The loan pool has a current balance of $400,000,000 of 30-year fixed rate mortgages. The weighted average coupon (WAC) rate is 5%. The weighted average life (WAL) of the mortgages in the pool is 310 months (so 50 months have elapsed). If the Conditional Prepayment Rate for the pool is 24% for the next month (month 1), what will be the total principal payment (scheduled plus prepayments) for that month?

Hints:

1. Calculate the mortgage payment for a mortgage balance of $400,000,000 and 310 months of payments, using the 5% annual interest rate.

2. Calculate the interest for the month on the $400,000,000 balance and subtract that from the total payment calculated in Step 1 to get the scheduled principal payment. Or, use the scheduled principal payment formula. If you use the scheduled principal payment formula, you have to use t = 1 and n = 310.

3. Calculate the SMM using the 24% CPR. You will need to go to 9 decimal places to get the correct answer.

4. Calculate the scheduled principal balance at time t=1. You can subtract the result from Step 2 from the $400,000,000 balance or use the appropriate formula.

5. Multiply the results of Step 4 by the results of Step 3. This will give you the monthly principal prepayments.

6. Add the scheduled principal payment to the prepayments. This is your answer. Round to the nearest dollar.