Answer: USD 7,000

## Explanation To calculate the expected principal prepayment for this month, we need to convert the annual conditional prepayment rate (CPR) to a monthly rate using the Single Monthly Mortality (SMM) formula: **Step 1: Convert CPR to SMM** \[ SMM = 1 - (1 - CPR)^{1/12} \] \[ SMM = 1 - (1 - 0.004)^{1/12} \] \[ SMM = 1 - (0.996)^{0.08333} \] \[ SMM ≈ 1 - 0.999666 \] \[ SMM ≈ 0.000334 \] **Step 2: Calculate monthly prepayment** \[ Monthly\ Prepayment = Current\ Balance × SMM \] \[ Monthly\ Prepayment = 20,000,000 × 0.000334 \] \[ Monthly\ Prepayment = 6,680 \] **Step 3: Compare to options** The calculated monthly prepayment of USD 6,680 is closest to **USD 7,000** (Option B). **Key Points:** - CPR is an annual rate that needs to be converted to monthly using SMM - The weighted average loan age of 60 months indicates seasoned loans - The 0.4% CPR is relatively low, suggesting moderate prepayment activity - The calculation assumes constant CPR throughout the year

Author: LeetQuiz .