Question 241173: the annual social security benefit of a retiree depends on the age at the time of retirement. the accompanying graph gives the annual benefit for persons retiring at ages 62 through 70 in the year 2005 or later. What is the annual benefit for a person who retires at age 64? at what retirement age does a person recieve an annual benefit of $11,600? find the slope of each line segment on the graph and interpret your results.Why do people who postpone retirement until 70 years of age get get the highest benefit?
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You didn't provide the graph, so I can only answer your questions in either very general or procedural terms.
Look at the  value of the point on the graph where 
Look at the  value where  on the graph.
Write down the ordered pairs that represent the end points of each segment of the graph, (,) = (age, amount)
For each pair of endpoints that define a segment, use the slope formula to calculate the slope of that segment:
where
) and )
are the coordinates of the endpoints. The highest slopes give the greatest benefit for waiting that particular year.
People wait until 70 to draw their social security because they are betting that they will live long enough to accumulate more benefits than would accrue if you took the lower benefit earlier.
For example, if the annual benefit is 18000 at age 65 and the annual benefit is 24000 at age 70 and
You live to be 80 years old: You will accumulate 15 times $18,000 = $270,000 if you take the benefit at 65, but only 10 times 24,000 = $240,000 if you take the benefit at 70. So if you are only going to live to be 80, it is better to start taking the money earlier
At age 85, with the given amounts, you break even. That is, it doesn't matter which you do, so you might as well enjoy the additional years of retirement -- leave early.
But if you are planning to live beyond age 85, you start to make money by delaying retirement to age 70.
John
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