The College Fund Savings Problem

Barbara Carstensen Deon Hickey Tom Dahlquist

John McMahan John Roberts Margaret Sanders

Class: Algebra II

Goals: This project should show the student the power of compound interest. It will allow the student to set up a table to model the answer and suggest patterns for a geometric sequence and series.

Time Required: Five days. The student will need to do research for some of the information. Parts of three class days should be allowed to: present the problem, monitor student progress, present solutions.

Background: A student should have knowledge of exponents and calculating simple interest. A student should be competent in the use of spreadsheets such as Lotus 123 or Excel.

Setting: Given a fixed interest rate, the student will find the amount of money to invest each year to raise the amount of money needed for four years of college. The student will do this without annuity formula.

Problem: Imagine that your parents were transported forward in time to the present day (Back to the Future I, II, or III?), and the only thing your parents found out was the yearly cost of a college education at any American school. Suppose your parents then decided when you were born that they would invest a certain amount of money each year for your college education. Assume that the average rate of interest for the investment is 8% annual interest rate. How much money should your parents invest each year to pay for your college education? Use the spreadsheet and Atrial and error@ to find solution.

1) Each group will choose a college to attend. The group needs to find the estimated cost to attend the college for four years. The groups will need to calculate how much the "parents" will have had to invest each year since your birth to finance the four years of college.

2) Each group will construct a chart using a spreadsheet to indicate the growth of the college fund from year 0 to year 21. The following headings should be on the chart.

 Year Beginning Balance Interest Amount Invested by Year Ending Balance Interest Rate Yearly College Cost

3) Each group will construct a graph based on the year and the ending balance on the spreadsheet.

4) Each group will give an oral presentation to the class about their findings and what assumptions they made.

5) After class discussion, each individual will write a paper about their impressions on the project. The paper should include the student=s thoughts about possible extensions to the project.

Sample Problem: Demonstrate in class how interest and total value of the investment can be tracked for a few steps.

Evaluation:

1) Chart (20%).

2) Graph (20%).

3) Neatness (15%)

4) Organization (15%).

5) Oral presentation (15%).

6) Follow-up paper (15%).

Extensions:

1) What if the interest is compounded at a rate other than yearly?

2) What about investing in stocks?

3) Can you write a formula to predict what it will take to raise a certain amount of money?

4) What if the interest rates vary and are locked in for periods of time?

5) What if the parents chose to invest less each year at the beginning of the fund and more later?

6) How can you account for inflation in your calculations?

7) What about the students? How can they plan for their children's education not knowing the exact cost?

Teachers Notes:

The students should be aware that they will have to seek the information to solve the problem from outside sources (banks, library, investment services, guidance counselor, college chosen). A representative of a local investment firm may be a good follow-up speaker.

The College Fund Savings Problem

Student Work Sheet

Setting: Given a fixed interest rate the student will find the amount of money to invest each year to raise the amount of money needed for four years of college.

Problem: Imagine that your parents were transported forward in time to the present day (Back to the Future I, II, or III?) and the only thing your parents found out was the yearly cost of a college education at any American school. Suppose your parents then decided when you were born that they would invest a certain amount of money each year for your college education. Assume that the average rate of interest for the investment is 8% annual interest rate. How much money should your parents invest each year to pay for your college education?

1) Each group will choose a college to attend. The group needs to find the estimated cost to attend the college for four years. The groups will need to calculate how much the "parents" will have had to invest each year since the Achild=s@ birth to finance the four years of college.

2) Each group will construct a chart using a spreadsheet to indicate the growth of the college fund from year 0 to year 21. The following headings should be on the chart.

 Year Beginning Balance Interest Amount invested by year Ending Balance Interest Rate Yearly College Cost

3) Each group will construct a graph based on the year and the ending balance on the spreadsheet.

4) Each group will give an oral presentation to the class about their findings and what assumptions they made.

5) After class discussion, each individual will write a paper about their impressions on the project. The paper should include the students thoughts about possible extensions to the project.

Evaluation:

1) Chart (20%).

2) Graph (20%).

3) Neatness (15%)

4) Organization (15%).

5) Oral presentation (15%).

6) Follow-up paper (15%).

Funded in part by the National Science Foundation and Indiana University 1995