The Cox-Ingersoll-Ross (CIR) model is defined by the following stochastic differential equation: $dr = k(\theta - r)dt + \sigma\sqrt{r}dw$

Given the variables:

• Time-step ($dt$) = $1/12$
• Initial rate ($r(0)$) = $2.11% = 0.0211$
• Volatility ($\sigma$) = $3.17% = 0.0317$
• Long-run rate ($\theta$) = $7.64% = 0.0764$
• Strength of reversion ($k$) = $0.57$
• Change in Wiener process ($dw$) = $0.160$

First, calculate the drift component (mean-reversion): $k(\theta - r(0))dt = 0.57 \times (0.0764 - 0.0211) \times (1/12)$ $= 0.57 \times 0.0553 \times 0.08333$ $\approx 0.002627$

Next, calculate the stochastic component (volatility): $\sigma\sqrt{r(0)}dw = 0.0317 \times \sqrt{0.0211} \times 0.160$ $= 0.0317 \times 0.145258 \times 0.160$ $\approx 0.000737$

The change in the short rate for the first month ($dr$) is: $dr = 0.002627 + 0.000737 = 0.003364$

Finally, the short-rate in the first month is: $r(1/12) = r(0) + dr = 0.0211 + 0.003364 = 0.024464$ or $2.446%$

Therefore, choice C is the correct answer.