Algebra represents some peoples' fondest memories of high school-and for
others, it goes down in personal history as the one activity that tuned them
out on math forever. But algebra offers instant help with an issue nearly
everyone needs to think about-personal finances. For an example, let's use
algebra to figure the age at which you should begin withdrawing Social
Security.
Social security remains a popular-yet always-controversial-government
program. When President Franklin Delano Roosevelt created it during the Great
Depression, critics accused him of moving the country toward socialism. Today, though
it remains a surefire issue with voters, it's also perennially up for reform. Policy
experts propose abolishing it, turning part of it over to private investment,
raising the retirement age required to collect it, reducing some Americans'
eligibility for it, or simply leaving it alone.
But in any case, despite gloomy predictions of a few years ago, it looks
like Social Security will be around for awhile. That means most of us need to
think about when to start collecting benefits-age 62 or 66.
After all, according to current law, you (or your grandpa) will be eligible
for benefits by the age of sixty-two. But that monthly check will get bigger if
you wait until age sixty-six to start withdrawing from the system to which
you've been contributing during your entire working life. Perhaps, thinking of
your grandchildren, you'd like to know how long you'll have to live to make it
more profitable to wait until age sixty-six to start taking payments. (For much
of this information, by the way, the author is indebted to the PUMAS [Practical
Uses of Math and Science] home page, maintained by NASA and the California
Institute of Technology.)
If you've been studying your algebra, however, you can figure this problem
simply. If you begin collecting social security at age sixty-two, the amount
you can draw will be reduced by twenty percent (20%). So simply turn the
problem into an equation. Let a represent
your age and b your social security
income per year. If you retire at age sixty-two, because of that twenty percent
penalty, your total earnings in any given year can be represented like this:
0.8b (a-62). (By the way, if you've already forgotten your algebra,
simply remember that 0.8b is another
way of saying "0.8 times b"; putting
the whole shebang next to another number in parentheses-as we've done
here-simply means that you multiply the number within the parentheses by the
0.8b.)
Why the 0.8 times b? Because,
given that twenty percent penalty, you'll get only eighty percent of b (100%-20%=80%), and 0.8 times any
number yields eighty percent of that number. So, if you begin withdrawing at
age sixty-two, it's 0.8b (a-62), with a indicating, again, your age.
Meanwhile, if you wait until age sixty-six to begin drawing your benefits,
your equation looks like this: b(a-65). In other words, b times your age minus sixty-five.
So, to find out at what age things even out-the age that, if you live past
it, it becomes more profitable to start withdrawing social security money at
age sixty-five-you posit that these two equations are equal to each other, and
you solve from there:
0.8b(a-62) = b(a-65)
Anyone who remembers middle-school algebra knows the first step to take:
simplify the equation by dividing y from
both sides. That gives us 0.8(a-62) =
a-65.
If we then solve for a, we find
ourselves with the solution 77. In other words, if you (or grandpa) think you
can live past age seventy-seven, then
at that point the earnings you get by waiting until you're sixty-five surpass
the earnings you'd get by beginning at sixty-two. So you're better off waiting
until you're sixty-five to begin withdrawing that social security money.
But these equations aren't just useful for people who are figuring their
future social security income. Algebra is useful for young children whose
parents may decide to apply the same delayed-gratification logic to their
allowances. Let's say that your parents decide that you can have twenty dollars
a week now-or thirty dollars a week if you can wait until a year from now,
while the money they would've given you sits in a savings account. Do the math!
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