Suppose you were just told that you will receive an end-of-the-year bonus of $15,000 from your company. Suppose further that your marginal income tax rate is 33.33% —which means that you will have to pay $5,000 in income tax on this bonus. And suppose that you expect the average rate of return on an investment account you have set up with your broker to be 10% annually (and, for purposes of this example, assume interest compounds annually.)
A: Suppose you have decided to save all of this bonus for retirement 30 years from now.
(a) In a regular investment account, you will have to pay taxes on the interest you earn each year.
Thus, even though you earn 10%, you have to pay a third in taxes — leaving you with an after-tax return of 6.67%. Under these circumstances, how much will you have accumulated in your account 30 years from now?
(b) An alternative investment strategy is to place your bonus into a 401K “tax-advantaged” retirement account. The federal government has set these up to encourage greater savings for retirement. They work as follows: you do not have to pay taxes on any income that you put directly into such an account if you put it there as soon as you earn it, and you do not have to pay taxes on any interest you earn. Thus, you can put the full $15,000 bonus into the 401K account, and you can earn the full 10% return each year for the next 30 years. You do, however, have to pay taxes on any amount that you choose to withdraw after you retire. Suppose you plan to withdraw the entire accumulated balance as soon as you retire 30 years from now, and suppose that you expect you will still be paying 33.33% taxes at that time. How much will you have accumulated in your 401K account, and howmuch will you have after you pay taxes? Compare this to your answer to (a)—i.e. to the amount you would have at retirement if you saved outside the 401K plan.
(c) True or False: By allowing individuals to defer paying taxes into the future, 401K accounts result in a higher rate of return for retirement savings.
B: Suppose more generally that you earn an amount I now, that you face (and will face in the future) a marginal tax rate of t (expressed as a fraction between 0 and 1), that the interest rate now (and in the future) is r and that you plan to invest for n periods into the future.
(a) How much consumption will you be able to undertake n years from now if you first pay your income tax on the amount I , then place the remainder in a savings account whose interest income is taxed each year. (Assume you add nothing further to the savings account between now and n years from now).
(b) Now suppose you put the entire amount I into a tax-advantaged retirement account in which interest income can accumulate tax-free. Any amount that is taken out of the account is then taxed as regular income. Assume you plan to take the entire balance in the account out n years from now (but nothing before then). How much consumption can you fund from this source n years from now?
(c) Compare your answers to (a) and (b) and indicate whether you can tell which will be higher.