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StyleBox[" YOUR RETIREMENT PROGRAM\n ",
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"AN INVESTIGATION INTO YOUR FINANCIAL FUTURE\n \t\t\t\t\t\t\t\t\t\t\t\t\t\t\
\t\t\t\t\t\t\t BY\n \t\t\t\t\t\t\t\t\t\t\t\t\t\t JAMES S. KRALIK\n \t\t\t\t\
\t\t\t\t\t\t\t\t\tWESTVILLE HIGH SCHOOL\n \t\t\t\t\t\t\t\t\t\t\t\t\t\t \
WESTVILLE, ILLINOIS ",
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"Recall that the expression \"bn\" (read \"b to the nth power\") represents \
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"We can apply the concept of exponentiation to the subject of interest \
rates and return on investment. Suppose a person deposits $1000.00 (the \
principal) in a bank that pays interest at an annual rate of 4%. Assuming \
that no money is withdrawn during the course of a year, at the end of the \
year the amount of money in the account will be:\n1000 + .04(1000) = \
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that to find the amount of money in the account at the end of one year, you \
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"\n = 1081.60\nAgain, notice that we did not have to calculate the \
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amount of money in the account after ",
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" times. \n\nThis leads us to a simple form of the compound (\"interest \
on interest\") interest formula. Let P be the amount of money invested at an \
annual interest rate of r, compounded annually. Let A be the total amount \
after t years. Then:\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t",
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"The Individual Retirement Account is one of the best investments available \
today. Your annual contributions ($2000.00 per year maximum for an \
individual) are tax deductible in most cases, and your investment earnings \
are allowed to accumulate tax free until you begin to withdraw your money \
when you retire. This is a tremendously powerful program that is worth \
investigating."], "Text",
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"When trying to see into the future and making projections about the value of \
an investment twenty or thirty years from now, the assumptions that you make \
about your investment at the beginning will determine the projected value of \
your account when you retire. Your assumptions generally fall into one of \
three categories: 1) the amount of your annual contribution; 2) the rate of \
return, or interest rate, of your investment; and 3) the conditions, or \
terms, of your investment, such as how often the interest on your investment \
is compounded. "], "Text",
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"For example, if you assume that you will put away $10,000.00 each year for \
twenty years and that your rate of return is 15% per year, you will have over \
ONE MILLION DOLLARS at the end of twenty years. "], "Text",
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"Sounds real good! But, ask yourself, \"Self, how realistic is this \
projection?\" Will you really be able to sock away ten thousand dollars each \
and every year? Is a 15% rate of return a realistic assumption in this day \
and age? During the early eighties, a lot of investments were sold because \
salesmen were able to show some very attractive projections based on 12-18% \
rates of return. Needless to say, in these days of 3% savings accounts, a \
lot of these invest-\nments have shown some disappointing results. So, if \
you really want a realistics projection of how much money you will have, \
start with some realistic assumptions!"], "Text",
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"Let's make our first projection of your IRA. We'll need some assumptions. \
Let's assume that you partied all through your twenties, and spent every \
dime you earned. How much did you party? ",
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". Let's just say that you did your share to fuel the nation's economic \
recovery. But you are thirty now, and it's time to get serious. Let's \
assume that you will manage to make the maximum allowable contribution, $2000 \
for an individual. What will you invest in? A good choice for many people \
is a stock market mutual fund that attempts to match the performance of the \
stock market. The average annual rate of return of the stock market for the \
last fifty years has been 10%. So let's be conservative and assume an annual \
rate of return of 8%. How much money will you have when you retire at the \
age of 65? ",
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"Think about what is happening. The first year, you put in $2000. That \
$2000 will give an 8% rate of return, compounded annually for 35 years. So, \
according to our formula, the total amount A for that ",
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"So the total return of the second $2000 will be added to the total return \
of the first $2000, and the total return of the third $2000 will be added to \
that, and so on. Well, we can automate that quite easily with ",
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"The first line cleared our variables. The second line defined our \
function. The third line added all of my totals for ",
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" years. Line four specifies n to be 35 (age 30 to age 65) and will \
display our annual cumulative totals. The following line will display the \
output in a pretty table:",
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"This may be pretty, but we don't need it to plot our results. Let's plot t \
and give our plot a name."], "Text",
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"\na=ListPlot[t,Prolog->PointSize[.01],\nAxesLabel->{\"Age\",\"Dollars\"},\n\
Epilog->Text[\"[a]\",{62,350000}]] "], "Input",
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"This is a pleasant looking graph that shows a nice, steady growth. So it \
looks like you will have a good deal of money when you hit 65. Let's compare \
this growth with the amount of money you actually contributed."], "Text",
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"A different kind of growth. Let's look at a and b together."], "Text",
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"Write a few paragraphs about the growth of your retirement fund. Some of \
the points you should address are:\n-What kind of growth does your retirement \
fund have? What kind of growth does the plot of your annual contributions \
have?\n-During what years do the plots seem to run together? About what year \
do the plots begin to diverge and your IRA really begins to take off? What \
is the reason for this?\n-What were your total annual contributions? What \
was the total value of your IRA at age 65? What is the difference between \
these two figures? What is the source of that difference? Are you suprised \
at the amount of money that you will have at age 65?\n-Comment about the \
relative importance of the annual contributions versus the annual interest \
earned through the years. For example, was your annual contribution at age \
60 as important as your annual contribution at age 30? Why? \n-What \
conclusions can you draw from this example?\n-Finally, at age 65, do you \
think that your relatives would be nicer to you if they knew that you had \
this much money? "], "Text",
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" difference if we start early? For instance, does it matter a whole lot \
if we start our IRA at age 21 instead of age 30? Try it out. Assume that \
you will begin your IRA at age 21, that you will contribute $2000 each year \
to age 64 (By the way, is this a reasonable assumption?), and that your \
annual rate of return will be 8%. Write a program and produce a table that \
shows the growth of your IRA each year until retirement. Plot your results \
and call your plot \"c\". Make another plot comparing the results starting \
at age 21 and starting at age 30. Finally, write a paragraph in which you \
describe your conclusions.",
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"First, clear some variables. Next, some make some minor changes to the \
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"Here's an interesting assumption to make. Suppose that you began your IRA \
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of return of 8%. You make your annual contributions for ten years, and then \
stop. You never put another cent into your IRA for the rest of your life. \
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plot \"d\". Next, make a table and plot that describes the growth of your \
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"Hey! What's going on here? In our scenario beginning with age thirty, we \
made total annual contributions of $70,000. In our new scenario, what was \
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other? How could this be? Please write a few paragraphs describing the two \
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able to save more (or less) than that, and there are other investments \
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could do better (or worse!) than eight percent?\n\nFor your projection, \
produce a table showing the value of your account each year until age 65, and \
a plot of those values. Do a comparison plot of your annual contributions \
only. \n\nFinally, write a few final paragraphs describing any final \
thoughts or conclusions you have about this lesson. In particular, talk \
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