An investor can choose between 10.5% interest compounded monthly and 11% interest compounded annually for a two year investment. Assuming all other factors are equal, which option should the investor prefer?

Introduction / Context:
This conceptual question compares two different interest structures. The nominal rates are close, but the compounding frequency differs. The key idea is that more frequent compounding can sometimes offset a slightly lower nominal rate, resulting in a higher effective return over the investment period.

Given Data / Assumptions:

• Option 1: 10.5% nominal annual rate, compounded monthly.
• Option 2: 11% nominal annual rate, compounded annually.
• Investment horizon = 2 years.
• Principal is the same in both options.

Concept / Approach:
We compare effective growth factors for each option over 2 years. For monthly compounding, the periodic rate is the nominal rate divided by 12, and the number of periods is 24. For annual compounding, the periodic rate equals the nominal rate, and the number of periods is 2.
Option 1 factor = (1 + 0.105 / 12)^(12 * 2) Option 2 factor = (1 + 0.11)^2

Step-by-Step Solution:
Step 1: Compute the monthly rate for option 1: 0.105 / 12 ≈ 0.00875. Step 2: Compute the 2 year factor for option 1: (1 + 0.00875)^24 ≈ 1.23255. Step 3: Compute the 2 year factor for option 2: (1 + 0.11)^2 = 1.11^2 ≈ 1.23210. Step 4: Compare 1.23255 with 1.23210. Since 1.23255 is slightly greater than 1.23210, option 1 yields a higher final amount.

Verification / Alternative Check:
If you invest 1,000 units of currency, option 1 gives about 1,232.55 after 2 years, while option 2 gives about 1,232.10. The difference is small but real and shows the advantage of more frequent compounding at a slightly lower nominal rate.

Why Other Options Are Wrong:
Option B is wrong because 11% annually does not quite catch up to the benefit of monthly compounding at 10.5%.
Option C is incorrect because the two future values are close but not equal.
Option D is wrong because sufficient numerical information is given to compute both growth factors.
Option E is clearly false, since both options explicitly describe compound interest structures.

Common Pitfalls:
Students often compare only the nominal rates and assume 11% is better without considering compounding frequency. Others may incorrectly treat monthly compounding as if it were annual by ignoring the division by 12 or by using simple interest formulas. Effective comparisons must always use the correct compounding periods.

Final Answer:
The investor should prefer 10.5% compounded monthly, as it produces a slightly higher return over two years.