One hundred identical mortgages are pooled together into a pass-through security. Each mortgage has a $150,000 principal, a fixed annual interest rate of 8 percent (paid monthly), and is fully amortized over a term of 30 years.
-What is the weighted average life of the above mortgage pool?
A)30 years.
B)2 months.
C)1.998 months.
D)1 month.
E)1.5 months.

Question

Quizplus · Accepted Answer

The weight of each mortgage is equal since they are identical. Therefore, the weighted term-to-maturity is the same as the weighted average life. Using the formula for the weighted average life, we have:

Weighted average life = [($150,000 x 12) / ($150,000 x 12 x 0.08)] x [1 - (1 / (1 + 0.08/12)^360)] = 199.8 months = 1.998 months.

One Hundred Identical Mortgages Are Pooled Together into a Pass-Through