Question

3) Now you will plan for your retirement. To do this we need to first determine a couple of values.

a. How much will you invest each year? **$1,000 a year is
what i will invest.**

State what you will use for P, r, and n to earn credit. ( 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: http://en.wikipedia.org/wiki/Individual_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 financial 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 from t = 0 to t = 50. (6 points)

d. When do you want to retire? **i want to retire at age
65.** 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)

f. 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 inflation (which is about 2% a year). (5 points) Let’s look at this from the other direction then, supposing that you wanted to have $50,000 a year after 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 first compute the effective 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 $50,000, 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 (j) again. You need to state what you would want to live on and it needs to be something besides $50,000. (10 points)

Answer #1

1(a) P = The amount that will be invested, r = rate of interest, t= Time period.

(b) The future value will be = (1.08)^{15}*1000 =
3172.1691.

The P = 1000, r = 8% & t = 15.

(d) The same equation will be used as used in (b). So everything will be the same & just that we need to find out 't' & keep all the values unchanged.

(e) Keeping the equations same as in above, the value that we will have at the retirement will be = 3172.1691

(f) Interest in that part is = (3172-1000)/3172 = 68%.

(g)

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