How much after-tax wealth would Motelli accumulate assuming the same facts as in Question 4 except that 50 percent of all capital gains are recognized each year?
（Question4 ：If Motelli’s current investment account of €250,000 is invested in an investment which is expected to earn a return of 7.5 percent, all of which are deferred capital gains, what is his expected after-tax accumulation in 15 years? The account’s market value is equal to its cost basis
）
问题是：下面答案的公式怎么推导的啊？
C is correct.
r* = r(1 – pcgtcg)
= 0.075(1 – (0.5)(0.10)) = 0.075(1 – 0.05) = 0.07125
T* = tcg(1 – pcg)/(1 – pcgtcg)
= 0.10[(1 – 0.5)/(1 – 0.5 × 0.10)] = 0.052632
FVIFTaxable = (1 + r*)n(1 – T*) + T* – (1 – B)tcg, B = 1
FV = €250,000 × [(1 + 0.07125)15(1 – 0.052632) + 0.052632]
= €678,158 (Institute 267)
Institute, CFA. 2018 CFA Program Level III Volume 2 Behavioral Finance, Individual Investors, and Institutional Investors. CFA Institute, 07/2017. VitalBook file.
