Session 2: The Time Value of Money (TVM)

Contents

Session 2: The Time Value of Money (TVM)#

The single most important concept in finance, and how it solves a real-life car deal.


Section 1: The Financial Hook - The Two Deals#

Imagine you’ve just graduated and landed your first real job. You need a reliable car. After weeks of searching, you find the perfect used Toyota RAV4 for $25,000. You have the cash saved up, but the dealership manager, seeing you’re a recent grad, offers you two “special” deals:

  • Deal A: The “Cash Discount” Deal. Pay $22,000 in full today.

  • Deal B: The “Zero-Worry” Deal. Pay nothing today. Make one single payment of $26,000 in exactly one year.

Timeline Visualization:

Deal A:  \$22,000 -----> [Car ownership starts immediately]
         Today

Deal B:  \$0 ----------> \$26,000 -----> [Car ownership starts immediately]
         Today         1 Year

Which deal is better? Your gut might say Deal A because you pay less total dollars. But your gut doesn’t understand the Time Value of Money (TVM): the universal law that a dollar today is worth more than a dollar tomorrow because of its potential to earn interest.

This session will give you the tools to answer that question with mathematical certainty—and recognize when financial decisions require TVM thinking.


Section 1.5: Self-Test Quiz - Check Your Starting Point#

Instructions: Choose the best answer for each question. Don’t use AI - this is to check what you already know.

Question 1: If someone offers to pay you $100 today or $100 next year, which is better?

  • a) $100 today

  • b) $100 next year

  • c) They’re exactly the same

  • d) It depends on your personal preference

Question 2: What does “interest” represent?

  • a) A penalty for borrowing money

  • b) The cost of using someone else’s money over time

  • c) A government tax on savings

  • d) Money that banks keep for themselves

Question 3: If you put $1,000 in a savings account earning 5% annually, approximately how much will you have after one year?

  • a) $1,000

  • b) $1,050

  • c) $1,500

  • d) $1,005

Question 4: The “present value” of a future payment means:

  • a) How much that future payment is worth today

  • b) The payment you make right now

  • c) The total of all future payments

  • d) The interest rate being charged

Answers: 1-a, 2-b, 3-b, 4-a


Section 2: Foundational Concepts & Formulas#

Part I: The Core Insight#

Time Value of Money (TVM) is the fundamental principle that money available today is worth more than the same amount in the future due to its potential earning capacity. This core principle underlies virtually every financial decision.

Key Concepts:

  • Present Value (PV): The value of a single future cash flow in today’s dollars

  • Future Value (FV): The value of a single present cash flow at a specified future date

  • Interest Rate (r): The rate of return or growth rate per period

  • Number of Periods (n): The number of periods (years, months) over which money grows

  • Compounding Frequency (k): The number of times per year interest is calculated

Part II: Valuing a Single Cash Flow (Lump Sums)#

Timeline for Single Cash Flow:

Present Value (PV)                      Future Value (FV)
     Today                               Future Date
       |                                      |
       |------------------------------------->|
                  n periods @ rate r

The Master Formulas for a Single Cash Flow:

  1. Future Value (FV): FV = PV × (1 + r/k)^(n×k)

  2. Present Value (PV): PV = FV ÷ (1 + r/k)^(n×k)

Where n is the number of years, r is the annual rate, and k is compounding frequency per year.

Part III: Valuing a Stream of Cash Flows (Annuities)#

An Annuity is a series of equal cash flows (C) made at fixed intervals for a specified number of periods (n).

Timeline for Ordinary Annuity (payments at end of period):

Today   Year 1    Year 2    Year 3    ...    Year n
  |        |         |         |                |
  |        C         C         C                C
  |<---- Present Value of All Payments ---->|

The Master Formulas for an Ordinary Annuity:

  1. Present Value of an Annuity (PVₐ): PVₐ = C × [(1 - (1 + r)^-n) ÷ r]

  2. Future Value of an Annuity (FVₐ): FVₐ = C × [((1 + r)^n - 1) ÷ r]

Where C is the cash payment per period, r is the rate per period, and n is the total number of periods.

