Eric Gaze, the Director of the Quantitative Reasoning Program at Bowdoin College, and also a Senior Lecturer in Mathematics, shares this example which can be easily employed in a Quantitative Reasoning or Math for Liberal Arts course. The mathematics included is also relevant for any mathematics course which includes exponential functions.
In this activity, Gaze has created a scenario in which a set of triplets all create retirement accounts with different investing timelines. It is a great group work activity, as students must grapple with creating an Excel spreadsheet that models the three different scenarios and allows for the students to conduct What-IF? analyses about possible alternatives.
Sal, Cal, and Val are triplets. Who will retire with the most money in their retirement account at age 65?
- Sal gets a paper route at age 14 and decides to invest $2000 a year in a mutual fund which averages a 10% annual return. Sal only makes deposits for 5 years and then leaves the balance to compound until retirement at age 65.
- Cal is impressed by Sal’s bank account, gets a job in college, dutifully makes annual $2000 deposits starting at age 19 into the same mutual fund for 8 years, and then leaves the balance to compound until retirement at age 65.
- Val travels the world for awhile after school without focusing on a career, but then settles down at the age of 27 and diligently makes annual $2000 deposits all the way to retirement at the age of 65.
Students must work together in groups to create a spreadsheet that models this situation, and determine which triplet ends up with the most money in their retirement account. This requires that students build on their prior knowledge of compound interest. Incorporating the deposits over different time frames illustrates the power of using a spreadsheet to model these scenarios.
Digital Resources
Excel or any other spreadsheet
Students are required to build on their prior knowledge of exponential functions and compound interest to create a robust spreadsheet model. The model allows groups to conduct sophisticated What-IF? analyses to answer questions that would be beyond their mathematical abilities otherwise, deepening student appreciation of the power of spreadsheet modeling. Having students build the Excel model in groups and explore outcomes efficiently leads to meaningful conversations regarding financial literacy. Gaze recommends that care must be taken when discussing finances to focus not on current situations or past struggles, but to focus on empowering students with tools and vocabulary to participate in financial decisions strategically.
Digital Enablement
This exploration is meant to be an eye-opening and engaging exercise for students, although they will likely struggle with making the spreadsheet model. Gaze often includes a Word document with instructions and a screenshot of what the model looks like to start. This gives students a concrete way to move forward, allowing them to check their numbers in the first years to verify their progress and strategy.
Solving for the ending balance using formulas and a calculator would be complicated, computationally intensive, and rife with all kinds of possible errors. Once the spreadsheet is built and students determine that Sal ends up with the most money at retirement, important conversations can take place. In particular the importance of the time variable in exponential functions is a clear take away. Sal only deposits $10,000 and then lets the power of exponential growth take over. Students are asked to determine at what interest rate will all three siblings end with the same amount of money. This again would require a complex calculation but is easily solved using guess and check, by simply changing the APR parameter in the spreadsheet. The class can then debrief on saving for retirement and what it means to invest in a mutual fund.