Explanation

To calculate the total return over multiple periods, we need to use the geometric mean (compounded return) rather than simply adding the annual returns.

Step-by-step calculation:

1. Convert percentage returns to decimal growth factors:

   • Year 1: 5% = 1 + 0.05 = 1.05
   • Year 2: 3% = 1 + 0.03 = 1.03
   • Year 3: 12% = 1 + 0.12 = 1.12

2. Calculate the cumulative growth factor:

   $$1.05 \times 1.03 \times 1.12 = 1.21128$$

3. Convert back to total percentage return:

   $$(1.21128 - 1) \times 100\% = 21.128\%$$

4. Compare with options:

   • 21.128% is closest to 21% (Option C)

Why not simply add the returns? If we simply added 5% + 3% + 12% = 20%, this would be incorrect because it ignores the compounding effect. Each year's return is applied to the accumulated value from previous years, not just the initial investment.

Verification:

• Starting with $100:
  • After Year 1: $100 × 1.05 = $105
  • After Year 2: $105 × 1.03 = $108.15
  • After Year 3: $108.15 × 1.12 = $121.128
• Total return: ($121.128 - $100)/$100 = 21.128%

Therefore, the correct answer is C. 21%.