rate of 9.5% compounded monthly is 0.7916% per month.