Wheels and Deals Project Outline
12th Grade Algebra with Finance • Applied Financial Modeling SMP 3 & 4 FOCUS
Wheels & Deals
Auto Loan Arbitrage • Financial Discourse • Amortization Analysis
Duration: 10 Class Sessions
Format: Collaborative Advisory Teams
Student Name:
Advisor Team:
Assigned Client:
The Advisory Brief
You are licensed junior financial analysts at Apex Capital Advisory. Real-world clients are preparing to finance automobile purchases across volatile credit conditions, dealer markups, and extended repayment terms. Your mission is to mathematically model amortization schedules, unmask predatory lending clauses, and rigorously defend a comprehensive loan recommendation through structured peer discourse and oral arbitration.
Core Algebraic Models & Equations
Derive • Calculate • Justify
Monthly Payment (\(M\))
\( M = \frac{P \cdot i(1+i)^n}{(1+i)^n - 1} \)
\(P\) = principal; \(i = \frac{r}{12}\) (monthly rate); \(n\) = total months.
Total Interest (\(I_{\text{tot}}\))
\( I_{\text{tot}} = (M \cdot n) - P \)
Cumulative financial cost over term \(n\), excluding down payment and trade-in.
Total Cost of Ownership
\( \text{TCO} = (M \cdot n) + D + F + I + M_{\text{rep}} \)
Integrates down payment (\(D\)), registration/fees (\(F\)), insurance (\(I\)), and repairs.
Essential Discursive Questions (The Math Debate Drivers)
Q1. Why is a lower monthly payment on an 84-month loan often an algebraic illusion that damages long-term net worth?
Q2. How does a 150-point drop in credit score compound the total financing cost through non-linear amortization curves?
Q3. At what mathematical inflection point does negative equity ("underwater") exceed vehicle depreciation?
Q4. How can quantitative financial evidence dismantle high-pressure dealership financing strategies in real time?
Project Milestones & Discourse Checkpoints
PHASE 1 Days 1-2
Dossier Audit
Analyze client credit tiers, income, down payments, and rate quotes (bank vs dealer).
Protocol: Think-Pair-Audit
PHASE 2 Days 3-5
Algorithmic Modeling
Construct 36, 48, 60, and 72-month amortization curves and calculate interest divergence.
Protocol: Number Talks
PHASE 3 Days 6-8
The Loan Arbitrage
Live fishbowl debate: Advisor teams defend optimal loan packages against rival teams.
Protocol: Socratic Fishbowl
PHASE 4 Days 9-10
Client Presentation
Publish comprehensive client dossiers with quantitative justification and oral debrief.
Protocol: Peer Cross-Exam
Wheels & Deals • Project Overview • Document 1 of 3 Standards: CCSS.MATH.CONTENT.HSA.CED.A.1, HSF.IF.C.8, MP.3
Discourse Architecture • CCSS MP.3 PHASE 2 & 3 ARTIFACT
Student Discourse Protocols & Argumentation
Constructing viable mathematical arguments and critiquing the quantitative reasoning of peers.
Mandatory Mathematical Discourse Protocols
Protocol A: The Fishbowl Loan Arbitration 20 Min Session
Teams rotate into the center ring. Team A presents their recommended loan structure. Outer circle teams act as Consumer Skeptics and Bank Examiners, challenging their interest projections and risk exposure using quantitative counter-models.
Role: Presenter (5m) • Cross-Examination (10m) • Outer Circle Synthesis (5m)
Protocol B: Socratic Calibration Circle 15 Min Session
Seminar-style whole-group inquiry into structural finance ethics: "Are 84-month subprime auto loans mathematically exploitative or functionally necessary for low-income mobility?" Every claim must cite calculated interest differentials and amortization rates.
Rule: No claim may be stated without an accompanying numerical proof.
Discourse Sentence Frames for Financial Argumentation
Senior Algebra Level
Proving with Quantitative Data
- • "Based on our amortization model, extending the term from 48 to 72 months saves \( \$X \) monthly, but inflates total interest by \( \$Y \)..."
- • "The derivative of the principal balance reveals that during months 1-18, \( Z\% \) of payments serve solely as bank profit..."
Challenging an Assumption
- • "Your model assumes steady vehicle depreciation of \( 15\% \), but does your risk plan account for negative equity if..."
- • "While you prioritized a lower APR, did you overlook the \(\$850\) dealer documentation fee built into the financed principal?"
