First, we calculate the unexpected loss (UL) of a single loan. The formula for the UL of an individual loan is: $UL_i = EA \times \sqrt{PD \times \sigma_{LR}^2 + LR^2 \times \sigma_{PD}^2}$

Given variables:

• EA = 3,000,000
• PD = 4% = 0.04
• LR = 15% = 0.15
• $\sigma_{LR}$ = 9% = 0.09
• The exact variance of the default event $\sigma_{PD}^2 = PD \times (1 - PD) = 0.04 \times 0.96 = 0.0384$. Note: The standard deviation is given as 19.6%, and $\sqrt{0.0384} \approx 0.19596 \approx 19.6\%$. Using the exact variance 0.0384 ensures calculation accuracy.

$UL_i = 3,000,000 \times \sqrt{0.04 \times 0.09^2 + 0.15^2 \times 0.0384}$ $UL_i = 3,000,000 \times \sqrt{0.04 \times 0.0081 + 0.0225 \times 0.0384}$ $UL_i = 3,000,000 \times \sqrt{0.000324 + 0.000864} = 3,000,000 \times \sqrt{0.001188}$ $UL_i = 3,000,000 \times 0.034467376 = 103,402.13$

For a large, homogeneous portfolio, the unexpected loss contribution (ULC) of a single loan is derived using the pairwise default correlation ($\rho$): $ULC_i = UL_i \times \sqrt{\rho}$

Given $\rho = 0.25$: $ULC_i = 103,402.13 \times \sqrt{0.25} = 103,402.13 \times 0.5 = 51,701.06$

This matches Option C exactly.