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.

Question

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?

What is the weighted average life of the above mortgage pool?
A)30 years.
B)2 months.
C)1.998 months.
D)1 month.

Quizplus · Accepted Answer

The weighted average life of a mortgage pool is calculated by taking the sum of the products of the outstanding principal balance of each mortgage and its remaining term to maturity and dividing by the total outstanding principal balance of the pool. In this case, all the mortgages have the same principal and term, so the calculation simplifies to the average remaining term to maturity. The formula for calculating the remaining term for a fully amortizing mortgage is:

Remaining Term = -log(1-(interest rate/12)*outstanding principal)/(12*log(1+interest rate/12))

Plugging in the values for a $150,000 mortgage at 8% annual interest paid monthly, the remaining term is approximately 358 months. Therefore, the weighted average life of the pool is 358/12, or 29.83 months, which rounds to 1.998 months (Option C).

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