Conceding & Synthesizing
- • "We acknowledge Team B’s critique regarding short-term cash flow constraints; however, mathematically our client risks..."
- • "Synthesizing both models, a compromise 60-month loan at a credit union yields the optimal Pareto frontier..."
Client Case Dossiers (Assigned per Group)
Each team models 1 client deeply
Client A: Maya L. Subprime (590)
Vehicle: 2021 Civic ($18,500)
Down Payment: $1,000 cash
Dealer Offer: 14.9% APR, 72 mo
Credit Union: 10.2% APR, 48 mo
Discourse challenge: High monthly burden vs debt trap.
Client B: Marcus T. Prime (740)
Vehicle: 2024 RAV4 ($34,000)
Down Payment: $7,000 trade-in
Dealer Offer: 1.9% APR (36 mo)
Alt Offer: $2,500 rebate + 5.5% APR
Discourse challenge: Low APR vs upfront cash rebate math.
Client C: Elena R. Near-Prime (650)
Vehicle: 2022 F-150 ($38,000)
Down Payment: $2,500 cash
Dealer Offer: 8.7% APR, 84 mo
Bank Offer: 7.1% APR, 60 mo
Discourse challenge: Negative equity & runaway interest.
Wheels & Deals • Discourse Protocols • Document 2 of 3 Standards: CCSS.ELA-LITERACY.SL.11-12.1, CCSS.MATH.PRACTICE.MP3
Deliverables & Evaluation Rubric 100 TOTAL POINTS
Project Deliverables & Discourse Rubric
Holistic criteria for algebraic precision, quantitative discourse, and peer defense.
Final Portfolio Components (Checklist)
1. Master Amortization Model:
Complete computational spreadsheet displaying principal, monthly interest (\(i_m\)), balance reduction, and total interest for 3 competing scenarios.
2. Comparative Visual Deck:
Graphical analysis of principal balance over time, showing the negative equity inflection point and crossover cost curves.
3. Live Arbitration Defense:
Participation in the Fishbowl Arbitration. Every student must make at least 2 substantiated claims and 1 evidence-based counter-critique.
4. Executive Client Memorandum:
A 2-page formal advisory letter written directly to the client, translating high-level algebra into actionable, ethical financial recommendations.
Discourse & Algebraic Evaluation Rubric
Domain
Exemplary (4 pts)
Proficient (3 pts)
Developing (2 pts)
Emerging (1 pt)
Algebraic Modeling & Precision Amortization formulas, TCO, rate conversions
All formulas derived without error; precise monthly payment and interest down to the cent.
Minor arithmetic slip; core amortization formula correctly applied across scenarios.
Formula misapplied (e.g., APR not converted to monthly rate \(r/12\)).
Incorrect equations; calculations missing or incomplete.
Mathematical Discourse (MP.3) Live arbitration, claim defense, counterarguments
Fluently uses financial frames; challenges peers with calculated counter-proofs; refines own ideas.
Constructs sound arguments citing numerical data; responds to peer critique effectively.
States opinions without citing specific amortization calculations; hesitant in debate.
Does not participate in discourse or relies entirely on subjective non-math statements.
Financial Logic & Trade-offs Opportunity cost, equity, credit tier impacts
Deep synthesis of credit score penalties, negative equity curves, and total life-of-loan costs.
Accurately weighs monthly payment vs cumulative interest; identifies basic credit traps.
Over-focuses on monthly payment alone; overlooks long-term compounding interest costs.
Recommends clearly detrimental financing terms without quantitative rationale.
Client Synthesis Memo Executive clarity, professional tone, visual graphs
Professional, ethical, persuasive memo; seamlessly blends algebra into executive advice.
Clear advice supported by graphs; accessible to a consumer client.
Informal tone; mathematical reasoning disconnected from the final advice.
Unfinished memo or lacks structured quantitative guidance.
Peer Discourse Observation & Audit Log (Fill During Live Fishbowl) Student Observer: _______________
Speaker & Claim Recorded:
Note the quantitative claim made by the opposing analyst.
Mathematical Proof Cited:
Did they cite monthly payment (\(M\)) or total interest (\(I_{\text{tot}}\))?
My Challenge / Counter-Model:
What mathematical flaw or risk did you raise in response?
Wheels & Deals • Deliverables & Rubric • Document 3 of 3 Apex Capital Advisory • Classroom Simulation Suite
