3. 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 the tax rate in the final 20 years will be 36%, commensurate with your higher income in that period. At retirement, you expect your tax rate to fall back to 28%. Under a standard IRA, the contributions come out of pre-tax income and reduce your taxable income in the year they 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 choose the account type you prefer from part (a) and that you expect to live another 25 years after you retire. If you expect to continue 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? c. If you could have both a Roth IRA and a traditional IRA, what would be the optimal investment strategy?