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Answer: USD 3,060.29
The correct estimate of the prepayment amount for the month is USD 3,060.29. Prepayment is defined as the "principal payment" in excess of the "scheduled principal payment." To calculate this, you subtract the month's scheduled total payment from the month's total payment. The scheduled total payment is calculated using the formula for an amortizing fixed-rate loan, considering the principal value (PV), the number of payments (N), and the interest rate per period (1/Y). In this case, the PV is USD 1,750,000, N is 360 (12 payments per year for 30 years), and the annual interest rate is 8%, which translates to a monthly rate of 0.67%. Using these values, the scheduled total payment per month (PMT) is calculated to be USD 12,889.71. The prepayment for the specified month is then the total payment made (USD 15,950.00) minus the scheduled total payment (USD 12,889.71), resulting in a prepayment amount of USD 3,060.29.
Author: LeetQuiz Editorial Team
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An analyst has been assigned by a risk manager to evaluate the prepayment risk associated with a portfolio of fixed-rate mortgages. To achieve this, the analyst must calculate the conditional prepayment rate (CPR) for the group. Specifically, the analyst begins by forecasting the monthly prepayments for an individual mortgage within the portfolio.
In this scenario, the individual mortgage is a 30-year loan of USD 1,750,000 with a fixed annual interest rate of 8%, structured with monthly payments. For a particular month, the borrower has made a total payment of USD 15,950.00, and the loan balance at the beginning of that month was USD 1,644,235.78. Based on this information, determine the accurate amount of prepayment for that month.
A
USD 3,060.29
B
USD 4,933.62
C
USD 11,016.38
D
USD 14,076.60
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