Work done in this assignment will be assessed against Criterion A,B,C,D, and F. While graphing technology may be helpful, the use of technology is not specifically required, nor will it be assessed.

- Mr. Santowski and his brother finish school and have started their first full-time jobs (my brother is a carpenter and I am a lab technician.) My brother has decided that he will start putting $100/month away in a Retirement Plan. I think that my brother is foolish because he is only 22 and he should enjoy his money now and worry about saving for retirement later, when he is older. Mr. Santowski is not going to worry about saving money until he is 45.

(a) Draw a timeline showing my brother’s retirement investment.

(b) List the first 6 terms of the sequence that represents my brother’s monthly retirement investment.

(c) Determine the equation of the general term of the sequence.

(d) List the first 6 terms of the series that represents my brother’s retirement investment.

(e) Prepare a graph showing my brother’s investment (you may want to use graphing technology to generate this graph.)

(f) Suppose both my brother and I retire at age 65. How much money will I have to contribute monthly, so that I can retire with the same amount of savings as my brother? Assume that the retire plan investment earns 9% compounded monthly. Present your response to this question in an algebraic method as well as a graphic method (for which again you may want to use graphing technology.)

(g) Write a convincing argument supporting either my investment strategy or my brother’s investment strategy.

- Mr.
Santowski has decided to set aside some money every month in an education
fund for his children. My oldest son, Alexander, was born on the 30
^{th}of October in 1998. Starting in November, I have contributed $125 every month into his education fund that yields 9.25% p.a. compounded monthly. I anticipate that Alexander will go to college in September of his eighteenth year. So, when he starts college in a 4 year program, I want to know how much money this education fund will give him every month, assuming that the fund will have zero balance when he finishes his fourth year.

(a) Draw a timeline showing the growth of Alexander’s education investment.

(b) Draw a timeline showing the decline of the investment given Alexander’s monthly allowance from the education investment.

(h) List the first 6 terms of the sequence that represents Alexander’s education investment.

(i) Determine the equation of the general term of this sequence.

(j) List the first 6 terms of the sequence that represents Alexander’s monthly allowance from the education investment.

(k) Determine the equation of the general term of this sequence.

(l) Prepare a graph showing the growth of Alexander’s education investment and showing the decline of the education investment given Alexander’s monthly allowance (you may want to use graphing technology to generate this graph.)

- My sister owns a company that is considering whether or not to develop a mining property. She estimates that an immediate expenditure of $7,000,000 will be needed to bring the property into production. After that, the net cash inflow will be $1,000,000 every 6 months for the next ten years. An additional expenditure of $3,200,000 at the end of 11 years will have to be made to restore the property to comply with government environmental policies. On projects of this type, my sister would expect to earn at least 20% per annum, compounded semi-annually on its capital. Advise my sister’s company whether they should proceed. Include all assumptions and include algebraic support for all monetary values you use in your report1

.