Part IV: When TVM Applies (And When It Doesn’t)#

TVM Works Best When:

  • Cash flows are reasonably predictable

  • Interest rates are relatively stable

  • Time periods are clearly defined

  • We can estimate appropriate discount rates

TVM Gets Complicated When:

  • Inflation is volatile (real vs. nominal rates matter)

  • Cash flows are highly uncertain (lottery winnings vs. business profits)

  • Time horizons are very long (30+ years)

  • Market conditions are rapidly changing

Quick Reality Check: Your friend says “I’ll pay you back $100 next week” vs. “I’ll start a business and pay you back in 5 years.” Which promise is easier to value using TVM? Why?

AI Learning Support - Concept Exploration

Learning Goal: Develop ability to test and refine your understanding of when TVM analysis is most reliable and practical.

Professional Prompt Sample A (Grade: A): “I’m studying TVM applications and I’ve noticed that TVM seems most reliable when cash flows are predictable and time periods are short. My hypothesis is that uncertainty in either cash flows or timing reduces the practical value of TVM analysis. Can you challenge my thinking by asking me about specific scenarios where this logic might not hold? I want to identify the boundaries of when TVM analysis is most/least useful.”

😊 What Makes This Excellent:

  • Clear hypothesis stated: Student shows prior thinking

  • Seeks challenging questions: Asks for intellectual stretch

  • Professional boundary testing: Wants to understand limitations

  • Learning ownership: Student drives the inquiry

😞 Weak Prompt Sample (Grade: D): “When is TVM useful? Give me examples of when it works and when it doesn’t.”

⚠️ Why This Fails Your Career Development:

  • No prior analysis: Shows zero intellectual preparation

  • Passive request: Asks for answers instead of questions

  • Vague scope: No specific learning objective

  • Spoon-feeding approach: Creates dependency, not competency

🎯 Your Professional Development Task: Transform the weak prompt into one that would impress a hiring manager evaluating your analytical thinking skills.

Your Task: Modify this prompt to include at least 2 improvements before using it. What changes would make it more effective for your learning?


Section 3: The Financial Gym - Partner Practice & AI Copilot Learning#

You’ve seen the formulas. Now, build your muscle memory through structured practice. Work with a partner to master the mechanics before you play the game.

Round 1: Solo Python Practice#

Work through Problems 1-2 individually using Python in Google Colab.

Problem 1 (FV): You invest $5,000 today at 6% annual interest, compounded annually. What is the value in 8 years?

Timeline:

\$5,000 -----------------> FV = ?
Today                   8 years
   |<---- 8 periods @ 6% ---->|

Your Python Implementation:

# IMPORTANT: This code is a starting point - understand the logic, don't copy-paste
# Explain each step to yourself. Code may contain errors - debug with AI copilot.

# Step 1: Define the investment parameters
present_value = 5000
annual_rate = 0.06
years = 8

# Step 2: Apply future value formula. Do you know what <**> Does?
future_value = present_value * (1 + annual_rate)**years

print(f"Future value: ${future_value:.2f}")

Problem 2 (PV): You want to have $25,000 in 5 years for a house down payment. If the account earns 4% annually, how much must you deposit today?

Timeline:

PV = ? -----------------> \$25,000
Today                   5 years
   |<---- 5 periods @ 4% ---->|

Your Python Implementation:

# IMPORTANT: This code is a starting point - understand the logic, don't copy-paste
# Explain each step to yourself. Code may contain errors - debug with AI copilot.

# Step 1: Define the goal parameters
future_value = 25000
annual_rate = 0.04
years = 5

# Step 2: Apply present value formula
present_value = future_value / (1 + annual_rate)**years

print(f"Present value needed: ${present_value:.2f}")

Round 2: Peer Teaching#

Partner with a classmate. for online or self-study, use AI copilot as your partner:

  • Person A explains Problem 1 solution step-by-step

  • Person B explains Problem 2 solution step-by-step

  • Both identify one point of confusion to research together

Round 3: Challenge Problems#

Work together on Problems 3-5, taking turns as “driver” and “navigator”

Problem 3 (PV with Monthly Compounding): You need to pay a tuition bill of $15,000 in 2 years. A CD offers a 5% annual rate, compounded monthly. How much do you need to invest today?

