Suppose WAC for the underlying mortgage for a pass-through is 9%. The pass-through rate is 8% with a WAM of 360 months. The par value of the mortgage is $500 million. Assume that in month 30 the beginning balance is 337,568,221 and the total principal payment in month 30 is $2,793,137. The conditional prepayment rate in month 31 is 9.9%. Answer the following questions:

1. Compute the single-month mortality rate in month 31

2. Calculate mortgage payment for month 31

3. Calculate

i) scheduled principal payment in month 31,

ii) prepayment in month 31, and

iii) beginning balance in month 32.