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. For the first monthly payment, what are the interest and principal portions of the payment?
A)$37,500 principal and $13,213 principal.
B)$37,500 interest and $13,213 principal.
C)$37,500 principal and $7,809 interest.
D)$37,500 interest and $7,809 principal.
E)$37,500 interest and $17,756 principal.

Question

Quizplus · Accepted Answer

The monthly interest rate is (9% per annum)/12 = 0.75%. 
The monthly payment for each mortgage is calculated using the formula for a fully amortizing loan: 
Monthly Payment = PV x r(1+r)^n / ((1+r)^n - 1) 
where PV = present value of the loan = face value = $100,000, r = monthly interest rate = 0.75%, and n = number of monthly payments = 180. 
Plugging in these values, we get: 
Monthly Payment = $100,000 x 0.0075(1+0.0075)^180 / ((1+0.0075)^180 - 1) = $871.96

Since this is the first monthly payment, the interest portion is simply the monthly interest rate times the initial balance of $100,000: 
Interest Portion = $100,000 x 0.0075 = $750

The remaining amount of the monthly payment goes towards principal repayment: 
Principal Portion = Monthly Payment - Interest Portion = $871.96 - $750 = $121.96

Therefore, for each mortgage, the first monthly payment consists of an interest portion of $750 and a principal portion of $121.96. When pooling 50 mortgages together into a pass-through security, the interest and principal portions will be distributed to the investors based on their share of the pool.

Overseas Bank Is Pooling 50 Similar and Fully Amortized Mortgages