1. Matt Saves for Retirement
Matt is a 40-year-old cabinet-maker. He recently decided he would start saving for retirement this year. He would like to live comfortably with his wife in retirement and take nice vacations once or twice a year. Matt bills his time at $65 per hour, and is able to work as many hours as he likes at that wage. Matt plans to retire at age 70. Assume that any tax rate Matt faces in this problem will be the same in all years from now through retirement unless stated otherwise.
(a) Matt begins his calculations ignoring taxes completely. Suppose that Matt would like the money he saves this year to be worth $45,000 when he retires. Any money Matt saves today can be invested for 30 years, earning annual pretax returns of 4 percent, to generate funds he can spend at age 70. Then how many extra hours would Matt need to work this year in order to generate the income he needs today in order to have an extra $40,000 when he is 70?
(b) Matt is already a bit disappointed about the amount of extra hours he will have to work this year to meet his goal, but now he realizes he must pay taxes too. Suppose Matt is subject to a 20% income tax on the income he gets from building cabinets. Now how many extra hours would he need to work this year in order to have an extra $45,000 when he is 70? (In answering this and subsequent questions, assume that neither James's hourly rate, nor the pretax return on investments, is a ected by whatever tax rate the government chooses.)
(c) Matt is now pretty discouraged. He wonders how much less he would have had to save if he had saved this money 15 years earlier. If he had saved the money when he was 25 instead of 40, how would your answer to part (b) change?
(d) Unfortunately, it is even worse for Matt, saving at age 40, than he had realized thus far. Matt discovers that the 20% income tax applies not only to his labor income but also to the investment income that he earns on his savings each year. Now how many extra hours would Matt need to work this year in order to have an extra $45,000 when he is 70?
(e) He talks to his wife about his depressing calculations and she reminds him that they could save their money in a traditional IRA. If he decides to save his money in a traditional IRA, how many extra hours would Matt need to work this year in order to have an extra $45,000 after he withdraws the money from his IRA and pays any necessary taxes when he is 70? How does this answer compare to your answer in part (b)?
(f) Matt is concerned that the tax rate on wage and investment income will rise to 40% when he turns 60 to help pay for the large budget de cit. How would your answer to part
(e) change if this were the case? What if Matt had put his money in a Roth IRA instead? Given these calculations, would you recommend that Matt put his money in a traditional or Roth IRA if he believes the tax rate will rise to 40% when he is 60?