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Created byCJ Jacobsen
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Banking on Interest: Designing and Modeling Your Own Bank

Grade 12Math2 days
Students step into the role of financial entrepreneurs to design a competitive bank tailored for high-net-worth "Gen-Z Influencers." By modeling simple, compound, and continuous interest, students analyze how different mathematical functions and the constant e drive long-term investment growth. The project culminates in a professional pitch where students must justify their financial products using data-driven evidence, balancing consumer appeal with institutional profitability.
Financial ModelingCompound InterestExponential GrowthContinuous CompoundingEffective Annual YieldEntrepreneurshipMathematical Constant E
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we, as financial entrepreneurs, design a competitive bank that uses mathematical interest models to balance consumer growth with institutional profitability?

Essential Questions

Supporting questions that break down major concepts.
  • How does the choice of interest model (simple, compound, or continuous) impact the long-term growth of an investment?
  • In what ways does the frequency of compounding ($n$) change the actual yield of a bank account?
  • How can a bank balance offering competitive rates for customers while ensuring the business remains profitable?
  • How does the mathematical constant $e$ function within the context of continuous financial growth?
  • What factors—both mathematical and branding-based—influence a consumer's decision to trust a financial institution?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Calculate and compare future values using simple interest, compound interest, and continuous compounding formulas.
  • Analyze how the frequency of compounding (n) impacts the total interest earned over time.
  • Evaluate the mathematical constant 'e' and its application in modeling continuous financial growth.
  • Design a business brand and set of financial policies that balance mathematical profitability with consumer appeal.
  • Construct and interpret linear and exponential functions to represent different banking products.

Common Core State Standards for Mathematics

HSF-LE.A.1
Primary
Distinguish between situations that can be modeled with linear functions and with exponential functions.Reason: The project requires students to differentiate between simple interest (linear growth) and compound interest (exponential growth) when designing their bank's products.
HSF-LE.A.2
Primary
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).Reason: Students must create their own interest-bearing accounts and policies, which involves constructing the mathematical functions that define those accounts.
HSF-IF.C.8.B
Secondary
Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)12^t, y = (1.2)t/10, and classify them as representing exponential growth or decay.Reason: This standard is directly applied when students calculate compound interest and interpret how the rate of change is affected by the compounding period (n).

Common Core State Standards for Mathematics - Standards for Mathematical Practice

MP.5
Supporting
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.Reason: Students will likely use calculators or spreadsheets to perform the multi-step calculations required for comparing different interest models across their bank's offerings.

Entry Events

Events that will be used to introduce the project to students

The 'Legacy Liquidation' Pitch

A high-profile "Gen-Z Influencer" posts a viral video announcing they are moving their $50 million portfolio out of traditional banks because they are 'stale and mathematically inefficient.' Students are invited to a secret 'Venture Capital' meeting where they must pitch a new bank brand that uses aggressive interest models (continuous vs. simple) to lure high-value, tech-savvy clients.
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

Bank Blueprint: Branding & Business Logic

In this foundational activity, students step into the role of financial founders. They will establish their bank's identity and define the logic behind their financial products. This involves creating a brand identity that appeals to high-net-worth clients and drafting 'Product Term Sheets' that outline how their bank's interest accounts will function conceptually before the heavy calculations begin.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Brainstorm a bank name and slogan targeted at 'Gen-Z Influencers' and high-tech investors. Create a visual logo.
2. Define three distinct tiers of savings accounts: The 'Steady Starter' (Simple Interest), the 'Growth Pro' (Compound Interest), and the 'Infinity Alpha' (Continuous Compounding).
3. Assign a competitive annual percentage rate (APR) to each account. Write a brief 'Policy Statement' for each, describing how the interest is applied and why a customer would choose it.
4. Draft the mathematical function (using variables like P, r, and t) that will be used to calculate the balance for each account type, identifying which represents linear growth and which represents exponential growth.

Final Product

What students will submit as the final product of the activityA 'Bank Charter' document containing the bank's name, slogan, logo, and a summary table of three proposed account types (Simple, Compound, and Continuous) with their respective interest rates and 'selling points.'

