Question

Life-cycle problem V Suppose the interest rate is 8%, the time horizon is 30 years, the marginal tax rate on ordinary income at the time of the contribution is 20%, the marginal tax rate at the time of withdrawal is 30%, and the marginal tax rate on investment income 20%.

(a) What is your final wealth after all taxes, if you save in a regular after-tax account?
(b) What is your final wealth after all taxes, if your save inside a 401(k) account?
(c) What is your final wealth after all taxes, if your save inside a Roth 401(k) account?
(d) Given your calculations above, which account type do you prefer?

Answer 1

The question asks for a calculation of final wealth after taxes in regular after-tax, 401(k), and Roth 401(k) accounts over 30 years with a given interest rate and various tax rates.

The solution requires understanding compound interest and the tax implications for each type of account.

Step-by-step explanation:

The student's question revolves around calculating the final wealth after taxes in different types of retirement accounts over a 30-year time horizon, given various marginal tax rates and an interest rate of 8%.

To compute the final wealth for each account type, one must understand how the contributions and withdrawals are taxed in addition to understanding the power of compound interest.

For the ordinary after-tax account, funds will be taxed initially and then again as investment income. In a 401(k), contributions are made pre-tax, and taxes are paid upon withdrawal.

In a Roth 401(k), contributions are made with after-tax dollars, but withdrawals are typically tax-free.

Determining the most advantageous account involves comparing the post-tax amount one would have in each account type after 30 years. It includes examining the effects of the different taxation timings on contributions and investment income across the accounts.