Answer: 10.0%

The probability that the company will survive in the first year and then default before the end of the second year is calculated using the constant hazard rate model. The hazard rate, denoted by \( \lambda \), is given as 0.12 per year. The formula for the joint probability of survival up to time \( t \) and default over \( (t, t+T) \) is: \[ P[t^* > t \text{ and } t^* < t+T] = 1 - e^{-\lambda(t+T)} - (1 - e^{-\lambda t}) = e^{-\lambda t}(1 - e^{-\lambda T}) \] Applying this formula to the scenario where the company is expected to survive the first year and default in the second year, we set \( t = 1 \) and \( T = 1 \) (since we are considering the period from the end of the first year to the end of the second year). Plugging in the values, we get: \[ P[1 < t^* < 2] = e^{-0.12 \cdot 1}(1 - e^{-0.12 \cdot 1}) \] \[ P[1 < t^* < 2] = e^{-0.12}(1 - e^{-0.12}) \] \[ P[1 < t^* < 2] \approx 10.03\% \] This calculation results in a probability of approximately 10.03%, which corresponds to option B (10.0%). This is the correct answer, as the calculated probability is very close to the given option B, and it is the closest to the calculated value among the provided options.

Author: LeetQuiz Editorial Team