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSF-LE.A.1 (Distinguishing between linear and exponential growth) and HSF-LE.A.2 (Constructing functions from descriptions). Students must decide which products represent linear growth (simple interest) and which represent exponential growth (compound/continuous).
Activity 2

The Interest Engine: Modeling Financial Growth

Now that the bank is established, students must prove their models work. Using a hypothetical 'Seed Deposit' from an influencer (e.g., $100,000), students will perform a comparative analysis of their three account tiers over various time horizons. This activity moves from conceptual design to rigorous mathematical modeling.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Calculate the future value for the 'Steady Starter' account using the Simple Interest formula (I=Prt) for the given time intervals.
2. Calculate the future value for the 'Growth Pro' account using the Compound Interest formula [A = P(1 + r/n)^(nt)], testing at least two different compounding frequencies (e.g., monthly vs. daily).
3. Calculate the future value for the 'Infinity Alpha' account using the Continuous Compounding formula (A = Pe^rt).
4. Create a line graph that plots all three models on the same axes to visualize the 'divergence point' where exponential/continuous growth significantly outpaces linear growth.

Final Product

What students will submit as the final product of the activityThe 'Interest Impact Spreadsheet'—a detailed data table and set of graphs comparing the growth of a $100,000 deposit across the three account types over 1, 5, 10, and 20 years.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSF-IF.C.8.B (Using properties of exponents to interpret growth) and MP.5 (Using tools like calculators or spreadsheets). Students specifically explore how the constant 'e' and the frequency of compounding 'n' change the outcome of the function.
Activity 3

Yield vs. Appeal: The Venture Capital Pitch

In the final stage, students must justify their mathematical models to a 'Venture Capitalist.' They will analyze their findings to determine the 'Effective Annual Yield' for their accounts and explain how the frequency of compounding creates a competitive edge. They must also address the 'Banker's Dilemma': how to offer high enough rates to attract clients while keeping enough profit for the bank.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Identify the 'Effective Annual Yield' for each account—calculating the actual percentage increase after one year to show clients the 'hidden' power of compounding.
2. Write a 'Mathematical Justification' paragraph explaining the role of the constant 'e' in their Continuous account and why it is the ultimate 'hook' for tech-savvy investors.
3. Conduct a 'Profitability Stress Test': Determine how much more the bank pays out in Continuous vs. Simple interest over 10 years and explain how the bank will offset this cost (e.g., through higher loan rates or fees).
4. Present the final pitch, highlighting the graph from Activity 2 as the primary evidence of the bank's growth potential.

Final Product

What students will submit as the final product of the activityThe 'Investor Pitch Deck'—a presentation (digital or poster) that uses the calculated data to argue why their bank is the most 'mathematically efficient' choice for the Legacy Liquidation event.

Alignment

How this activity aligns with the learning objectives & standardsAligns with HSF-LE.A.1 (Distinguishing growth situations) and HSF-IF.C.8.B (Identifying percent rate of change). This activity requires students to interpret the 'Rate of Change' in a real-world business context, explaining the mathematical advantage of their bank.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Billion Dollar Bank: Financial Modeling Rubric

Category 1

Mathematical Modeling & Calculation

Evaluates the student's ability to accurately use mathematical formulas, constants, and functions to model and visualize financial growth.
Criterion 1

Interest Modeling & Accuracy

Selection and application of Simple (I=Prt), Compound [A=P(1+r/n)^nt], and Continuous (A=Pe^rt) interest formulas to model financial growth.

Exemplary
4 Points

All three formulas are applied flawlessly with sophisticated notation. Calculations for various time horizons (1, 5, 10, 20 years) are 100% accurate, demonstrating an advanced grasp of the mathematical constant 'e'.

Proficient
3 Points

All three formulas are applied correctly. Calculations for the different time horizons are accurate with only minor, non-conceptual errors. Demonstrates a clear understanding of the 'e' constant.

Developing
2 Points

Formulas are identified, but application is inconsistent. There are several calculation errors, or one formula (likely continuous compounding) is applied incorrectly. Understanding of 'e' is emerging but not fully realized.

Beginning
1 Points

Formulas are missing, incorrectly chosen, or contain significant errors that prevent accurate modeling. Little to no evidence of understanding the role of 'e' in financial growth.

Criterion 2

Functional Analysis & Representation

Construction and interpretation of linear and exponential functions through data tables and multi-line graphs to visualize divergence.

Exemplary
4 Points

Creates a high-fidelity graph that clearly identifies the 'divergence point' where exponential growth outpaces linear growth. Data tables are comprehensive, and the relationship between 'n' and yield is expertly analyzed.

