The authors of your textbook make six assumptions and then draw a comparison between

a Roth IRA and a Traditional IRA. Those six assumptions are as follows: $($a$)$ the

contribution rate is exactly $$1,000$ after tax dollars per year, $($b$)$ the tax rate is a constant

$30\%$ for all years involved, $($c$)$ the retirement plan, Roth or Traditional, earns $8\%$ per year

before taxes, $($d$)$ all applicable taxes are taken out of the contribution $($the plan is self$-$

sufficient in handling its tax burden$)($e$)$ the traditional IRA pays tax upon withdraw in $30$

years, and $($f$)$ the Roth IRA pays tax on contributions annually. Based on these

assumptions the authors conclude that both investments will produce an exactly equal

accumulated balance at the end of a $30-$year investment period. But, we know that in real

life there are significant differences between Roth and Traditional IRAs.

a$.$ First, explain why the authors conclusion doesn't properly evaluate the

differences between a Roth IRA and a Traditional IRA as these two investment

opportunities are actually being used by most high income workers who are trying

to maximize their retirement savings?