NO.PZ2023091701000063
问题如下：
A risk manager asks a junior risk analyst to assess the prepayment risk on a pool of fixed-rate mortgages. Inorder to calculate the conditional prepayment rate (CPR) for the pool, the analyst begins by estimating themonthly prepayments on one selected mortgage. At origination, the 30-year mortgage was a USD 1,750,000loan making monthly mortgage payments at a fixed mortgage rate of 8% per year. Assuming the borrowermade a total payment on the mortgage of USD 15,950.00 in one specific month, and the loan balance at thebeginning of that month was USD 1,644,235.78, what is the correct estimate of the prepayment amount forthat month?
选项：
A.USD 3,060.29
B.USD 4,933.62
C.USD 11,016.38
D.USD 14,076.60
解释：
Prepayment for any given month is defined as “principal payment” in excessof “scheduled principal payment” and is computed as:
(i) month’s total payment, less
(ii) month’s scheduled interest payment, less
(iii) month’s scheduled principal payment.
Or,
(i) month’s total payment, less
(ii) month’s scheduled total payment.
To compute scheduled total payment, consider an amortizing fixed-rate loan withparticulars as follows: PV = 1,750,000; N = 12x30 = 360; FV = 0; I/Y = 8%/12 = 0.67.Therefore, using a calculator, PMT = 12,889.71 = constant scheduled total payment permonth.
Therefore, prepayment in the specified month = total payment made – scheduled totalpayment = 15,950.00 – 12,889.71 = USD 3,060.29.
(Also, given the specified month,Interest payment = 0.67% x beginning balance = 0.0067 x 1,644,235.78 = USD 11,016.38)
B is incorrect. USD 4,933.62 is the total payment less scheduled interest payment for themonth. It is incorrect because it includes the scheduled principal payment.
C is incorrect. USD 11,016.38 is the scheduled interest payment for the month = 0.0067 x1,644,235.78.
D is incorrect. USD 14,076.60 is the total payment made less the scheduled principalpayment for the month = USD 15,950.00 – (12,889.71 – 11,016.38). It is incorrect becauseit includes the scheduled interest payment.
老师，在计算SMM时，分母是（月初本金-本月偿还本金）还是（月初本金-本月偿还总额（含利息））？
这道题我算成D了，和SMM有点儿混了，所以再向您确认一下SMM的计算。
也就是计算prepayment，用总还款要减去月供（本金+利息）对吧？
