I’m having a hard time with EOC question # 6. I can’t follow the logic used in their answer. I also didn’t memorize any formula they gave in the chapter and just worked out each question logically and it’s worked thus far, but doesn’t seem to apply for Q6. Any adivce or thoughts?
you cannot do this without the formula (for this one case).
In each year you pay up taxes on 50% of the capital gains.
So year 1:
you earn 1.075 on 1$ of returns.
Pay (1.075 - 1)*0.5*0.1 as tax = .00375 as tax.
So you are left with 1.075 - 0.00375 = 1.07125
So end of the 15 years - total amount = 1.07125 ^15 * 250,000 = 701944 $.
Now at the end you pay Capital Gains tax of (701944 -250000)*.5*.1/0.95 = 23787 in taxes
So you are left with 701944 - 23787 = 678157 – Ans.
the weird formula of dividing by 0.95 for the taxes is because you are effectively paying taxes on 0.95 of the principal growth - because 0.5 * 0.1=0.05 is being paid out each period already (considered in the 1.07125 portion).