As baby boomers enter retirement, they will look to the investment industry for ways to generate retirement income from a stock of accumulated saving. A longstanding puzzle is why most retirees do not purchase longevity insurance in the form of lifetime annuities. This question is rising in importance due to the rapid decline of defined benefit pensions, which traditionally provided such guaranteed lifetime income. This study applies the lessons of behavioral finance to understand how well-documented anomalies in decision-making under risk may affect the annuity purchase decision. We demonstrate how mental accounting—where an annuity is evaluated as a gamble distinct from the retirement spending and investment plan—can be a powerful reason for the unpopularity of annuities. We also explain the prevalence of “period certain” annuities which guarantee a minimum number of payouts. Finally, we show that delayed payout or “longevity annuities,” which are purchased today to begin payouts in the future, may be more desirable than immediate payout annuities due to the overweighting of small probabilities.