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王昕彤 · 2023年09月19日

Statement 3 可以详细讲解一下吗

NO.PZ2021090805000012

问题如下:

Tom and Jerry are husband and wife, both born in the same year. Tom is considering buying annuity insurance for them, and he and his investment advisor Johnson discuss some of the characteristics of these annuities. Assuming that their investment amount in the product is the same, he makes the following statement:

Statement 1

If both Tom and Jerry were to purchase the annuity immediately, they would both receive the same annual income yield.

Statement 2

If Tom 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 Jerry were to add a 10-year period certain option to her annuity, her income yield would be reduced when compared with not having the option, but it would be reduced by greater amounts the longer she waits to purchase the annuity.

Which of Johnson's statements about life annuities is the most inaccurate?

选项:

A.

Statement 1

B.

Statement 2

C.

Statement 3

解释:

A is correct. Statement 1 is incorrect. Because Tom and Jerry are of the same age, Tom will receive a higher income than Jerry, as women's average life expectancy is longer than men's, resulting in a longer expected payment period.

B is not correct. 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 that of an elderly person. For example, an 85 year old person is more likely to die within 10 years than a 50 year old person, which means that the decline in income return rate is much greater compared to choosing no specific period.

A是正确的。陈述1不正确。因为Tom和Jerry年龄一样,Jerryn将比Tom获得更低的收入,因为女性的平均预期寿命比男性长,因此预期支付期也更长。

B不正确。陈述2是正确的。如果在以后的生活中进行同样的投资,预期的支出流会更短,因此会带来更高的收入收益。

C不正确。陈述3是正确的。在年金中增加10年期的特定选项可确保承运人至少支付10年。一个50岁的人在10年内死亡的概率比一个老年人低得多,例如,一个85岁的人比一个50年的人更有可能在10年之内死亡,这意味着与没有特定时期的选择相比,收入收益率的下降幅度要大得多。

老师,Statement 3 的题目和答案没读懂,可以详细解释一下吗

1 个答案

王暄_品职助教 · 2023年09月20日

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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NO.PZ2021090805000012 问题如下 Tom anJerry are husbananwife, both born in the same year. Tom is consiring buying annuity insuranfor them, anhe anhis investment aisor Johnson scuss some of the characteristiof these annuities. Assuming ththeir investment amount in the prois the same, he makes the following statement:Statement 1If both Tom anJerry were to purchase the annuity immeately, they woulboth receive the same annuincome yielStatement 2If Tom were to purchase the annuity in 10 years rather thimmeately, his annuincome yielwoulhigher thtime thnow.Statement 3If Jerry were to a a 10-yeperiocertain option to her annuity, her income yielwoulrecewhen comparewith not having the option, but it woulrecegreater amounts the longer she waits to purchase the annuity.Whiof Johnson's statements about life annuities is the most inaccurate? A.Statement 1 B.Statement 2 C.Statement 3 A is correct. Statement 1 is incorrect. Because Tom anJerry are of the same age, Tom will receive a higher income thJerry, women's average life expectanis longer thmen's, resulting in a longer expectepayment perioB is not correct. Statement 2 is correct. If the same investment were to ma later in life, the expectepayout strewoulshorter antherefore result in a higher income yielC is incorrect. Statement 3 is correct. The aition of a 10-yeperiocertain option to annuity ensures ththe carrier will make payments for least 10 years. The probability of a 50 yeolperson ing within 10 years is mulower ththof elrly person. For example, 85 yeolperson is more likely to e within 10 years tha 50 yeolperson, whimeans ththe cline in income return rate is mugreater compareto choosing no specific perioA是正确的。陈述1不正确。因为Tom和Jerry年龄一样,Jerryn将比Tom获得更低的收入,因为女性的平均预期寿命比男性长,导致预期支付期也更长。B不正确。陈述2是正确的。如果在以后的生活中进行同样的投资,预期的支出流会更短,因此会带来更高的收入收益。C不正确。陈述3是正确的。在年金中增加10年期的特定可确保承运人至少支付10年。一个50岁的人在10年内死亡的概率比一个老年人低得多,例如,一个85岁的人比一个50年的人更有可能在10年之内死亡,这意味着与没有特定时期的选择相比,收入收益率的下降幅度要大得多。 Statement 3 前半句(逗号前)根据老师上课说的 当买年金,PV,FV,IY都是确定的,题目中多10年,就是n变大,对应的PMT就变小,所有income yie变小,所有前半句是对的。这么理解对吗?后半句,后半句的完全没看懂,老师解答一下

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