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 present value of the mortgage pass-through if, immediately after origination, interest rates increase to 8.25 percent per annum?
A)$15,000,000.
B)$14,650,591.
C)$14,000,000.
D)$15,115,493.
E)$15,267,549.

Question

Quizplus · Accepted Answer

Step 1: Calculate the monthly payment for each mortgage using the formula:

P = (r(PV))/(1-(1+r)^(-n))

where:
r = monthly interest rate = 8%/12 = 0.6667%
n = number of months = 30 years * 12 = 360
PV = present value = $150,000

Using the formula, we get:

P = (0.006667(150,000))/(1-(1+0.006667)^(-360)) = $1,101.94

Step 2: Calculate the total monthly payment for all 100 mortgages:

Total monthly payment = $1,101.94 * 100 = $110,194

Step 3: Calculate the present value of the pass-through security using the formula:

PV = Total monthly payment / (r + (r / ((1+r)^n - 1)))

where:
r = monthly interest rate = 8.25%/12 = 0.6875%
n = number of months = 30 years * 12 = 360

Using the formula, we get:

PV = $110,194 / (0.006875 + (0.006875 / ((1+0.006875)^360 - 1))) = $14,650,591

Therefore, the answer is B) $14,650,591.

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