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