An often-touted advantage of annuities is that they offer mortality credits due to the pooling of mortality risk – survivors receive a return boost from those who die. Although the general concept of mortality credits is widely understood, the underlying math is not. Understanding the math can help with decisions such as the best age to purchase an annuity and which type of annuity to purchase. Such an understanding can also be useful in debunking some popular beliefs about annuities.

For this article I’ll concentrate on “fixed” annuities that provide lifetime income. These include:

- Single-premium immediate annuities (SPIAs), which pay a lifetime income beginning at purchase;
- Deferred-income annuities (DIAs), which pay lifetime income after a delay period; and
- Qualified longevity annuity contracts (QLACs), a subset of DIAs that are funded through an IRA or other qualified retirement plan where the payments begin after age 70 ½.

I’ll base the examples on annuities that provide level nominal payments (rather than payments that increase to adjust for inflation), because they are the most popular and provide easy comparisons among SPIAs, DIAs and QLACs. This will be a pre-tax analysis, most applicable to funds held in qualified retirement plans. The analysis gets more complicated for taxable funds.

**Mortality credit math**

We’ll start with an example of a SPIA purchased by a 65-year-old female that will provide level annual lifetime payments, with the first payment one year after purchase. Based on rates provided by the annuity pricing service CANNEX as of late June 2017, the average of the best three prices from the 20 companies CANNEX monitors is an annual payment of $6,520.09 based on a $100,000 purchase. This can also be stated as a payout rate of approximately 6.52%.

Before calculating the value of mortality credits, we first need to estimate the internal rate of return that a purchaser of such an annuity could expect to earn, which is a function of expected longevity. I based my longevity estimates on the Society of Actuaries’ 2012 individual annuity mortality table and applied a projected mortality improvement scale. Using this approach, the average age at death for a 65-year-old female is 90. This may seem surprisingly old for those used to Social Security statistics and other published sources, but this table assumes that annuity purchasers will be a healthier-than-average. Also, there is evidence that socio-economic status affects longevity prospects and we would expect typical advisor clients to be somewhat upscale.

To calculate the IRR, we use the mortality table to estimate the percentage of survivors at each age and then multiply this percentage by the $6,520.09 payout. This produces declining expected payments by age as illustrated in the following graph.