Calculation Explanation

To calculate the expected principal prepayment for this month:

Given:

• Current balance = USD 20,000,000
• Conditional Prepayment Rate (CPR) = 0.4% per year
• Need monthly prepayment

Step 1: Convert annual CPR to monthly prepayment rate The Single Monthly Mortality (SMM) rate can be calculated from CPR using: $\text{SMM} = 1 - (1 - \text{CPR})^{1/12}$ $\text{SMM} = 1 - (1 - 0.004)^{1/12}$ $\text{SMM} = 1 - (0.996)^{0.08333}$ $\text{SMM} ≈ 1 - 0.999667$ $\text{SMM} ≈ 0.000333$

Step 2: Calculate monthly prepayment $\text{Monthly Prepayment} = \text{Current Balance} × \text{SMM}$ $\text{Monthly Prepayment} = 20,000,000 × 0.000333$ $\text{Monthly Prepayment} = 6,660$

Step 3: Compare to options The calculated amount of USD 6,660 is closest to USD 7,000 (Option B).

Note: A simpler approximation would be to divide the annual prepayment by 12: $\text{Annual Prepayment} = 20,000,000 × 0.004 = 80,000$ $\text{Monthly Prepayment} ≈ 80,000 ÷ 12 = 6,667$ This also gives approximately USD 6,667, confirming that Option B (USD 7,000) is the closest.