Answer: USD 16,045

## Explanation To calculate the expected principal prepayment this month, we need to convert the annual Conditional Prepayment Rate (CPR) to a Single Monthly Mortality (SMM) rate, then apply it to the current balance. **Step 1: Convert CPR to SMM** The relationship between CPR and SMM is: \[ \text{CPR} = 1 - (1 - \text{SMM})^{12} \] Rearranging to solve for SMM: \[ \text{SMM} = 1 - (1 - \text{CPR})^{1/12} \] Given CPR = 0.6% = 0.006: \[ \text{SMM} = 1 - (1 - 0.006)^{1/12} \] \[ \text{SMM} = 1 - (0.994)^{1/12} \] \[ \text{SMM} = 1 - 0.9994986 \] \[ \text{SMM} = 0.0005014 = 0.05014\% \] **Step 2: Calculate expected principal prepayment** \[ \text{Expected Prepayment} = \text{Current Balance} \times \text{SMM} \] \[ \text{Expected Prepayment} = 32,000,000 \times 0.0005014 \] \[ \text{Expected Prepayment} = \text{USD 16,044.80} \] This rounds to USD 16,045, which matches option D. **Why other options are incorrect:** - **A (USD 3,210)**: Uses incorrect formula SMM = 1 - (1 - CPR)^(1/60) - **B (USD 9,600)**: Incorrectly computes 5% of annual coupon payment - **C (USD 16,000)**: Uses simple monthly rate CPR/12 = 0.6%/12 = 0.05% instead of proper SMM conversion

Author: LeetQuiz .