Question

2. The Taxpayer Relief Act of 1997 created the Roth IRA, which permits qualifying individuals to make after-tax retirement contributions of up to $6,000 annually as of 2019. Contributions to a Roth IRA are not tax-deductible, but no taxes are paid on earnings generated from a Roth IRA. In contrast, contributions made to traditional IRAs are tax- deductible, but individuals will pay taxes on all future distributions. In short, investors using the Roth IRA make contributions that have already been taxed and have earnings that grow tax-free, while those using the traditional IRAs defer taxes until funds are withdrawn. Consider an individual who is five years away from retirement and will need to withdraw all her retirement funds at that time. She has $6,000 in pretax income to allocate each year to a retirement plan, faces a fixed tax rate of 15 percent now as well as at retirement, and anticipates a stable 8 percent return on her investments. She can set up a Roth IRA for a one-time, up-front fee of $50, or she can set up a traditional IRA for free. Which option should she choose? (Spoints)

Answer 1

Given information
Years she would contribute   5 Years
Pretax amount    6000
Anticipated interest 8%
Tax Rate 15% Fixed

Scenario 1 Roth IRA
Pretax amount 6000
Onetime Fee 50
In this scenario she should pay tax of 15% before investment
That is 6000*15/100 =900
After tax Amount she can invest in Roth IRA is
Pretax amount -Tax
=6000-900
=5100
Total amount she would invest 5100*5=25500
Interest amount she would earn 25500*8/100
=2040

Total amount she would get 25500+2040=27540
But She would have paid onetime fee of 50 on this so total amount is
27540-50
Net amount she would receive at retirement =   27490

Scenario 2 regular IRA investment

This is tax deductible so she won’t be paying tax before the maturity
Total amount she would invest= annual amount *no of years
               =6000*5
=30000

Interest earned is 30000*8%
=30000*(8/100)
=2400

Amount at Maturity is
Amount invested +interest earned
=30000+2400
=32400
Whereas in this scenario she should pay tax of 15% on total amount
Tax = total amount *15%
=32400*15/100
=4860
Net amount she would receive is Amount at maturity -Tax
=32400-4860
=27540

Considering both scenarios it is better in this case for her to invest in Regular IRA investment rather than Roth IRA