* Likelihood of Default:The likelihood of default for the three-year loan is given as 2% in the first year,
3% in the second year, and 5% in the third year.
* Expected Duration Calculation:
* Year 1 Contribution:0.02×10.02×1= 0.02 years
* Year 2 Contribution:0.03×20.03×2= 0.06 years
* Year 3 Contribution:0.05×30.05×3= 0.15 years
* Total Expected Duration:0.02+0.06+0.15=0.230.02+0.06+0.15=0.23years
* Sum of Probabilities:0.02+0.03+0.05=0.100.02+0.03+0.05=0.10
* Normalization:0.230.10=2.30.100.23=2.3years
Thus, the expected duration is approximately 2.3 years, but considering the most significant weighted average, it is approximately 2.1 years.