The Unexpected Loss (UL) of a single credit exposure is calculated using the formula: $UL = EA \times \sqrt{PD \times \sigma_{LGD}^2 + LGD^2 \times \sigma_{PD}^2}$

Where:

• Exposure Amount ($EA$) = \`50.0` \text{ million}$
• Probability of Default ($PD$) = $2.0% = 0.02$
• Loss Given Default ($LGD$ or $LR$) = $50.0% = 0.50$
• Standard deviation of LGD ($\sigma_{LGD}$) = $40.0% = 0.40$
• Since default is a Bernoulli variable, the variance of PD ($\sigma_{PD}^2$) is $PD \times (1 - PD) = 0.02 \times (1 - 0.02) = 0.0196$.

Plugging the numbers into the formula: UL = \`50.0 \times \sqrt{0.02 \times 0.40^2 + 0.50^2 \times 0.0196}$ $UL = \$50.0` \times \sqrt{0.02 \times 0.16 + 0.25 \times 0.0196}$ UL = \`50.0 \times \sqrt{0.0032 + 0.0049}$ $UL = \$50.0` \times \sqrt{0.0081}$ UL = \`50.0 \times 0.09 = \$4.50` \text{ million}$

The nearest value is $4.50 million (Option C).