Now you will plan for your retirement. To do this we need to first determine a couple of values. How much will you invest each year? Even $50 a month is a start ($600 a year), youll be surprised at how much it will earn. For this example, we will assume that you are investing in an I.R.A. earning 8% interest compounded annually.

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.

c. Graph this function from t=0 to t=50.

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)

e. Determine how much you will have at retirement using the values you decided upon above.

f. How much of that is interest?

g. Now lets 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? 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). Lets look at this from the other direction then, supposing that you wanted to have $75,000 a year after retirement.

i. j. k. How much would you need to have accumulated before retirement? 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 will need to invest each year. That was just using $75,000, how much would you want to have each year to live on? Now using that value, repeat parts (i) and (j) again. Your answer to (k) would work, if you withdrew all of your retirement funds at once and divided it up. However, if you left the money in the account and let it draw interest, it is possible that the interest itself would be enough to live on, or at the very least if you had to withdraw some of the principle, the remaining portion would still continue to earn interest. Essentially, what you have found is the upper bound for the amount of money that you well need to invest each year to attain your financial goals

Please DO NOT REPLY if you're not going to provide a FULL answer to a-k. I'm really struggling and need a COMPLETE answer that touches on ALL points a-k. Please please help me out and give me a full and complete thought out steps to ALL of the points. I've posted a couple times and only gotten the same partial response. I'm really bad at math and can't work through on my own with just a partial help. I need a full walk through of all points. Thanks.