为什么这里跟blend taxing里稅基不是1的公式不一样

NO.PZ2018091705000024

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 capital gain of 8%, which are deferred capital gains. The investment account is expected to be taxed 15% when capital gains are realized. Assume at beginning of the investment period, the investment has a cost basis of $80,000, Calculate the post-tax value of the investment after 20 years later.

选项：

$411,181.36

$372,756.35

$ 408,181.36

解释：

C is correct.

考点：Deferred Capital Gain Tax

解析：首先，我们计算一下B = 80,000/100,000=0.8

接着我们运用税基基础不等于1时候的Deferred Capital Gain Tax计算，即

${l}FV=PV{\lbrack{{(1+R)}^N-\lbrack{(1+R)}^N-B\rbrack\times T_{CG}}\rbrack}\\100,000{\lbrack{(1+8\%)}^{20}-{\lbrack{(1+0.08)}^{20}-0.8\rbrack}\times15\%\rbrack}=408,181.36$

可否这样计算：(1+8%)^20-[(1+8%)^20-1]*0.15-(1-0.8)*0.15

上面这个是blend taxing里稅基不是1的算法，为什么两个地方不一样？