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highsix · 2020年03月18日

问一道题：NO.PZ2018091705000022

  1. CFA III
  2. 个人IPS

问题如下：

Allen is an investment manager, who recently recruited a new customer, Polly. Polly invested $100,000 in an asset for 20 years that promises to offer an annual interest of 8% before tax without any capital gain. But the investment account is expected to be taxed 15% annually. Calculate the accrual equivalent return on this investment.

选项：

A.

6.8%

B.

7.5%

C.

8%

解释：

A is correct.

考点：Effective annual return

解析：先计算FV：

FV=PV[1+R(1−T)]N=100,000×(1+8%(1−15%))20=372,756.35FV_{}=PV{\lbrack1+R(1-T)\rbrack}^N=100,000\times{(1+8\%{(1-15\%)})}^{20}=372,756.35

依据Effective annual return公式可得

100,000(1+RAE)20=372,756.35100,000{(1+R_{AE})}^{20}=372,756.35，反解这个方程得：RAE=6.8%R_{AE}=6.8\%

怎么辨别是accural tax、deferred CG tax和wealth-based?

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Olive_品职助教 · 2020年03月19日

嗨，爱思考的PZer你好：


题目说了是 taxed annually，accrual taxes are paid periodically。

每个税种的征税方式不一样，题目信息会给的很明确的。


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努力的时光都是限量版，加油！


mario · 2021年04月24日

But the investment account is expected to be taxed 15% annually. 是对增值部分收税么？为什么不是对整个账户TAX 的计算公式啊？

王暄_品职助教 · 2021年04月24日

But the investment account is expected to be taxed 15% annually. 是对增值部分收税么？为什么不是对整个账户TAX 的计算公式啊？


15%只针对【annual interest of 8%】缴税；而你说的针对整个账户缴税的是属于wealth tax，基本做题的时候，只要没有明确提到是wealth tax，并且题目里提到了有annual interest，那么我们直接认为是针对利息收入交的税。

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Allen is investment manager, who recently recruitea new customer, Polly. Polly investe$100,000 in asset for 20 years thpromises to offer annuinterest of 8% before twithout any capitgain. But the investment account is expecteto taxe15% annually. Calculate the accruequivalent return on this investment. 6.8% 7.5% 8% A is correct. 考点Effective annureturn 解析先计算FV FV=PV[1+R(1−T)]N=100,000×(1+8%(1−15%))20=372,756.35FV_{}=PV{\lbrack1+R(1-T)\rbrack}^N=100,000\times{(1+8\%{(1-15\%)})}^{20}=372,756.35FV​=PV[1+R(1−T)]N=100,000×(1+8%(1−15%))20=372,756.35 依据Effective annureturn公式可得 100,000(1+RAE)20=372,756.35100,000{(1+R_{AE})}^{20}=372,756.35100,000(1+RAE​)20=372,756.35，反解这个方程得 RAE=6.8%R_{AE}=6.8\%RAE​=6.8% 你这题应该是wealth base，原文是investment account is expecteto taxe15% annually，所以应该是指这个投资账户每年征收15% ，而不是只对interest 征收

2020-02-27 11:26 1 · 回答

Allen is investment manager, who recently recruitea new customer, Polly. Polly investe$100,000 in asset for 20 years thpromises to offer annuinterest of 8% before twithout any capitgain. But the investment account is expecteto taxe15% annually. Calculate the accruequivalent return on this investment. 6.8% 7.5% 8% A is correct. 考点Effective annureturn 解析根据Accrutaxes的公式，可得 FVAT=PV[1+R(1−T)]N=100,000×(1+8%(1−15%))20=372,756.35FV_{AT}=PV{\lbrack1+R(1-T)\rbrack}^N=100,000\times{(1+8\%{(1-15\%)})}^{20}=372,756.35FVAT​=PV[1+R(1−T)]N=100,000×(1+8%(1−15%))20=372,756.35 依据Effective annureturn公式可得 100,000(1+RAE)20=372,756.35100,000{(1+R_{AE})}^{20}=372,756.35100,000(1+RAE​)20=372,756.35，反解这个方程得 RAE=6.8%R_{AE}=6.8\%RAE​=6.8% 这道题怎么看出是用accrutax呢

2019-12-18 23:36 1 · 回答

是不是也可以直接用R*（1-T）即8%*（1-15%）

2019-10-14 12:30 1 · 回答