Question

*Can you explain the results and consumption stream also?*

1.The difference between a Roth IRA and a traditional IRA is that in a Roth IRA taxes are paid on the income that is contributed but the withdrawals at retirement are tax-free. In a traditional IRA, however, the contributions reduce your taxable income, but the withdrawals at retirement are taxable. Assume you plan to devote $5,000 to retirement savings in each year. You will retire in 30 years and expect to live for an additional 20 years after retirement.

a. Assume the before-tax interest rate is 5%. What will be your after-tax 20-year retirement consumption stream if you choose to save in a traditional IRA? Assume your tax rate is fixed at 30%.

b. What will be your 20-year retirement consumption stream if you choose to save in a Roth IRA?

Answer 1

a. FV of $5000 tax-free contributed each year for 30-years: FV(5%,30yrs) = 5000*PVAF(5%,30yrs) = 5000*66.4388 = $332,194 Now calcualte the retirement consumption stream per year for next 20-yrs, using the formula: Payment = r(PV)/(1-(1+r)-n), where: r = rate per period = 5% PV = value at starting of retirment cosumption stream = $332,194 n = number of periods = 20 years Payment = 0.05(332,194)/(1-(1+0.05)-20) = $26,656.11 This is the amount of withdrawl pre-tax, which will be taxed @ 30%. Therefore, post tax amount of withdrawls = $26,656.11*(1-0.30) = $18,659.27

b.FV of $5000(1-0.30) = $3500 after-tax contributed each year for 30-years: FV(5%,30yrs) = 3500*PVAF(5%,30yrs) = 5000*66.4388 = $232,536 Now calcualte the retirement consumption stream per year for next 20-yrs, using the formula: Payment = 0.05(232,536)/(1-(1+0.05)-20) = $18,659.29, which is a tax-free amount of withdrawl.