Timeline:

PV = ? -----------------> \$15,000
Today                   24 months
   |<-- 24 periods @ 5%/12 -->|

Your Python Implementation:

# IMPORTANT: This code is a starting point - understand the logic, don't copy-paste
# Explain each step to your partner. Code may contain errors - debug with AI copilot.

# Step 1: Define parameters
future_value = 15000
annual_rate = 0.05
monthly_rate = annual_rate / 12
months = 24

# Step 2: Calculate present value with monthly compounding
present_value = future_value / (1 + monthly_rate)**months

print(f"Investment needed: ${present_value:.2f}")

Problem 4 (Annuity PV): You won a lottery paying $10,000 at the end of every year for 20 years. If the discount rate is 7%, what is the present value of your winnings?

Timeline:

PV = ?    \$10K   \$10K   \$10K  ...  \$10K
Today   Year 1  Year 2  Year 3    Year 20
  |       |       |       |         |
  |<------- 20 payments @ 7% ------>|

Your Python Implementation:

# IMPORTANT: This code is a starting point - understand the logic, don't copy-paste
# Explain each step to your partner. Code may contain errors - debug with AI copilot.

# Step 1: Define annuity parameters
annual_payment = 10000
discount_rate = 0.07
years = 20

# Step 2: Apply annuity present value formula
pv_annuity = annual_payment * ((1 - (1 + discount_rate)**(-years)) / discount_rate)

print(f"Lottery present value: ${pv_annuity:.2f}")

AI Learning Support - Code Development#

Learning Goal: Learn to use AI as a debugging partner while maintaining ownership of your programming logic.

💻 Professional Prompt Sample A (Grade: A-): “I’m implementing a present value calculation and my logic is: calculate PV for FV=$10,000, 3 years, 5% annually using PV = FV/(1+r)^n. My code structure is [student shows their pseudocode]. Before I write the actual Python, what edge cases should I consider for input validation? What financial logic errors am I most likely to make in TVM coding that you could help me anticipate?”

🚀 Why This Builds Your Career Value:

  • Shows financial logic: Demonstrates understanding before coding

  • Proactive planning: Asks about edge cases and validation

  • Error anticipation: Professional debugging mindset

  • Maintains ownership: You create the code, AI advises

💔 Weak Prompt Sample (Grade: D+): “Write Python code to calculate present value. Make sure it works correctly.”

😬 Career-Limiting Problems:

  • Complete delegation: Shows no technical thinking

  • No learning objective: Misses skill development opportunity

  • Dependency creation: You become helpless without AI

  • Interview disaster: Can’t explain code you didn’t write

💡 Your Professional Growth Challenge: Redesign this prompt to demonstrate the analytical and coding skills that finance employers actually want to see.

Partner Teaching Protocol: After working with AI on your code:

  1. Explain to your partner the financial logic behind your calculations

  2. Walk through each line of code and what it accomplishes financially

  3. Discuss any assumptions your model makes about the financial scenario

  4. Partner must verify they understand before moving to next problem

Debrief Discussion#

What’s one insight your partner shared that clicked for you?


Section 4: The Financial Coaching - Your DRIVER Learning Guide#

You’ve done your reps in the gym. Now it’s time to step onto the field. In the real world, problems are messy stories, not clean equations. To solve them, professionals use a structured process. Our process is the DRIVER framework—a playbook that turns a confusing story into a clear, validated answer.

Let’s walk through your first case together with your coach.

Case Scenario for Coaching: Your friend wants to start a small business. She needs $20,000 for initial equipment. She plans to launch in 18 months. She’s found an investment account offering a 5.4% APR, compounded monthly. How much must she deposit today?

Timeline:

PV = ? -----------------> \$20,000
Today                   18 months
   |<-- 18 periods @ 5.4%/12 -->|

The DRIVER Playbook in Action#

Discover & Design: Frame the Problem#

AI Learning Support - Problem Framing

Learning Goal: Master systematic problem analysis and assumption identification.

🎯 Professional Prompt Sample A (Grade: A): “I’m framing this funding decision and have identified these key variables: FV=$20,000 needed in 18 months, 5.4% APR with monthly compounding, need to find required deposit today. I’m assuming the account is risk-free and rates remain constant. Before proceeding, what critical questions should I ask myself about the reliability of these assumptions? What alternative framings of this problem might lead to different conclusions?”

