I currently use 3 assignments that apply Arithmetic/Geometric Series. Depending on your curriculum, you may use them at different times throughout the year. All 3 of these assignments are deeply embedded with important Personal Finance concepts:
The "Race to the Emergency Fund" (& Teacher Example) - Financial experts agree that one of the most important things that we can do is to save an "emergency fund" of 3-6 months of living expenses. Since "unexpected" expenses are inevitable, this "emergency fund" is absolutely necessary to avoid going into debt. With this assignment, students research their own "entry-level" income and create and Arithmetic Series to estimate their realistic savings goals.
The Cool Car vs. IRA (& Teacher Example) is a great project that reviews exponential growth and introduces Geometric Series.
The "Mortgage Project" (& Teacher Example) - This is one of my favorite projects because it has so much real-world significance for students! (Students have fun searching for houses and they learn about the processes of establishing credit and the importance of saving for a Down Payment.) A Mortgage is actually the sum of a Finite Geometric Series. Admittedly, this concept is a lot for my students to grasp. I usually call-in Sal from Khan Academy to explain the mathematical details.
The "Wha-Oh Investment Problem" (& Teacher Example) - Although this technically used a Geometric Series, I typically use it as a preview to our "Long-Game Investing" project when I teach Exponential Growth & Logarithms.
New for the 2024-25 school year, we'll be using these "Hook Lessons" for Arithmetic Series and Geometric Series. We'll also suggest that teachers print out a poster-sized copy of the "Menu of Covariaton" and post it in the front of their classrooms.