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加加大 · 2022年08月28日

请解释一下statement 3

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NO.PZ202109080500000206

问题如下:

Which of Boylan’s statements about life annuities is least accurate?

选项:

A.Statement 1 B.Statement 2 C.Statement 3

解释:

Solution

A is correct. Statement 1 is incorrect. Because Janice and Jason are the same age, Jason will receive a higher income yield than his sister because women have a longer average life expectancy than men and, therefore, a longer expected payout period.

B is incorrect. Statement 2 is correct. If the same investment were to be made later in life, the expected payout stream would be shorter and therefore result in a higher income yield.

C is incorrect. Statement 3 is correct. The addition of a 10-year period-certain option to an annuity ensures that the carrier will make payments for at least 10 years. The probability of a 50-year-old person dying within 10 years is much lower than for an older individual, e.g., it is much more likely for an 80-year-old person to die within 10 years than a 50-year-old person to do so. It is more likely that the period-certain option would be invoked for the older person, meaning a much bigger decline in income yield compared to not having the period-certain option.

请解释一下statement 3

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已采纳答案

王暄_品职助教 · 2022年08月28日

前半句:

如果一个人买了一个年金,但是同时他又买了个10-year period certain,那么就是即使他买完年没几年就死了,他依然可以拿到10年的年金。所以是增加了N,增加了N,则PMT下降,则yield income下降。所以Statement 3前半句说:相比没有10-year period certain,有10-year period certain的yield inconme会低


而后半句:

比如一个人30岁买annuity with 10-year period certain,她努力活到40岁对他没什么问题,所以30岁的时候买年annuity with 10-year period certain没什么意义,N不会被拉长

如果这人83岁买annuity with 10-year period certain,85岁就死,N原本=2,那么现在被拉长成了10,N上升,PMT下降。

这个statement想表达的是这个意思。其实这个Statement确实表达的不咋清晰

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