The periodic interest rate on an investment is 0.83% per month. Assuming this is a nominal rate quoted monthly, determine the corresponding nominal annual rate of interest (in percent per annum).

Introduction / Context:
This problem focuses on converting a periodic monthly interest rate into a nominal annual interest rate. Such conversions are very common when comparing financial products, because banks and investment firms often quote either monthly or annual rates, and you must be able to interpret one in terms of the other.

Given Data / Assumptions:

• Periodic interest rate r_per = 0.83% per month.
• Compounding frequency per year m = 12 months.
• The nominal annual rate is defined as r_nom = m * r_per.
• We are asked to find the nominal annual rate r_nom in percent per annum.

Concept / Approach:
The nominal annual interest rate is obtained by multiplying the periodic monthly rate by the number of periods per year. This nominal rate does not itself describe compounding but is a simple linear scaling of the monthly rate. The formula used is r_nom = m * r_per, where r_per is in percent per month and m is 12 for monthly compounding over one year.

Step-by-Step Solution:
Step 1: Note the monthly periodic rate r_per = 0.83%.Step 2: The number of months in a year is m = 12.Step 3: Use the formula r_nom = m * r_per.Step 4: Compute r_nom = 12 * 0.83%.Step 5: 12 * 0.83 = 9.96.Step 6: Therefore, the nominal annual rate is approximately 9.96% per annum, which rounds to 10% per annum.

Verification / Alternative check:
This is mainly a linear scaling, so for a quick check, approximate 0.83 as a little less than 0.84. Then 12 * 0.84 = 10.08%, which is very close to 10%. Since our exact result was 9.96%, it makes sense to round to the nearest whole percent, which is exactly 10%. Therefore, the answer 10% is reasonable and matches the available options.

Why Other Options Are Wrong:

• 7%: This would imply a monthly rate of about 0.58%, not 0.83%.
• 8%: This corresponds to approximately 0.67% per month, which is lower than the given monthly rate.
• 9%: This would imply a monthly rate of 0.75%, still below 0.83% per month.

Common Pitfalls:
Students sometimes treat 0.83% as a decimal 0.83 instead of converting to 0.83 percent properly, which leads to huge errors. Others mistakenly apply compound interest formulas and raise numbers to powers of 12, which is not required when the question asks specifically for the nominal annual rate. It is also common to forget that 12 months make one year and to use an incorrect number of periods, such as 10 or 6, leading to wrong annual rates.

Final Answer:
The nominal annual rate corresponding to a periodic rate of 0.83% per month is approximately 10% per annum.