EXAMPLE: If you invest $1200 every year (P = 1200) for 3 years (t=3) at an interest rate of 5% (r = 0.05) compounded weekly (n = 52), then the rst year's investment of $1200 would earn interest for 3 years. but then the next year, the next investment of $1200 would only earn interest for 2 years, and then the nal investment of $1200 would only earn interest for 1 year. This lends itself to the following: 52 52(3) Doing] 1[1+%] 52 52 = $3,981.74- CO) = You have to be sure not to round until the very end where you round to the nearest cent. (80 be sure to keep as many decimal places as possible until the end, as you will be taken off for rounding before then.) For more information about round-off errors click on the link: hgu'lmathworld.wolframcomlRoundoffErrorhtml Your answers should be typed and in a single document. If you would like to attach your work, scan it and add it to the end of your typed document. You can either attach a Word le or a pdf le. Many word processing programs will save a document as a pdf le if you select Save as and look for file types. 1) How much will you have accumulated over a period of 30 years if, in an IRA which has a 11% interest rate compounded monthly, you annually invest: a. $1 b. $3000 c. $8,000 d. Part (a) is called the eizctive yield of an account. How could Part (a) be used to determine Parts (b) and (c)? (Your answer should be in complete sentences free of grammar, spelling, and punctuation mistakes.) (Total of 15 points) 2) How much will you have accumulated, if you annually invest $2500 into an IRA at 10% interest compounded quarterly for: a. 5 year b. 10 years c. 40 years d. How long will it take to earn your rst million dollars? Your answer should be exact rounded within 2 decimal places. Please use logarithms to solve. (Total of 15 points) 3) Now you will plan for your retirement. To do this we need to rst determine a couple of values. a. How much will you invest each year? Even $25 a month is a start ($3 00 a year), you'll be surprised at how much it will earn. You can choose a number you think you can a'ord on your life circumstances or you can dream big. State what you will use for P, r, and n to earn credit. (3 points) The typical example of a retirement investment is an I.R.A., an Individual Retirement Account, although other options are available. However, for this example, we will assume that you are investing in an I.R.A. (for more information see: hpenwikipediaorgfwikindividual Retirement Account } earning 8% interest compounded annually. (This is a good estimate, basically, hope for 10%, but expect 8%. But again this is just one example; I would see a nancial advisor before investing, as there is some risk involved, which explains the higher interest rates.) List your P, r, and n to earn points for this question. b. Determine the formula for the accumulated amount that you will have saved for retirement as a function of time and be sure to simplify it as much as possible. You need to be able to show me what you used for r, n, and P so that I can calculate your answers. Plug in those values into the formula and simplify the equation. (5 points) c. Graph this function 'om t = 0 to t = 50. (6 points) Ways to show graphs: 0 Excel 0 Hand draw, take a pic with phone and import it into your document as a picture. 0 Online graphing calculator program (try googling free graphing calculators or use one listed in the Tech websites om Module 1) d. When do you want to retire? Use this to determine how many years you will be investing. (65 years old is a good retirement-age estimate). You need to say how old you are if you are retiring when you are 65 or tell me how long until you retire. State what you will use for t. (2 points) e. Determine how much you will have at retirement using the values you decided upon above. (5 points) 1'. How much of that is interest? (4 points) g. Now let's say you wait just 5 years before you start saving for retirement, how much will that cost you in interest? How about 10 years? How about just 1 year? (10 points) Now you need to consider if that is enough. If you live to be 90 years old, well above average, then from the time you retire, to the time you are 90, you will have to live on what you have in retirement (not including social security). So if you retired at 65, you will have another 25 years where your retirement funds have to last. h. Determine how much you will have to live on each year. Note, we are neither taking into account taxes nor ination (which is about 2% a year). (5 points) Let's look at this -om the other direction then, supposing that you wanted to have $35,000 a year aer retirement. i. How much would you need to have accumulated before retirement? (5 points} j. How much would you need to start investing each year, beginning right now, to accumulate this amount? A "short-cut" to doing this is to rst compute the efective yield at your retirement age, then divide this amount into Part (i). This is the amount you well need to invest each year. (5 points) k. That was just using $35,000, how much would you want to have each year to live on? Dream big or reasonable depending on your occupation! Now using that value, repeat parts (i) and 0) again. You need to state what you would want to live on and it needs to be something besides $35,000. (10 points)