Minecraft
Preparation
Lesson Narrative
In this lesson, students explore the mathematical engine of wealth creation: compound interest. Students will compare linear growth (simple interest) to exponential growth (compounding) through mathematical exercises, and apply the Rule of 72 to estimate how fast an investment will double. By the end, students will understand why starting to invest early is mathematically more important than the principal amount invested.
Learning Goals
• Calculate the future value of an investment using the compound interest formula.
• Apply the Rule of 72 to estimate doubling times.
• Differentiate between linear and exponential financial models.
Student Facing Learning Goals
• Let's see how time makes money multiply itself.
Student Facing Learning Targets
• I can calculate compound interest over time.
• I can use the Rule of 72 to figure out when my money will double.
• I can explain why starting to invest young is a massive advantage.
Required Academic Standards
National Jump$tart Standards:
• Saving and Investing (Standard 1): Compare how saving and investing build wealth and help meet financial goals.
Glossary Entries
Compound Interest: Interest calculated on the initial principal and also on the accumulated interest of previous periods.
Simple Interest: Interest calculated only on the principal amount.
Rule of 72: A mental math shortcut to estimate the number of years required to double your money at a given annual rate of return.
Exponential Growth: Growth whose rate becomes ever more rapid in proportion to the growing total number or size.
Lesson
Warm Up
3.1.1: The Penny vs. The Million
Launch: Have students stand in randomized groups of 3 at vertical whiteboards. Present the prompt verbally or project it. Give them 4 minutes to debate.
Synthesis: Select two groups to share. Explain that the penny yields over $5.3 million. This highlights the human brain's inability to intuitively grasp exponential growth.
Student Facing Task
Option A: I will give you $1,000,000 cash right now. Option B: I will give you a single penny today, and double it every day for 30 days. Which do you choose and mathematically why?
Activity 1
3.1.2: Graphing the Growth
Launch: Keep students at whiteboards. Project the math scenarios. Give groups 8 minutes to calculate and sketch.
Synthesis: Have the class observe the boards. (Teacher Key: Simple = linear straight line. Compound = upward curve). Show the graphs side-by-side. Explain that in the first few years they look identical, but time is the catalyst that creates the massive curve.
Student Facing Task
Calculate the balances. Person A gets $10,000 at 10% Simple Interest. Person B gets $10,000 at 10% Compounding Interest.
1. Calculate Person A's balance after 1 year, 2 years, and 3 years.
2. Calculate Person B's balance after 1 year, 2 years, and 3 years.
3. Sketch a quick line graph comparing the trajectories of both accounts over 20 years.
Activity 2
3.1.3: The Rule of 72
Launch: Present the formula (72 ÷ Interest Rate = Years to Double). Give groups 8 minutes to run the math.
Synthesis: Facilitate a class review. (Key: HYSA = 18 years. S&P 500 = 7.2 years. Mattress = Never). Debate the opportunity cost of hiding cash under a mattress versus investing it.
Student Facing Task
Use the Rule of 72 (72 ÷ Interest Rate = Years to Double) to answer the following:
1. If you put $5,000 in a High-Yield Savings Account earning 4%, how many years until it becomes $10,000?
2. If you invest $5,000 in the stock market averaging 10%, how many years until it becomes $10,000?
3. If you leave it under your mattress (0%), when does it double?
Lesson Synthesis
Lesson Synthesis (5 min)
Narrative: Bring the class back to their seats. Review the student-facing learning targets. Ask the class: "What is the most powerful variable in the compound interest formula: the principal (cash) or the time?" (Answer: Time, because the exponent creates the exponential curve).
Cool Down
3.1.4: The Early Bird
Narrative: This exit ticket serves as a formative assessment on the mathematical power of time.
Teacher Rubric: A successful response must articulate that investing earlier gives the exponent (time) more periods to multiply the base, making it nearly impossible for the older person to catch up just by depositing more principal later.
Student Facing Task
Explain mathematically why a 20-year-old who invests $100 a month will likely end up with significantly more wealth than a 40-year-old who invests $500 a month, assuming they both earn the exact same interest rate and retire at age 65.