An investor can choose between an interest rate of 10.5% per annum compounded monthly and 11% per annum compounded annually for a two year investment. Other things being equal, which option is financially better for the investor?

Introduction / Context:
This question asks you to compare two investment choices with different nominal interest rates and different compounding frequencies over a fixed period of two years. It tests understanding of effective interest rates and how compounding frequency affects the overall return, even when nominal rates are close in value.

Given Data / Assumptions:

• Option 1: 10.5% per annum, compounded monthly.
• Option 2: 11% per annum, compounded annually.
• Investment horizon: two years.
• The same principal amount is invested under either option, and there are no additional deposits or withdrawals.

Concept / Approach:
To compare the options, we need to compute the effective growth factor over two years for each choice. For a nominal rate j with m compounding periods per year, the periodic rate is j / m, and the effective annual growth factor is (1 + j / m)^m. Over two years, we raise the annual growth factor to the power of 2. The option that gives a larger final multiplier on the principal is better, regardless of the actual principal value, because the same principal would be scaled by that factor in both cases.

Step-by-Step Solution:
Step 1: For Option 1, nominal rate j1 = 0.105 and m1 = 12, so periodic rate i1 = 0.105 / 12.Step 2: The effective annual factor for Option 1 is (1 + i1)^12.Step 3: Over two years, the total growth factor for Option 1 is (1 + i1)^(24).Step 4: For Option 2, the annual factor is simply (1 + 0.11), because interest is compounded once per year.Step 5: Over two years, the growth factor for Option 2 is (1.11)^2.Step 6: Numerical calculation shows that (1 + 0.105 / 12)^(24) is slightly greater than (1.11)^2, so Option 1 yields a slightly higher amount.

Verification / Alternative check:
As a quick mental check, compute the approximate effective annual rate for the monthly compounding option. The effective annual rate is (1 + 0.105 / 12)^12 minus 1, which is slightly above 11% per year. Since Option 2 offers exactly 11% effective per year, the first option with monthly compounding must be marginally better. Over two years, this small difference in annual effectiveness produces a slightly higher final amount for Option 1.

Why Other Options Are Wrong:

• 11% compounded annually is better: This is not correct, because the monthly compounding at 10.5% produces an effective annual rate that slightly exceeds 11%.
• Both options give exactly the same total return: The effective rates are very close but not identical, so the returns are not exactly equal.
• It is impossible to compare without knowing the principal amount: The principal cancels out in a ratio comparison, so any principal value leads to the same conclusion about which multiplier is larger.

Common Pitfalls:
Many students look only at the nominal rates and conclude that 11% must be better than 10.5% without considering compounding frequency. Others use the nominal rates directly in calculations without dividing by the number of compounding periods or they compare only one-year returns when the question specifies a two year horizon. It is essential to convert nominal rates into effective growth factors over the exact period of interest before making a comparison.

Final Answer:
The investor should prefer the first option, because 10.5% compounded monthly is better, but only slightly better than 11% compounded annually over the two year period.