“The Piggy Bank or The Safe” is a lesson I made as a way to introduce the contrasts between exponential growth or compound interest with linear growth or simple interest. This context asks students to compare a magic safe, which magically adds $100 to its contents reach day, against a piggybank which magically doubles the value of its contents each day. As the safe starts with $100 on Day 0, and the piggy bank starts with $.01, the question to ask students is: “Which would you rather have for the next 20 days?” Of course many other interesting questions could be posed, and students should also be pushed to make predictions along the way.

This Google slide presentation shows the amount of money, day-by-day, in US currency, in order to help people visualize the change over time.

After three days the presentation pauses to see if anyone would change their prediction. It might be a good time to ask kids to make a table with the first the days, and see if they can find some evidence for their prediction, it even an equation.

After 20 days it shied that the piggy bank has more value in it by a huge margin. It might be a good time to ask how big the piggy bank would be in 30 days, or how long it would take until it has over one million dollars.

After the 20 days I began making an extension, with a “Super safe” and a “Mini-piggy” which grow at different rates. The “Super safe” grows by $2000 each day, while the “Mini-piggy” grows by a multiplier of 1.5 each day, and they each begin with $1000 and $10 respectively. I didn’t make slides for the extension, but if you carry it out for 20 days you’ll find that the “Super-safe” ends up ahead by a slim margin, so that begs the question: “If you let any exponential function grow towards infinity, will it eventually pass a linear function?”

Edit: A good follow up question that was suggested by @jlanier: What would grow faster, a piggybank placed in a safe, or a safe placed inside of a piggybank?

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