SMM的问题

NO.PZ2019052801000107问题如下 If the contionprepayment rate (CPR) for a pool of mortgages is assumeto 5% on annubasis anthe weighteaverage maturity of the unrlying mortgages is 15 years, whiof the following amounts is closest to the .constant maturity mortality? 0.333%. 0.405%. 0.427%. 0.5%. C is correct. The constant maturity mortality (or single monthly mortality rate) is a monthly measure. Its relationship to CPR is follows:（1-SMM）12 =1-CPR SMM=1− (1−CPR) 1/ 12 =1− (1−0.05) 1/ 12 =1− 0.95 1/ 12 =0.43%解析 已知CPR=5%p.基础资产的平均到期日为15年，求constant maturity mortality也就是SMM是多少？选C，SMM=1-(1-CPR)^(1/12)=1-(1-5%)^(1/12)=0.427% 那个等式跟时间没关系吗？必须是12？谢谢

NO.PZ2019052801000107问题如下 If the contionprepayment rate (CPR) for a pool of mortgages is assumeto 5% on annubasis anthe weighteaverage maturity of the unrlying mortgages is 15 years, whiof the following amounts is closest to the .constant maturity mortality? 0.333%. 0.405%. 0.427%. 0.5%. C is correct. The constant maturity mortality (or single monthly mortality rate) is a monthly measure. Its relationship to CPR is follows:（1-SMM）12 =1-CPR SMM=1− (1−CPR) 1/ 12 =1− (1−0.05) 1/ 12 =1− 0.95 1/ 12 =0.43% 请问我是那里理解错误了，为什么次方是12次而不是题目中说的15 unrlying years？感谢解答！