Predicting Your Financial Future

The activity involves comparing what happens to a principal amount of money when interest is compounded. The students are able to adjust the interest rate, time period, compounding periods, and whether it is increasing (savings) or decreasing (debt). There are also some static questions included to guide the students. This might be used as an introductory activity in an Algebra 2 course, but it is more appropriately designed for Algebra 1.

Weblink address (URL): 
Predicting Your Financial Future

Standards & Objectives

Learning objectives: 

Students will:

  • Determine the future value of an investment using the formula A = P(1 + r/n)nt.
  • Decide how much to invest to guarantee a future amount.
  • Realize how damaging carrying credit card debt can become, even when making the monthly minimum payment.
Essential and guiding questions: 
  • For invested money, is the growth linear or expontential?
  • Which is more important, the amount invested or the interest rate?

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 
  • A well known formula for calculating the doubling time of an investment is 72/interest rate. This tells us the number of years it will take for an investment to double its value if interest is compounded yearly. If interest is compounded quarterly, then divide the result by 4, and so on. Have students use the simulator and calculate the doubling time for an investment of $1,000 with no monthly contributions. Once that is done, have them change the investment amount to a different amount. The doubling time will remain the same. Tell them that the number 72 is related to this and challenge the class to explain why this doubling formula works regardless of the investment amount.
  • Fill out the following table, plot it, and then run a regression. This is a fun activity to do as a curve-fitting exercise. After some trial and error, students will observe that the correct regression to choose is the power regression. The exact equation for the fitted curve is f(x) = 70.76x–0.99, but an approximate equation is y = 72/x, hence the name “The Rule of 72.” To get better results, more data points are needed. The equation above was arrived at using 4 data points. If a unit on statistics is going to be covered next, this would be a great time to introduce the concept of sample size. The larger the sample, the closer the results mimic the expected value. This is also known as the law of large numbers.

Helpful Hints

Material:

  • Calculator
  • Computer with Internet connection
  • Savings Account Activity Sheet 
  • Credit Card Activity Sheet 

References

Contributors: 
Eric Istre
Originator: 
Ayers Institute for Learning & Innovation