Compound Interest

*** This lesson was written by me as an assignment for C-I 304. I actually taught the "Hook" portion of the lesson to my classmates.

Compound Interest and Exponential Growth

General Info:    9th grade algebra class, 90 minute period, Exponents and Powers unit,
                            second lesson of the unit. Students have already studied compound interest.

Materials:    Newspapers, magazines, financial brochures, calculators, large sheets of graph paper, markers

Objectives:    The students will know how to calculate compound interest formulas.  They will be able to construct                         a graphic representation of exponential growth.

Standards:    F.12.2 Use mathematical functions* (e.g., linear*, exponential*, quadratic*, power) in a variety of                             ways, including:

                        -Recognizing that a variety of mathematical and real-world phenomena can be modeled* by the                                 same type of function
                        -Translating different forms of representing them (e.g., tables, graphs, functional notation*, formulas)
                        -Describing the relationships among variable quantities in a problem
                        -Using appropriate technology to interpret properties of their graphical representations (e.g.,                                         intercepts, slopes, rates of change, changes in rates of change, maximum*, minimum*)

Hook:        Explain the housesitting problem to students. You are housesitting for your rich neighbor.  Lay out                         both payment plans for students.  Ask students to choose a plan.  Ask two or three students to explain                     their choices.  Call on a couple of students if no one volunteers.  Go through the calculation of the                         second payment plan with the class.  The students will see the difference between exponential growth                     and constant increase. (10 minutes, approximate time for each activity will be in parentheses)

Activities:    Compound interest project.  Newspapers and other sources will be laid out on a table somewhere in                         the room.
                   
                    -Students will number off and get into groups of three. (2)
                    -One student will pick up a large sheet of graph paper and some markers for his/her group. (3)
                    -The other two group members will select a couple of sources to research interest rates from.                                         (occurring at same time as above activity)
                    -Students will find three different interest rates for things like mortgages, car loans, credit cards,                                     savings, etc. (15)
                    -Students will then inform the teacher of what kind of rates they found (i.e. savings, mortgage). (5)
                    -The teacher will give them a dollar amount for each, and students will calculate the growth of that                             amount over a 10-year period. (10)
                    -Each year will be calculated, and students will plot points and graph their results on the graph paper.                          The teacher will be walking around the room, answering questions and helping them locate the                             interest rates if necessary. (10)

Assessment:    The graphs made by the students will show the students’ understanding of compound interest.                                  They will also reflect the students’ knowledge of exponents.  The students will also give a brief oral                         presentation about their graphs.  They will be asked to discuss their experiences with the rest of the                         class.  The teacher will ask questions of each group member during the presentation.  Some                                     possible questions include: Where did you find your rate? Can you think of any other kinds of rates                         that could be used? What is the importance of paying your bills right away (if a credit card)? Why                         should you begin saving money early (if a savings rate)? Is there an easier way of illustrating the                             growth? Does the amount of money involved affect the shape or growth of the graph?  Other                                 questions will be asked by the teacher based on the students work.  Students will be assessed on the                         following conditions: explanation during oral presentation, individual participation, neatness, and                             accuracy.  The primary emphasis will be on the explanations of the graphs. (30 min.)

Closure:        With approximately five minutes left in the period, the students will put away their materials and                             come together as a large group. The main ideas of compound interest will be repeated by the                                 teacher.  The teacher will also reinforce the ideas of exponential growth vs