The interest rate at the lowest node after 2 months, based on the Ho-Lee model, is calculated using the formula:

$r_0 + \left(\frac{a_1 + a_2}{2}\right)dt - \frac{\sigma^2}{2}dt$

where:

• $r_0$ is the current annualized short-term rate (3.2% or 0.032 in decimal form),
• $a_1$ is the annualized drift for the first month (0.8% or 0.008 in decimal form),
• $a_2$ is the annualized drift for the second month (1.2% or 0.012 in decimal form),
• $dt$ is the time step (1 month or 1/12 of a year in this case),
• $\sigma$ is the annual basis point-volatility (2.1% or 0.021 in decimal form).

Plugging in the values, we get:

$0.032 + \left(\frac{0.008 + 0.012}{2}\right)(\frac{1}{12}) - \frac{0.021^2}{2}(\frac{1}{12})$

$= 0.032 + (0.01)(\frac{1}{12}) - (0.000441)(\frac{1}{12})$

$= 0.032 + 0.000833 - 0.0000367$

$= 0.032 + 0.000796$

$= 0.032796$

Converting this back to a percentage, we get 3.2796%, which is approximately 3.28%. However, since the options provided are 1.82%, 2.15%, 2.76%, and 3.03%, and none of these match our calculated value, it seems there might be a mistake in the provided options or in the calculation process described in the file content.

The provided explanation in the file content uses an incorrect formula and calculation method, which leads to the incorrect answer of 2.15% (Option B). The correct formula and calculation process should yield a different result, as shown above.