这题

问题如下：

Based on the case study illustration and the effect of changing the annual compensation rate, the annual unit credit for the average participant would decrease by an amount closest to:

选项：

A.

€4,349.

B.

€4,858.

C.

€5,446

解释：

B is correct.

The final year’s estimated earnings at the end of Year 1 for the average participant would decrease by approximately €35,747.71.

Because there are now 17 years until retirement, there are 16 years until retirement from the end of Year 1. The final year’s estimated earnings, estimated at the end of Year 1, are as follows:

Current year’s salary × [(1 + Annual compensation increase)^{Years until retirement}]

Annual compensation increase of 6%: €100,000 × [(1.06)¹⁶] = €254,035.17

Annual compensation increase of 5%: €100,000 × [(1.05)¹⁶] = €218,287.46

The estimated annual payment for each of the 20 years (retirement life expectancy) is (Estimated final salary × Benefit formula) × Years of service

Annual compensation increase of 6%: (€254,035.17 × 0.01) × (10 + 17) = €68,589.50

Annual compensation increase of 5%: (€218,287.46 × 0.01) × (10 + 17) = €58,937.61

The value at the end of Year 17 (retirement date) of the estimated future payments is the PV of the estimated annual payment for each of the 20 years at the discount rate of 4%:

Annual compensation increase of 6%: PV of €68,589.50 for 20 years at 4% = €932,153.69

Annual compensation increase of 5%: PV of €58,937.61 for 20 years at 4% = €800,981.35

The annual unit credit = Value at retirement/Years of service:

Annual compensation increase of 6%: €932,153.69/27 = €34,524.21

Annual compensation increase of 5%: €800,981.35/27 = €29,665.98

The annual unit credit for the average participant would decrease by €34,524.21 – €29,665.98 = €4,858.23.

考点：annual unit credit计算

解析：

步骤一：计算final salary。

注意是从current salary往后复利16年。因为题干discount rate下面有一句话， 在每年的服务年限的第一天就实现工资的增长，所以相当于是每年的第一天工资已经涨上去了。求第17年年末的final salary，这个值就等于第17年年初的值，因为是年初涨工资。现在是0时刻，我们要计算第17年年初的工资金额，也就是第16年年末，所以是16次方。

步骤二：计算退休后每年的PMT。

用benefit formula=final salary*1%*预计总服务年限

根据题目条件可知，预计总服务年限=10+17。其中10年是vested service year，17是预计员工退休前未来还需要服务的年限。

• 10年vested service year，即到现在为止，员工已经有10年的服务满足了可获得养老金的要求，会给公司带来员工退休后养老金的给付义务。从现在开始往后还要工作17年才能退休，因此预计员工总共有27年的服务可以带来退休后养老金的PMT。

N=20（Retirement life expectancy），I/Y=4%（Discount rate），PMT=上一步算出来的数字，FV=0，求PV。

退休金是保障到员工去世的，根据题目条件，预计员工退休后还能活20年，公司就要付20年的退休金。

步骤四：计算annual unit credit=value at retirement/预计总服务年限。

上述四个步骤分别代入6%和5%的工资增长率，计算出annual unit credit差额。