The correct answer is B.

Step 1. Break the evaluation period into two periods based on timing of cashflows:
Holding period 1:
Begging price: $100
Dividend received: $3.0
Ending Price: $110

Holding period 2:
Begging price: $220 (2 shares)
Dividend received: $6.0 (2 shares)
Ending Price: $240 (2 shares)

Step 2. Calculate the holding period return, HPR, for each period:
Period 1: $\text{HPR} = \left[\frac{(110 + 3 - 100)}{100}\right] = 0.13$
Period 2: $\text{HPR} = \left[\frac{(240 + 6 - 220)}{220}\right] = 0.12$

Step 3. Calculate the total return for the entire period:
$\text{Total return} = 1.13 \times 1.12 = 1.2656$

Step 4. Compute the annualized time-weighted rate of return
$(1 + \text{annualized time-weighted rate of return})^2 = 1.2656$
$\text{annualized time-weighted rate of return} = 1.2656^{0.5} - 1 = 0.1249 - 1 = 0.1249$ or $12.49%$