# Engaging students: Compound interest

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Daniel Littleton. His topic, from Precalculus: compound interest.

How has this topic appeared in the news?

In a publication entitled Business Insider, Sam Ro published an article entitled “Every 25 Year Old In America Should See This Chart” on March 21, 2014. In this article Ro stated that in past times companies would offer pension plans to long term employees in order to support them in retirement. He goes on to state that in modern times employees need to contribute to retirement plans such as a 401K or an IRA in order to save for retirement. These plans function by the mathematical principle of compound interest. While the mechanics of compound interest are not presented in the article an illustration is shown how individuals who save their money through this formula accumulate a greater amount of money over time. He even presents a situation in which one individual can save money for a less amount of time than another and still accrue a greater total amount of savings because of compound interest. This illustration, presented below, can be a useful tool in engaging students in the possibilities that compound interest could have in their own futures.

This information was collected from the following web page on Friday, April 04, 2014; http://www.businessinsider.com/compound-interest-retirement-funds-2014-3.

How can this topic be used in your students’ future courses in mathematics or science?

Compound interest is introduced at the Pre-Calculus level of secondary education. At the Post-Secondary Education level compound interest is a concept that is included in several areas of study. For example, students that wish to study business will need to have a mastery of compound interest. Additionally, those studying finance or economics will constantly use the principle of compound interest in their computations. Not only does this formula come into play in the mathematics of monetary systems, but also in the workings of political science as well. Those that wish to pursue political aspirations will need a firm understanding of economics and the means by which funds can be grown over time. As is evident, compound interest is a mathematical formula, but like many realms of mathematics it affects multiple realms of interest and practice in a real world environment.

What interesting word problems using this topic can your students do now?

There are an innumerable amount of problems that can be presented to students involving compound interest. One could deal with the monetary worth of valuable or precious items. For instance, “A necklace is appraised at \$7200. If the value of the necklace has increased at an annual rate of 7.2%, how much was it worth 15 years ago?” This question is asking the student to solve for the original principle of the necklace, rather than the accrued value which is given. Another problem could be “A sum of \$7000 is invested at an interest rate of 7% per year. Find the time required for the money to double if the interest is compounded quarterly.” This problem requires the student to determine the amount of time necessary for the investment to yield the desired amount. These are only two problems that I have presented that will allow the students to practice the concept of compound interest. There are undoubtedly multiple others that could be written with the same effect.

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