We looked at longevity insurance as it applies to a sixty-five-year-old female purchasing a deferred income annuity with income starting at eighty-five. We may also consider the alternative of just waiting until age eighty-five and then buying an immediate annuity. During those twenty years, interest rates and mortality tables can change in unexpected ways, which will impact the future pricing calculations.
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Exhibit 4.4 shows the calculated cost for this income annuity if we assume that interest rates and mortality data remain the same (an unlikely outcome, of course). An eighty-five-year-old will experience higher mortality rates and a shorter time horizon, reducing the cost of an income annuity at this age. In this case, the premium is $81,054, which raises the payout rate to 12.34 percent.
This payout rate is noticeably higher than that available at age sixty-five, but it is lower than that available with the longevity insurance contract. Longevity insurance contains two key differences: twenty years of asset growth within the contract and the survival-based discount a sixty-five-year-old receives, thanks to her lessened chance of living to eighty-five to receive income.
Waiting until eighty-five to make the purchase means sharing fewer mortality credits with the risk pool. If we discount this $81,054 premium by the 72.3 percent survival probability from age sixty-five and by twenty years of investment growth at 3 percent (a 55.4 percent discount factor), we arrive at the $32,444 premium (after rounding) for the longevity insurance contract.
Exhibit 4.4 Calculating the Cost of a $10,000 Income Stream for an 85-Year-Old Female (Life-Only)
Retirement Researcher
Note: Survival Probabilities are calculated from the Society of Actuaries 2012 Individual Annuitant Mortality Tables with improvements through 2019.
This is an excerpt from Wade Pfau’s book, Safety-First Retirement Planning: An Integrated Approach for a Worry-Free Retirement. (The Retirement Researcher’s Guide Series), available now on Amazon
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