答案的Tecg公式是不是错了

问题如下：

Allen is an investment manager, who recently recruited a new customer, Jack. Jack invested $2,000,000 in a portfolio for 20 years that promises to offer an annual return of 8% before tax. The ratio of interest, dividends, realized capital gains, unrealized capital gains to earnings and related tax rates are shown in the following table.

Calculate the post-tax value of the investment 20 years later.

选项：

$6,202,275

$7,908,343

$6,687,503

解释：

A is correct.

考点：Blend Taxing Environments

解析：这道题考法非常常规。对于Blend Taxing，我们首先还是要计算其$R_{ART}$以及$T_{ECG}$

${l}R_{ART}=R\times\lbrack1-(P_I\times T_I+P_D\times T_D+P_{CG}\times T_{CG})\rbrack\\=0.08\times{\lbrack1-{(0.3\times0.4+0.35\times0.2+0.15\times0.3)}\rbrack}=6.12\%$

${l}T_{ECG}=\frac{\lbrack1-(P_I+P_D+P_{CG})\rbrack\times T_{CG}}{1-(P_IT_I+P_DT_D+P_{CG}T_{CG})}\\=\frac{\lbrack1-(0.30+0.35+0.15)\rbrack\times0.3}{\lbrack1-{(0.3\times0.4+0.35\times0.2+0.15\times0.3)}\rbrack}=7.843\%$

接下来直接套用Blend Taxing的公式，题目没有明确说明税基的情况，那么就默B=1。

${l}FVIF_T={(1+R_{ART})}^N-{\lbrack{(1+R_{ART})}^N-1\rbrack}T_{ECG}-{(1-B)}T_{CG}\\FV=2,000,000{\{{(1+6.12\%)}^{20}-{\lbrack{(1+6.12\%)}^{20}-1\rbrack}7.843\%\}}\\=6,202,275$