You are starting to plan for your retirement and want to determine the optimal type of retirement account to establish in light of different tax treatments on the accounts. Suppose that you are 30 years from retirement and that your investments will be in government and corporate bonds. You expect that you will be able to afford pre-tax contributions of $5,000 per year for the next ten years. After that, you expect to have gotten promoted at work, allowing for pre-tax contributions of $10,000 per year for the remaining 20 years. During the first 10 years, you expect your income tax on wages and interest to be only 25% but that commensurate with your higher income, the tax rate in the final 20 years will be 36%. At retirement, you expect your tax rate to fall back to 28%.

Under a standard IRA, the contributions reduce your taxable income in the year the contributions are made but the total balance in the account is taxable at the normal income tax rate upon withdrawal. Under a Roth IRA, the contributions do not reduce your taxable income (meaning that you will only be able to afford to contribute $3,750 ( = $5,000 * (1-25%)) per year in the first ten years and $6,400 per year in the final 20 years) but the principal and interest are tax-free.

a. If you expect to earn 8% on the account and must put all of your money into only one of the investment vehicles for the entire 30 years, which do you prefer? Hint: Calculate the after tax values in each of the accounts at the end of the 30 years.

b. Assume that you expect to live another 25 years after you retire. If you expect to earn a pre-tax return of 8% on the investment account and would like to withdraw the same amount every year for the next 25 years (the first payment occurring one year after retirement), how much would you receive every year, on an after-tax basis?

3. If you could have both a Roth IRA and a traditional IRA, what would be the optimal investment strategy?

4. Suppose that you are going to invest in a retirement account annually for 30 years starting today. Instead of saving as much as possible, you would prefer to purchase more now and decide that all you need for retirement is $2,000 monthly for 25 years with the first withdrawal occurring 30 years from today. A new account exists that allows you to invest and pay lump-sum tax (at the rate of 28% from above) on the interest that has accrued in the account at the end of the 30 years (before the first withdrawal). After which the marginal tax rate is assumed to be zero. How much must you deposit annually in order to guarantee that your needs will be meet if the interest rate throughout the entire period is 8%?