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.

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 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.

Quizplus · Accepted Answer

The first step is to calculate the monthly mortgage payments. We can use the PMT function in Excel or a financial calculator. The monthly payment for each mortgage is $1,099.59.

Next, we calculate the total monthly payment for the pool of mortgages, which is 100 multiplied by the monthly payment of $1,099.59, or $109,958.80.

To calculate the present value, we need to discount the future cash flows (monthly payments) at the new interest rate of 8.25%, which is equivalent to a monthly rate of 0.006875%. We can use the PV function in Excel or a financial calculator to calculate the present value.

The present value of the monthly cash flows is $14,650,590.57, which is the answer (option B).

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