Question

1) Keisha (50 years of age) is considering whether to participate in her company's Roth 401(k) or traditional 401(k). This year, she plans to invest either $4,000 in a Roth 401(k) or $5,000 in a traditional 401(k). Keisha plans on leaving the contribution in the retirement account for 20 years when she will receive a distribution of the entire balance in the account. Her employer does not have a matching program for employee contributions to retirement accounts. Assume Keisha can earn a 6 percent before tax return in either account and that she anticipates that in 20 years her tax rate will be 30%.

1) What would be Keisha's after-tax accumulation in 20 years if she contributes $4,000 to a Roth 401(k) account?

2) What would be her after-tax accumulation in 20 years if she contributes $5,000 to a traditional 401(k) account? (Round future value factors to 5 decimal places and the future value and final answers to the nearest whole number)

Topic: Defined Contribution Plans

Learning Objective: 13-02 Explain and determine the tax consequences associated with employer-provided defined contribution plans, including traditional 401(k) and Roth 401(k) plans.

Answer 1

1. Contribution of $ 4,000 in Roth 401(k) account for 20 years

Earning rate = 6%               Tax rate = 30%

= (0.70 * $ 4,000) * (1.06)^20

= $ 8,979.97932

= $ 8,979.97932 - $ 2,800 = $ 6,179.97932

= $ 6,179.97932 * (1-30%) = 4,325.98552

After tax amount = $ 2,800 + 4,325.98552

                                 = $ 7,126

2. Contribution of $ 5,000 in Traditional 401(k) account for 20 years

Earning rate = 6%               Tax rate = 30%

= ($ 5,000 * 1.06^20) * 0.70

= $ 11,224.97420

= $ 11,224.97420 - $ 2,800 = $ 8,424.97420

= $ 8,424.97420 * (1 – 30%) = $ 5,897.48194

After tax amount = $ 2,800 + 5,897.48194

                                 = $ 8,697