EXAMPLE 15 Life Income Annuity

Suppose that your 65-year-old father retires and purchases for $250,000 a life income annuity. According to the table from one particular insurance company, he would receive $6.3448 per month for every $1000, so his monthly income would be $1586. According to the Social Security Administration actuarial life table, his life expectancy at age 65 is about 17 years = 204 months. If he lived exactly that long, he would receive a total of .

However, simple algebra cannot be used to find the rate of interest that the annuity would need to earn to last that long. We use the RATE function in a spreadsheet (for more details, see Spotlight 21.3 (page 888); entering gives a monthly rate of 0.2636%, for an effective annual rate of .

Now let’s consider instead the case of your mother retiring now, also at age 65 and also with a $250,000 life income annuity; she would receive $5.9010 per month for every $1000, or $1475 per month. Her life expectancy would be about 19.72 years = 237 months. If she lived exactly that long, she would receive a total of . The rate of interest that her annuity would need to earn to last that long can be calculated from the amortization formula; using gives a monthly rate of 0.2997%, for an effective annual rate of 3.66%. The difference between this rate and the one for your father probably reflects the fact that the company uses life expectancies (which vary by region of the country) that differ from those for the nation as a whole.

Notice that a man and a woman who save the same amount receive different monthly incomes at retirement: The woman receives less per month but for longer—93% as much for 16% longer. Yet their living expenses are likely to be the same. That consideration has resulted in some companies offering “merged gender” rate schedules for annuity payments, so that the individual receives the same monthly payment regardless of gender.