Difficulty: Easy
Correct Answer: 10% per annum
Explanation:
Introduction / Context:
This question reverses the usual nominal to periodic conversion. You are given the periodic monthly rate and must find the corresponding nominal annual rate, assuming the same compounding frequency used for quoting the APR.
Given Data / Assumptions:
Concept / Approach:
Nominal annual rate r_nom is obtained by multiplying the periodic rate by the number of periods per year:
r_nom = i * m where m = 12 for monthly compounding. Here we are not asked for the effective annual rate, only the nominal rate.
Step-by-Step Solution:
Step 1: Take the periodic rate i = 0.83% per month. Step 2: Determine the number of months per year, m = 12. Step 3: Compute r_nom = 0.83% * 12. Step 4: r_nom = 9.96% per annum, which is usually rounded to 10% per annum. So the nominal annual rate is approximately 10% when quoted to the nearest whole percent.
Verification / Alternative Check:
If the nominal rate is 10% compounded monthly, the periodic rate is 10% / 12 ≈ 0.83% per month, which matches the given periodic rate. This confirms that the two descriptions are equivalent.
Why Other Options Are Wrong:
A 7%, 8%, or 9% annual nominal rate corresponds to monthly rates lower than 0.83%.
An 11% annual nominal rate would give a monthly rate of about 0.9167%, which is higher than 0.83%.
Only 10% per annum matches the monthly rate of 0.83% given in the question.
Common Pitfalls:
Students sometimes divide instead of multiply, mistakenly calculating 0.83% / 12, which would give a tiny rate. Others confuse nominal rate with effective annual rate and try to use exponentiation unnecessarily. For nominal rates, simple multiplication by the number of periods is the correct approach.
Final Answer:
The nominal annual interest rate is approximately 10% per annum.
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