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zxy · 2024年08月06日

模拟题一(B)的题目

Boylan tells the audience that life annuities are a convenient investment to deal with longevity risk. He again uses the twins, Jason and Janice, as an example, in discussing some of the characteristics of these annuities. Assuming that they were both to invest the same amount into this product, he makes the following statements:

Statement 1 If both of them were to purchase the annuity immediately, they would both receive the same annual income yield.

Statement 2 If Jason were to purchase the annuity in 10 years rather than immediately, his annual income yield would be higher at that time than now.

Statement 3 If Janice were to add a 10-yearperiod certain option to her annuity, her income yield would be reduced when compared to not having the option, but it would be

reduced by greater amounts the longer she waits to purchase the annuity.


Aorrect Answer: B

Statement 1 is incorrect: since they are both the same age, Jason will receive a higher income yield than his sister as females have a longer average life expectancy than males and therefore a longer expected payout period.

考点:个人IPS-Risk Management for Individuals-Annuities


1、为什么statement 1是错的?我理解女性活的比男性久,但是income yield分子是PMT啊,那么女性的PMT应该更高带动income yield更高,但是答案说的是男性income yield更高。

2、有一个option应该要付更多的保费,income yield应该更高啊?但是题目说的是reduced是对的,这个是为什么?

1 个答案

王暄_品职助教 · 2024年08月07日

1、为什么statement 1是错的?我理解女性活的比男性久,但是income yield分子是PMT啊,那么女性的PMT应该更高带动income yield更高,但是答案说的是男性income yield更高。

由于女性获得的更久,因此N上升,在PV相同的情况下,PMT则下降,则income yield低,相对的,男性则income yield高


2、有一个option应该要付更多的保费,income yield应该更高啊?但是题目说的是reduced是对的,这个是为什么?

Statement 3分两部分理解:

1. If Janice were to add a 10-year period certain option to her annuity, her income yield would be reduced when compared to not having the option,

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。

 

2. but it would be reduced by greater amounts the longer she waits to purchase the annuity.

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的后半句想表达的是这个意思,确实不够清晰

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