Answer: USD 7,000

## 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.

Author: LeetQuiz .