Traditional and Roth IRAs. With a traditional IRA, you get to deduct the amount you contribute from your current taxable income, invest the funds free from tax, but then pay taxes on the full amount you withdraw when you retire. Suppose your tax rate is 50 percent and you initially deposit $2,000 in an IRA. The proceeds double in seven years to $4,000. You then retire and pay taxes on the $4,000 at your 50 percent rate.

a. Taking into account your tax deduction for the IRA, how much did your investment in the IRA really cost you? What is your return after seven years?

b. With a Roth IRA, you do not get a deduction for your savings but the interest you earn is tax free. Is the outcome for a Roth IRA the same as for the traditional IRA if you invest $1,000 for seven years and double your initial investment?

c. Suppose you believed that in seven years tax rate