Proficient
3 Points

Creates a clear graph plotting all three models. Correctly identifies the difference between linear and exponential growth. Data tables support the visual evidence effectively.

Developing
2 Points

Graph is attempted but may lack clear labeling, or the scales are inappropriate for visualizing growth. Recognition of linear vs. exponential patterns is basic or inconsistent.

Beginning
1 Points

Graph is missing, incomplete, or fails to represent the data correctly. Unable to distinguish between the growth patterns of the different account types.

Category 2

Business Logic & Financial Strategy

Evaluates the student's ability to apply mathematical findings to business strategy, branding, and economic decision-making.
Criterion 1

Strategic Brand Identity

Development of a bank brand, slogan, and specific account policies that align mathematical models with consumer psychology.

Exemplary
4 Points

Branding is professional and highly innovative, specifically tailored to the 'Gen-Z Influencer' persona. Policies show a sophisticated balance between high-yield 'hooks' and institutional sustainability.

Proficient
3 Points

Branding is clear and appropriate for the target audience. Policies are logical and effectively describe why a customer would choose each account type based on its interest structure.

Developing
2 Points

Branding is generic or lacks a clear connection to the audience. Account policies are basic and do not fully explain the 'selling points' of the different interest models.

Beginning
1 Points

Branding is incomplete or missing. Policies are vague or fail to differentiate between the three account types.

Criterion 2

Profitability & Yield Analysis

Analysis of Effective Annual Yield (EAY) and the 'Banker's Dilemma' regarding payout costs vs. profitability.

Exemplary
4 Points

Provides a profound analysis of EAY, identifying exactly how much 'extra' the bank pays for continuous compounding. Proposes a realistic and clever strategy to offset costs while maintaining a competitive edge.

Proficient
3 Points

Calculates EAY correctly and provides a logical justification for why the bank can afford high-interest accounts. Addresses the trade-off between customer attraction and bank profit.

Developing
2 Points

Calculation of EAY is attempted but contains errors. The 'Profitability Stress Test' is addressed but lacks depth or a clear plan for bank sustainability.

Beginning
1 Points

Fails to calculate EAY or address the financial risks of the chosen interest rates. Profitability is not considered.

Category 3

Communication & Evidence

Evaluates how effectively students communicate their mathematical findings to stakeholders and justify their business decisions.
Criterion 1

Mathematical Argumentation & Pitch

Ability to explain complex mathematical concepts (like continuous compounding and 'e') and use data as evidence in a persuasive pitch.

Exemplary
4 Points

Pitch is exceptionally persuasive, using data-driven arguments and professional-grade visuals. The explanation of 'e' is both mathematically rigorous and accessible to a lay investor.

Proficient
3 Points

Pitch is clear and organized, using the 'Interest Impact Spreadsheet' as primary evidence. Provides a solid mathematical justification for the bank's account offerings.

Developing
2 Points

Pitch is present but relies more on branding than mathematical evidence. The explanation of the models is superficial or lacks clarity.

Beginning
1 Points

Pitch is disorganized or missing key mathematical evidence. Fails to explain why the bank's models are 'mathematically efficient.'

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

How did your perspective on the mathematical constant 'e' change after comparing the 'Infinity Alpha' account (continuous) to the 'Growth Pro' account (discrete compounding)?

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Question 2

On a scale of 1 to 5, how difficult was it to find an interest rate that was high enough to attract 'Gen-Z Influencers' but low enough to keep your bank profitable?

Scale
Required
Question 3

Looking at your final graph, describe the 'divergence point' where the exponential models (Compound/Continuous) began to significantly outperform the linear model (Simple). How would you use this specific data point to convince a skeptical investor?

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Required
Question 4

Based on your calculations in Activity 2, which mathematical factor had the most substantial impact on the total interest earned over a 20-year horizon?

Multiple choice
Required
Options
Increasing the frequency of compounding (n)
Increasing the base interest rate (r)
Relying solely on the passage of time (t) in a simple interest model
Using branding and logos to distract from the interest model
Question 5

Which part of the 'Venture Capital Pitch' felt more persuasive to you: the creative branding (name/slogan) or the mathematical evidence (Effective Annual Yield/Graphs)? Why?

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Optional