Required distributions were determined using the Uniform Lifetime Table in Appendix C of IRS Publication 590. Any remaining account balance was distributed at age 90. Distributions were made at the end of each year.

I assumed 2006 federal income tax brackets. It was not necessary to escalate the tax brackets because the investment return was expressed net of inflation. That is, the inflation adjustment cancels out when calculating the tax rate so long as the same adjustment would be applied to the IRA balance and hence to the amount distributed.

The average tax is the cumulative tax paid divided by the cumulative amount distributed. No second tax calculation was required in this instance because there was no tax in the absence of the IRA distributions.

Accelerated distributions were three times the required distributions.

These data are available at www.cdc.gov/nchs/data/nvsr/nvsr53/nvsr53_06.pdf.

Life expectancies should be adjusted to reflect your current health, family history and whether your spouse is your plan beneficiary. The value of the aftertax contribution was escalated from the date of contribution by 5% real.

The value of the pretax contribution was reduced by the average future tax and then escalated from the date of contribution by 5% real.

The value of the deferred tax was escalated from the date of contribution by 3% real. That is, the return differential was 2%.

The benefit in a specific year is the escalated value of the pretax contribution plus the escalated value of the deferred tax less the escalated value of the aftertax contribution. The risked benefit in a specific year is the benefit in a that year times the risk of dying in that year.

The total risked benefit, on which rest the recommendations of Table 2, is the sum of the risked benefits from age 66 through age 100.

There should be a benefit from aftertax contributions after age 65 for certain combinations of tax rates, but this was not investigated.

The minimum distribution rules limit a traditional IRA at death to about one half the value of a Roth pension. For example, a $1 million Roth IRA at age 65 growing at 5% real is worth $2.4 million at age 83 while a traditional IRA with a $1 million aftertax value at age 65 is limited to $1.2 MM at age 83.

A $1.2 million aftertax traditional IRA has the potential to be worth $2.4 million in present value terms to young heirs aftertax. Add $1.2 million dollars of other assets, and the traditional pensioner has potentially left $3.6 million to his or her heirs.

Assuming a doubling in the present value of an IRA distributed over the lives of younger heirs is aggressive, especially for a traditional IRA, but it is not implausible.

I also recommend Reichenstein's "Integrating Investments & the Tax Code" (with William Jennings, John Wiley, 2003) for anyone who seeks higher effective returns through better management of tax issues.