题目
Below is an extract from a mortality table (ages 30 to 34 for males and females):「huixue_img/importSubject/1564169525644103680.png」Suppose a woman aged 30 years old buys a $1.0 million whole life insurance policy and she pays an annual premium of $6,000. What is approximately the surplus premium in the first year of the policy?
选项
A.There is no surplus premium; i.e., zero
B.$5,336.00
C.$5,885.00
D.$5,919.00
答案
B
解析
For a 30-year female, the conditional one-year probability of death is 0.000664 such that the surplus premium is equal to $6,000-($1,000,000×0.0006640)=$6,000-$664=$5,336.00可以将终身寿险的年度保费与当年的定期寿险成本进行比较。例如：假定一个40岁的男性买人面值为100万美元的终身寿险，每年所付的保费为20000美元。如果一个40岁男性在一年内死亡的概率为0.0022，这说明一年的保险的公允价值为2200美元，这意味着在第一年的保费中有17800美元的盈余数量（surplus premium）可被用于投资。一个41岁男性在一年内死亡的概率为0.0024，这说明第二年保险的公允价值为2400美元，这意味着在第二年的保费中有17600美元的盈余数量可被用于投资。每年保险成本随着投保人年龄的增大而逐渐增长。在某一个时间段，保险成本会超过保费。就这道题而言30岁女性条件死亡概率为0.000664 ，盈余数量为$6,000－($1,000,000×0.0006640)=$6,000－$664=$5,336.00