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? [Hint: the PMT is 50,713]

Question

BlackTom AI · Accepted Answer

Monthly interest = outstanding balance × (annual rate/12). The pooled balance is 50 × $100,000 = $5,000,000 and the monthly rate is 9%/12 = 0.0075. So the interest portion for the first payment on the entire pool is 5,000,000 × 0.0075 = $37,500.

The total monthly payment (PMT) for the pool is given as $50,713. The principal portion of the first payment equals PMT − interest. Thus principal = 50,713 − 37,500 = $13,213.

Step-by-step with intermediate values:
1. Pool principal = 50 × $100,000 = $5,000,000.
2. Monthly rate r = 0.09/12 = 0.0075.
3. First-month interest = 5,000,000 × 0.0075 = 37,500.
4. Given PMT (total monthly payment) = 50,713.
5. First-month principal = PMT − interest = 50,713 − 37,500 = 13,213.

(If you want per-mortgage numbers: PMT per mortgage = 50,713/50 = $1,014.26; interest per mortgage = 100,000 × 0.0075 = $750; principal per mortgage = 1,014.26 − 750 = $264.26; multiplied by 50 gives the $13,213 total principal above.)

Why this answer is correct: interest is purely the outstanding balance times the monthly rate; the remainder of the fixed payment reduces principal. That calculation yields $37,500 interest and $13,213 principal for the first month.

Why other choices are incorrect:
- b and d mislabel interest and principal and give impossible values (e.g., $37,500 as principal is wrong because interest must be that amount).
- c gives the correct interest but an incorrect principal ($7,809) that does not equal PMT − interest.
- e gives the correct interest but an incorrect principal ($17,756) inconsistent with the given PMT.

Final confirmation: the correct choice is a. $37,500 interest and $13,213 principal.

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