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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 ", CellFrame->True, CellMargins->{{18, 144}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontFamily->"CalcMath", FontColor->GrayLevel[0.333333]] }], "Input", CellFrame->True, CellMargins->{{18, 144}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["The Basics"], "Section", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["Exponentiation"], "Subsection", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Recall that the expression \"bn\" (read \"b to the nth power\") represents \ an operation called exponentiation, or powering. The variable b is called \ the base, n is called the exponent, and the expression bn is called a power. \ So, \n53 = 5 x 5 x 5,\n(-1/2)4 = (-1/2)(-1/2)(-1/2)(-1/2),\n(1.05)2 = \ (1.05)(1.05),\nand, in general, bn is b multiplied by itself n times."], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["Compound Interest & Return on Investment"], "Subsection", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "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 Assuming \ that no money is withdrawn during the course of a year, at the end of the \ year the amount of money in the account will be:\n1000 + .04(1000) = \ 1000(1+.04)\n = 1000(1.04)\n = 1040\nNotice \ that to find the amount of money in the account at the end of one year, you \ did not have to add the interest to the principal. You simply could have \ multiplied the principal by 1.04.\n\nNow suppose you leave all of your money \ in for a second year. At the end of the second year you will have:\n\ 1040(1.04) = [1000(1.04)](1.04)\n = 1000[(1.04)(1.04)]\n = \ 1000(1.04)", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["2", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontVariations->{"CompatibilityType"->"Superscript"}], StyleBox[ "\n = 1081.60\nAgain, notice that we did not have to calculate the \ interest separately and add it to the principal. We can simply calculate the \ amount of money in the account after ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["n", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" years by multiplying the principal by 1.04 ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["n", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " 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", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["A=P(1+r)", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontWeight->"Bold"], StyleBox["t", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontWeight->"Bold", FontVariations->{"CompatibilityType"->"Superscript"}] }], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True]}, Open]]}, Open]], Cell[CellGroupData[{Cell[TextData["The Individual Retirement Account"], "Section", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "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", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["Assumptions"], "Subsection", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "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", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "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", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "f[x_]:=10000*1.15^x\nz=Sum[f[x], {x,1,n}];\nt=Table[{30+n, \ z},{n,1,20}]//Round"], "Input", AspectRatioFixed->True], Cell[TextData[ "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", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["Your IRA"], "Subsection", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[{ StyleBox[ "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? ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["A LOT", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontWeight->"Bold"], StyleBox[ ". 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? ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["Answer"], "Subsubsection", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "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 ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["first", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" $2000 will be:", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData["2000(1.08^35)"], "Input", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[{ StyleBox["The next year (age 31) we put in $2000, and that ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["second", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[" $2000 will return 8%, compounded annually, for 34 years. ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData["2000(1.08^34)"], "Input", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "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 ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["Mathematica.", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontSlant->"Italic"] }], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Clear[f,x,v,t]\nf[x_]:=2000*1.08^x\nv=Sum[f[x], {x,1,n}];\nt=Table[{30+n, \ v},{n,1,35}]//Round"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "The first line cleared our variables. The second line defined our \ function. The third line added all of my totals for ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["n", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " 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:", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData["t//TableForm"], "Input", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "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", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "\na=ListPlot[t,Prolog->PointSize[.01],\nAxesLabel->{\"Age\",\"Dollars\"},\n\ Epilog->Text[\"[a]\",{62,350000}]] "], "Input", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "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", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Clear[v]\ng[v_]:=2000+2000*v\ns=Table[{30+v, g[v]},{v,0,34}]"], "Input", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "b=ListPlot[s, AxesLabel->{\"Age\", \"Dollars\"}, \n\t\ Epilog->Text[\"[b]\",{60,100000}],\n\tPlotRange->{0,360000}]"], "Input", AspectRatioFixed->True], Cell[TextData[ "A different kind of growth. Let's look at a and b together."], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData["Show[a,b]"], "Input", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData["Well! Put in a little, get a lot!"], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True]}, Open]]}, Open]]}, Open]], Cell[CellGroupData[{Cell[TextData["What Do You Think?"], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "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", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True]}, Open]]}, Open]], Cell[CellGroupData[{Cell[TextData["Starting Early"], "Section", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[{ StyleBox["Does it make a ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], StyleBox["big", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " 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.", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[{ StyleBox["Answer:\n", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True, FontWeight->"Bold", FontColor->GrayLevel[0.333333]], StyleBox[ "First, clear some variables. Next, some make some minor changes to the \ function we used before. ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData["Your code should look something like this: "], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "Clear[f,x,c,p,w,n]\nf[x_]:=2000*1.08^x\np=Sum[f[x], {x,1,n}];\n\ w=Table[{21+n, p}, {n,1,44}]//Round"], "Input", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "c=ListPlot[w, Prolog->PointSize[.015], \n\tAxesLabel->{\"Age\", \ \"Dollars\"}, \n\tEpilog->Text[\"[c]\", {60,650000}], \n\t\ AxesOrigin->{21,0}]"], "Input", AspectRatioFixed->True], Cell[TextData["Show[c,a]"], "Input", AspectRatioFixed->True], Cell[TextData[ "Well, what do you think? Is the difference between the two totals at age 65 \ enough to make you want to start early? Why or why not?"], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True]}, Open]]}, Open]]}, Open]], Cell[CellGroupData[{Cell[TextData["The Power Of Compound Interest"], "Section", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[ "Here's an interesting assumption to make. Suppose that you began your IRA \ at age 21. You make annual contributions of $2000.00 each year, with a rate \ 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. \ However, you leave your IRA alone, and allow your balance to grow to age 65. \ How much money will you have when you retire? \n\nMake a table and a plot \ that describes the growth of your account for the first ten years. Call you \ plot \"d\". Next, make a table and plot that describes the growth of your \ IRA from 31 to 65. Call this plot \"e\". Show[d,e] and name this plot \ \"f\". Finally, Show[f,a]. Compare your results. Write a few paragraphs \ describing your conclusions from this example."], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[{ StyleBox["Answer\n", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->GrayLevel[0.333333]], StyleBox[ "First, use your function to calculate your growth during the ten years you \ will make an annual contribution. Then, multiply that balance by 1.08 to the \ 34th power. ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True] }], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["Your code looks like this:"], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox[ "Clear[f,x,d,e,f,p,q,r,s,n]\nf[x_]:=2000*1.08^x\nq=Sum[f[x], {x,1,n}];\n\ r=Table[{21+n, q}, {n,1,10}]//Round\n ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, AspectRatioFixed->True, FontColor->GrayLevel[0.333333]]], "Input", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[ "d=ListPlot[r, Prolog->PointSize[.015], \n\tAxesLabel->{\"Age\", \ \"Dollars\"}, \n\tEpilog->Text[\"[d]\", {30,35000}], \n\t\ AxesOrigin->{21,0}]"], "Input", AspectRatioFixed->True], Cell[TextData["s=Table[{31+p,31291*1.08^p},{p,1,34}]//Round"], "Input", AspectRatioFixed->True], Cell[TextData[ "e=ListPlot[s, Prolog->PointSize[.015], \n\tAxesLabel->{\"Age\", \ \"Dollars\"}, \n\tEpilog->Text[\"[e]\", {60,400000}], \n\tAxesOrigin->{21,0}] \ \n\t"], "Input", AspectRatioFixed->True], Cell[TextData["f=Show[e,d, Epilog->Text[\"[f]\", {60,400000}]]"], "Input", AspectRatioFixed->True], Cell[TextData["Show[f,a]"], "Input", AspectRatioFixed->True], Cell[TextData[ "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 \ the total of our annual contributions? Which scenario ourperformed the \ other? How could this be? Please write a few paragraphs describing the two \ scenarios, tell me what happened, and tell me what you think about all this. \ "], "Text", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True]}, Open]]}, Open]]}, Open]]}, Open]], Cell[CellGroupData[{Cell[TextData["Your Retirement Plan "], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "For your final project you will write a plan for your own retirement. \ Begin by writing down your assumptions, and describing your rational for \ those assumptions. For example, you don't have to limit yourself to a \ $2000.00 annual contribution to an IRA. You may decide that you would be \ able to save more (or less) than that, and there are other investments \ besides an IRA. You may feel that you might not be able to save very much \ fresh out of high school or college, but you would be able to increase your \ annual contributions in your thirties or forties. On the other hand, what \ about paying for a house, or supporting a family? Describe how you think you \ would balance the need to start saving early with the desire to buy things ", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True], StyleBox["now!", CellMargins->{{Inherited, 144}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " What about rates of return? Do you think you are an investment whiz who \ 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 \ about the likelihood that you will actually follow your plan. 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