Please answer using life-cycle problem. A young person begins employment at age 22. The employer offers a pension plan (401(k)) with options to invest in stock and bond mutual funds. The tax law allows the employee to contribute another $18,000 per year. The expected rate of return on a mixed stock- bond mutual fund is 6% per year. The marginal tax rate at contribution is 30%, and the expected marginal tax rate at the time of withdrawal is 20%. The marginal tax rate on investment income is also 20%.

(a) The newly employed person thinks he will work until he turns 62 years old and then retire. To support a nice life in retirement, the person decides to contribute $6,000 per year to the pension plan. What is the end account balance from investing in the mixed stock-bond fund after all taxes have been paid?

(b) The employer also offers a Roth 401(k) option. What is the end Roth account balance from investing in the mixed stock-bond fund after all taxes have been paid?

(c) Which withdrawal tax rate would make the person indifferent between the regular 401(k) and the Roth 401(k)?