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. For the first monthly payment, what portion is principal and what portion is interest?
A)$100,000 principal and $10,065 interest.
B)$12,000 interest and no principal.
C)$100,000 interest and no principal.
D)$100,000 interest and $10,065 principal.
E)$10,000 interest and $2,000 principal.

Question

Quizplus · Accepted Answer

To calculate the first monthly payment, we need to find the monthly interest rate and the total number of payments.

Monthly interest rate = (8% / 12) = 0.00667
Total number of payments = 30 years x 12 months/year = 360 months

Using the formula for a fully amortized loan, we can calculate the monthly payment as follows:

Monthly payment = P x (r(1+r)^n) / ((1+r)^n - 1)
where P = principal, r = monthly interest rate, and n = total number of payments

Plugging in the numbers, we get:

Monthly payment = $150,000 x (0.00667(1+0.00667)^360) / ((1+0.00667)^360 - 1) = $1,102.64

Now we need to determine the portion of the payment that goes towards principal and the portion that goes towards interest.

The interest portion of the payment is simply the monthly interest rate times the remaining balance on the loan. For the first payment, the remaining balance is equal to the original principal, since no payments have been made yet.

Interest portion = 0.00667 x $150,000 = $1,000.50

The principal portion is the difference between the monthly payment and the interest portion.

Principal portion = $1,102.64 - $1,000.50 = $102.14

Since there are 100 identical mortgages in the pool, the total interest portion of the first payment is:

Total interest = 100 x $1,000.50 = $100,050

And the total principal portion is:

Total principal = 100 x $102.14 = $10,214

Therefore, the answer is D: $100,000 interest and $10,065 principal.

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