Having just started a nice job after graduation, you would like to be financially responsible and start planning for your expected retirement in $40$ years. You have two main options to choose from:

A$)$ Use pretax money and invest in a $401$k $($paying taxes on the back end$)$

B$)$ Use after$-$tax money and invest in a Roth IRA $($paying taxes on the front end$)$

Assume:

$-$ you are looking to invest $$3,000$ worth of your pre$-$tax salary each year.

$-$ your current marginal tax rate is $22\%$ based on your $$70,000/$year salary using current tax law

$-$ both options provide identical investment choices and you expect to earn $7\mathrm{.}5\%$ per year in either alternative

$-$ the distributions from Roth IRA accounts will continue to not be taxed in future years

$-$ your estimated marginal tax rate will be $24$ percent when you retire

Which option will provide you with the highest retirement amount in $40$ years when you plan to retire?

Please provide a sensitivity analysis to assist in your decision$-$making.