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 weighted average life of a mortgage pool is the time it takes for half of the principal of the mortgages to be paid back.

First, calculate the monthly payment for each mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]
M = 150000 [ 0.08/12(1 + 0.08/12)^360 ] / [ (1 + 0.08/12)^360 – 1]
M = $1,102.64

Next, calculate the total monthly payment for the pool of 100 mortgages:
100 * $1,102.64 = $110,264

To find the weighted average life, calculate the amount of time it takes for half of the principal to be repaid:

Half of the principal = 100 * $150,000 / 2 = $7,500,000

Using the formula for the present value of an annuity, we can find out how many payments it will take to repay $7,500,000 at $110,264 per payment:

n = -log(1 - (PV/PMT)) / log(1 + i)
n = -log(1 - (7500000/110264)) / log(1 + 0.08/12)
n = 238.9722 months

Therefore, the weighted average life of the mortgage pool is approximately 238.9722/12 = 19.9143 years, or 1.998 months.

The correct answer is C, 1.998 months.

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