Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security.The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum.

If the entire mortgage pool is repaid at the end of the second month,what is the weighted average life of the mortgage pool?
A)2.10 months.
B)2 months.
C)1.997 months.
D)1.95 months.

Question

Overseas bank is pooling 50 similar and fully amortized mortgages into a pass-through security.The face value of each mortgage is $100,000 paying 180 monthly interest and principal payments at a fixed rate of 9 percent per annum.

If the entire mortgage pool is repaid at the end of the second month,what is the weighted average life of the mortgage pool?

If the entire mortgage pool is repaid at the end of the second month,what is the weighted average life of the mortgage pool?
A)2.10 months.
B)2 months.
C)1.997 months.
D)1.95 months.

Quizplus · Accepted Answer

The total cash flow from the mortgage pool is calculated as follows:

Total cash flow = $100,000 x 50 x 2 = $10,000,000

Since the entire mortgage pool is repaid at the end of the second month, the weighted average life of the mortgages can be calculated using the formula:

Weighted average life = (Σ(Pn x tn))/Σ(Pn)

where Pn is the outstanding principal balance at the end of month n, and tn is the time elapsed since the beginning of the pool.

At the end of the second month, the outstanding principal balance for each mortgage is:

PV = $100,000 / (1 + 0.09/12)^180 = $31,505.53

Therefore, the total outstanding principal balance for the pool is:

Total outstanding principal = $31,505.53 x 50 = $1,575,276.50

The weighted average life of the mortgage pool is then:

Weighted average life = [(1 x $1,575,276.50) + (2 x $8,424,723.50)] / $10,000,000 = 1.997 months

Therefore, the best answer is C, 1.997 months.

Overseas Bank Is Pooling 50 Similar and Fully Amortized Mortgages