Why are investment costs important? In this Desmos activity, students analyze how fees affect the exponential growth of investments over time. See how Desmos helps students visualize and link that impact to changing the growth factor into an exponential function.

DESMOS: The Impact of Investing Fees on Exponential Growth is 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 reimbursements

First, students consider Bruno, who invests \$1,000 in an actively managed mutual fund that he predicts will have an average annual growth rate of 7%. Students write an equation and then adjust their equation to account for Bruno’s realization that he will pay 1.25% in fees each year.

Then students use the interactive chart to “count the cost.” The fees actually decrease Bruno’s annual return, which means a lower growth rate for the exponential model.

Part 2: Lina chooses an investment

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

Next, the students determine what return Lina would need from the mutual fund to offset the higher annual fees. They can check their answers using the interactive chart.

Part 3: Frank’s Fees Pile Up

Finally, students predict investment growth for two people, Frank and Rania, who both have an average annual return of 7%, but pay different fees. On the next slide, an animation shows what is happening with their investments.

Then the students calculate the return that Frank would need to achieve 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

During this activity, you can track student progress, mark student responses to share with the class, and provide feedback using the teacher dashboard. You’ll see check marks if students answer correctly, x-marks if students answer incorrectly, and warning signs if 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 and then choose a few responses to highlight for the class.

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

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This post Math Monday: use Desmos to investigate the impact of investment costs

was original published at “https://www.ngpf.org/blog/math/math-monday-use-desmos-to-explore-the-impact-of-investing-fees/”