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