7-55. A Roth IRA enables an individual to invest after-tax dollars during the accumulation phase of a retirement plan. The money is then income tax free when it is withdrawn during retirement. A tax-deductible IRA, on the other hand, provides an up-front tax deduction for the annual contribution, but it then requires income taxes to be paid on all future distributions. A basic assumption as to which plan is more beneficial concerns the current income tax rates versus their projected rates in the future. To illustrate, suppose that $2,000 is available to invest at the end of each year for 30 years. The income tax rate now and into the foreseeable future is 28%, so $2,000(1 − 0.28) = $1,440 is invested annually into the Roth IRA. However, $2,000 per year can be invested into a tax-deductible IRA. Money invested under either plan will be deposited into a mutual fund earning 8% per year, and all accumulated money will be withdrawn as a lump sum at the end of year 30. (7.7)

a. Which plan is better if future distributions of the traditional (tax-free) IRA are taxed at an income tax rate of 28%?

b. Which plan is better if the future income tax rate at retirement (end of year 30) is 30%?