Mathematics: Credit Cards as an Application of Exponential Equations

Title: The Mathematics of Credit Cards (as an application of exponential equations)
Discipline(s) or Field(s): Mathematics
Authors: Kirthi Premadasa, Paul Martin, Clare Hemenway, University of Wisconsin-Marathon County
Submission Date: December 14, 2008

Goals of the lesson:

  1. Students will learn how to make basic interest calculations, when calculating the monthly payments and the monthly interest charges on credit card balances.
  2. Students will learn what “amortization” means and will learn to fill in an amortization table.
  3. Students will use logarithms to solve the exponential equations encountered in the calculations of the payment periods for different payment methods.
  4. Students will develop an insight to the advantages and the disadvantages of the different payment methods.

Mathematics: Simple and Compound Interest in Investment Contexts

Title: Simple and Compound Interest in Investment Contexts
Discipline(s) or Field(s): Mathematics
Authors: Kathryn Ernie, Laurel Langford, and Erick Hofacker, University of Wisconsin-River Falls
Submission Date: March 2, 2009

Executive Summary

Our main goal for this lesson is for students to understand the difference between simple interest and compound annual interest. Prerequisite to understanding these concepts is the understanding of the mathematics concepts of rate (interest rate) and percents. A related goal is the recognition of the additive nature of simple interest providing a linear rate of growth (additive sequence) and the multiplicative nature of compound interest providing an exponential rate of growth (geometric sequence). Included in our goals is the ability to represent these relationships in numeric, tabular, and graphical forms.

Part of the rationale for this project defined in the fall of 2007 was the recent home foreclosures problem in the U.S. (indicating that individuals did not understand the mathematics perhaps of home loan agreements). Unfortunately, the impact of the foreclosure crises was felt even more strongly a year later during our lesson study with the failure of numerous financial institutions and major losses in the stock market.

The recent national interest in financial literacy as it relates to citizens understanding rates, percents, investment, interest earned, and growth relate directly to this lesson study. This first lesson on the mathematics of financial literacy is on simple interest earned in contrast to compound interest earned annually.

The investment context first introduced was the additive application of simple interest. Students represented an investment in numeric and tabular form and extended the data by working in small groups using a calculator. This data was also analyzed using its graphical form. The compound interest earned (exponential rate of growth) was studied in the same fashion by small groups of students. Students made longer term predictions as to which form of investment would be best over time. Excel was used to investigate further the impact of longer term investments in contrast to each other. These activities were at an appropriate level and resulted in students analyzing differences between the two types of interest earned both numerically and graphically. By the end of the lesson, students readily recognized the type of interest earned directly from only a graphical representation.

Below are links to the lesson plan materials used to teach it.

Handouts for Activities
All 3 handouts are linked here.

Excel Examples

Excel examples from the lesson with graphs.

Bonds and Prices
 Link to current source of bonds.

CDs and Pricing
 Link to current source of CDs.

Below are links related to the study of the lesson.

Field Notes
 Observation notes on the lesson.

Student Responses
 Sample student work and summary

Assignment and Solutions