Question

A pool of mortgages contains 3.75%, 30-year loans with the total beginning balance of $100.75 million....

A pool of mortgages contains 3.75%, 30-year loans with the total beginning balance of $100.75 million. In the first month, the total payments from the pool were $491.4 thousand. What are the total prepayments, to the nearest $0.01 thousand? E.g., if your answer is $25,345.39, record it as 25.35. Assume no defaults.

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Answer #1

ANSWER:

Annual Interest Rate = 3.75 %, Beginning Balance = $ 100.75 million and Tenure = 30 years or 360 months

Applicable Monthly Rate = (3.75/12) = 0.3125 %

Let the monthly repayments be $ M

Therefore, 100.75 = M x (1/0.003125) x [1-{1/(1.003125)^(360)}]

M = 100.75 / 215.929

= $0.46658855million or $ 466588.55

Interest of First Month = 0.003125 x 100.75

= $ 0.31484375million or 314843.75

Total Monthly Payout = Prepayment + Monthly Repayments

491400 - 466588.55= Prepayments

Prepayment = $ 24811.45

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