Jan can invest $4,000 of after-tax dollars (AT$)directly in a taxable bond outside an IRA,or she can contribute the $4,000 to a nondeductible IRA and invest in the same bond through the IRA vehicle.In either case,the bond yields an annual 4% before-tax rate of return (BTROR).Jan's marginal tax rate is 15%,and she expects it to remain so for the entire investment horizon of 25 years.What is her annualized after-tax rate of return (annualized ATROR)for the "bond inside the IRA"?

Question

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If Jan invests directly in the taxable bond, she will need to pay taxes on the bond's interest earnings each year at her marginal tax rate of 15%. Therefore, her after-tax rate of return would be:

After-tax rate of return = BTROR x (1 - marginal tax rate)
After-tax rate of return = 0.04 x (1 - 0.15)
After-tax rate of return = 0.034 or 3.4%

On the other hand, if Jan contributes the $4,000 to a nondeductible IRA and invests in the same bond through the IRA vehicle, she can defer taxes until she withdraws the money from the IRA. However, all withdrawals from the IRA will be taxed at her ordinary income tax rate, which she expects to be 15% for the entire investment horizon of 25 years.

To calculate her annualized after-tax rate of return for the bond inside the IRA, we need to use a different formula. Let's call the amount of money Jan contributes to the IRA P (which is $4,000 in this case), and let's call the annual tax-deferred rate of return on the bond R (which is 4% in this case). Then, the formula for the annualized after-tax rate of return for the bond inside the IRA is:

Annualized after-tax rate of return = (1 + R)^n x (1 - ordinary income tax rate) - 1
Annualized after-tax rate of return = (1 + 0.04)^25 x (1 - 0.15) - 1
Annualized after-tax rate of return = 1.036 or 3.6%

Therefore, the best choice is A) 3.6%, which is the annualized after-tax rate of return for the bond inside the IRA. By investing in the bond inside the IRA, Jan can achieve a higher after-tax rate of return compared to investing directly in the taxable bond.

Jan Can Invest $4,000 of After-Tax Dollars (AT$)directly in a Taxable