Social Security and Life Expectancy
The average annual Social Security benefit in 2009 was about $13,800. The amount of a retiree's benefit depends on the retiree's lifetime earnings, the person's full retirement age, and the age at the time of retirement. The following function gives the annual6 benefit in dollars for a person retiring in 2009 at ages 62 through 70 with a full retirement benefit of $12,000 at full retirement age of 66.
B = {600a - 28,200 62 ≤ a <64
804a - 41,064 64≤ a <67
960a - 51,360 67 ≤ a ≤ 70
a) Graph the benefit function.
b) What is the annual benefit for a person who retires at age 64?
c) At what age does a person receive an annual benefit of $14,880?
d) What is the average rate of change of the benefit for the ages 62 through 63? Ages 64 through 66? Ages 66 through 70?
e) Do the answers to part (d) appear in the annual benefit formula?
The life expectancy L for a U.S. white male with present age a can be modeled by the formula L = 67.0166(1.00308)a.
f) Bob is a white male retiring in 2009 at age 62. What total amount can he be expected to draw from Social Security before he dies? Figure his Social Security benefit using the formula given above.