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Answer: USD 3,109.12
## Explanation Prepayment for any given month is defined as "principal payment" in excess of "scheduled principal payment" and is computed as: **Method 1:** - Month's total payment, less - Month's scheduled interest payment, less - Month's scheduled principal payment **Method 2 (simpler):** - Month's total payment, less - Month's scheduled total payment To compute the scheduled total payment, we use the original loan parameters: - PV = $1,750,000 - N = 12 × 30 = 360 months - FV = 0 - I/Y = 8%/12 = 0.67% per month Using a financial calculator: PMT = $12,840.88 (constant scheduled total payment per month) Therefore, prepayment in the specified month = total payment made - scheduled total payment: $15,950.00 - $12,840.88 = **USD 3,109.12** **Verification:** - Interest payment = 0.67% × beginning balance = 0.0067 × $1,644,235.78 = $11,016.38 - Scheduled principal payment = $12,840.88 - $11,016.38 = $1,824.50 - Actual principal payment = $15,950.00 - $11,016.38 = $4,933.62 - Prepayment = Actual principal payment - Scheduled principal payment = $4,933.62 - $1,824.50 = $3,109.12 Both methods confirm the prepayment amount of USD 3,109.12.
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A risk manager asks a junior risk analyst to assess the prepayment risk on a pool of fixed-rate mortgages. In order to calculate the conditional prepayment rate (CPR) for the pool, the analyst begins by estimating the monthly prepayments on one selected mortgage. At origination, the 30-year mortgage was a USD 1,750,000 loan making monthly mortgage payments at a fixed mortgage rate of 8% per year. Assuming the borrower made a total payment on the mortgage of USD 15,950.00 in one specific month, and the loan balance at the beginning of that month was USD 1,644,235.78, what is the correct estimate of the prepayment amount for that month?
A
USD 3,109.12
B
USD 4,933.62
C
USD 11,016.38
D
USD 14,076.60
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