Answer: 53.47%

## Explanation To calculate the Conditional Prepayment Rate (CPR), we need to determine the prepayment amount and then annualize it. **Step 1: Calculate total principal payment** - Beginning balance: $10,500,000 - Ending balance: $9,800,000 - Total principal reduction = $10,500,000 - $9,800,000 = $700,000 **Step 2: Calculate prepayment amount** - Scheduled principal payment: $54,800 - Prepayment = Total principal reduction - Scheduled principal payment - Prepayment = $700,000 - $54,800 = $645,200 **Step 3: Calculate Single Monthly Mortality (SMM)** - SMM = Prepayment / (Beginning balance - Scheduled principal payment) - SMM = $645,200 / ($10,500,000 - $54,800) - SMM = $645,200 / $10,445,200 ≈ 0.0618 or 6.18% **Step 4: Convert SMM to CPR** - CPR = 1 - (1 - SMM)^12 - CPR = 1 - (1 - 0.0618)^12 - CPR = 1 - (0.9382)^12 - CPR = 1 - 0.4653 ≈ 0.5347 or 53.47% Therefore, the CPR for this month is **53.47%**, which corresponds to option C.

Author: LeetQuiz .