Why do investing fees matter? In this Desmos activity, students analyze how fees impact the exponential growth of investments over time. See how Desmos helps students visualize that impact and connect it to changing the growth factor in an exponential function. 

DESMOS: The Impact of Investing Fees on Exponential Growth is a part of the first lesson in the new Financial Algebra unit: Investing Strategies & Exponential Functions. Dive into the activity below!

Part 1: Bruno Factors in the Fees

First, students consider Bruno, who is investing $1000 in an actively managed mutual fund that he predicts will average 7% annual growth. Students write an equation, then adjust their equation to account for Bruno’s realization that he’ll be paying 1.25% in fees each year.

Then, students use the interactive graph to “factor in the fees”. The fees effectively reduce Bruno’s annual rate of return, which means a lower growth rate for the exponential model.

Part 2: Lina Chooses an Investment

Next, students consider Lina, who is choosing between two different funds: an index fund with 0.1% annual fees and a mutual fund with 1.3% annual fees. Starting with the index fund, they calculate her rate of return after fees (the growth rate of the exponential function) and write an equation to predict her investment’s growth.

Then, students determine what rate of return Lina would need from the mutual fund in order to offset the higher annual fees. They can check their answers using the interactive graph.

Part 3: Frank’s Fees Stack Up

Lastly, students make a prediction about the growth of investments for two people, Frank and Rania, who both average 7% annual returns but pay different fees. On the next slide, an animation reveals what happens to their investments.

Then, students calculate the rate of return Frank would need to achieve in order to match Rania's earnings.

Finally, students imagine they have $200 to invest and answer: would you focus more on the potential returns or the fees?

Using the Teacher Dashboard

Throughout this activity, you can monitor student progress, highlight student answers to share with the class, and give feedback using the teacher dashboard. You’ll see check marks when students answer correctly, x marks when students answer incorrectly, and warning signs when students repeatedly check their work.

The teacher dashboard is also a great tool for generating discussion. If you click on a specific slide, you can see how students responded to a prompt, then choose a few responses to highlight for the class.

We hope you enjoyed this activity! You can find this and more in the NGPF Financial Algebra Desmos Collection.

—----------------------------------------------

Teaching investing? Check out MOVE: Let’s Make a Mutual Fund!

—----------------------------------------------

About the Author

Kathryn Dawson

Kathryn (she/her) is excited to join the NGPF team after 9 years of experience in education as a mentor, tutor, and special education teacher. She is a graduate of Cornell University with a degree in policy analysis and management and has a master's degree in education from Brooklyn College. Kathryn is looking forward to bringing her passion for accessibility and educational justice into curriculum design at NGPF. During her free time, Kathryn loves embarking on cooking projects, walking around her Seattle neighborhood with her dog, or lounging in a hammock with a book.

More posts by Kathryn