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.