荔枝酱 · 2019年12月18日
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： 6.8%
7.5%
C.8%
解释：
A is correct.
考点：Effective annual return
解析：根据Accrual taxes的公式，可得：
依据Effective annual return公式可得
，反解这个方程得：
这道题怎么看出是用accrual tax呢
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% 怎么辨别是accurtax、ferretax和wealth-base
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
是不是也可以直接用R*（1-T）即8%*（1-15%）