🏆 Why This Demonstrates Professional Competency:

  • Structured analysis: Shows systematic variable identification

  • Explicit assumptions: Demonstrates risk awareness

  • Self-directed questioning: Seeks analytical improvement

  • Alternative thinking: Considers multiple approaches

🚩 Weak Prompt Sample (Grade: C-): “Help me understand what variables I need for this TVM problem and what assumptions to make.”

📉 Why This Damages Your Professional Credibility:

  • Zero preparation: Shows no analytical foundation

  • Delegates thinking: Abdicates intellectual responsibility

  • Passive approach: Employer red flag for initiative

  • No value creation: Contributes nothing to the analysis

📈 Your Career Advancement Task: Transform this into a prompt that showcases the analytical rigor finance teams demand.

Represent: Visualize the Logic#

       <------------------ 18 Monthly Periods (n=18) ------------------>
       Each period grows at r_monthly = 0.054 / 12 = 0.0045
       |                                                                   |
      PV=?                                                               FV=\$20,000
      (Today)                                                          (18 Months)

Formula: PV = FV ÷ (1 + r_monthly)^n

AI Learning Support - Logic Mapping

Learning Goal: Develop visual and logical representation skills for financial problems.

📊 Professional Prompt Sample A (Grade: A): “I’ve structured this problem using the timeline above where I convert 5.4% APR to monthly rate of 0.0045 and use 18 monthly periods. My logic flow is: identify given values → convert rates → apply PV formula → calculate result. Is my visual representation capturing the essential financial relationships? What aspects of my timeline might be unclear or misleading to someone else reviewing my analysis?”

🎯 Why This Shows Professional Financial Thinking:

  • Student-created framework: Demonstrates analytical ownership

  • Clear process mapping: Shows logical thinking sequence

  • Seeks peer review: Professional quality-check mindset

  • Communication focus: Ensures clarity for stakeholders

🤷 Weak Prompt Sample (Grade: D): “Show me how to draw a timeline for this TVM problem and explain what formulas to use.”

💸 Why This Kills Your Career Prospects:

  • Zero intellectual contribution: Shows no analytical thinking

  • Requests basic tutoring: Entry-level skill gap exposed

  • No value creation: Produces nothing of professional worth

  • Dependency mindset: Cannot function independently

🌟 Your Professional Excellence Challenge: Redesign this to showcase the visual thinking and communication skills that senior analysts possess.

Implement: Code the Solution#

AI Learning Support - Code Development

Learning Goal: Build confidence in financial coding while learning debugging strategies.

⚡ Professional Prompt Sample A (Grade: A-): “I’ve coded my TVM calculation using this approach: [student shows code]. My financial logic is: convert APR to monthly rate, apply PV formula with 18 periods, validate result makes sense (PV < FV). I’m concerned about potential errors in my rate conversion. Can you help me identify potential errors in my financial reasoning before I run the code? What validation steps should I build in?”

💼 Why This Builds Employer Confidence:

  • Student-written code: Shows technical capability

  • Financial logic explained: Demonstrates conceptual understanding

  • Proactive risk management: Identifies potential issues

  • Quality assurance mindset: Seeks validation protocols

😱 Weak Prompt Sample (Grade: D): “Check my code and fix any errors.”

🔥 Why This Destroys Your Professional Reputation:

  • No analytical explanation: Cannot defend your work

  • Complete delegation: Shows zero problem-solving ability

  • No learning intent: Misses skill development opportunity

  • Quality blind spot: No awareness of validation needs

🚀 Your Technical Excellence Mission: Redesign this prompt to demonstrate the coding competency and analytical rigor that top finance firms demand.

# IMPORTANT: This code should be YOUR creation - understand the logic
# Work with AI to improve YOUR code, don't copy-paste AI solutions

def calculate_present_value(future_value, annual_rate, periods, compounding_frequency):
    """
    Calculate present value for monthly compounding investment.
    
    Parameters:
    future_value (float): Target amount needed in the future
    annual_rate (float): Annual percentage rate (as decimal)
    periods (int): Number of periods until future date
    compounding_frequency (int): Compounding periods per year
    
    Returns:
    float: Present value required today
    """
    # Implementation follows...

Validate: Professional Skepticism#

AI Learning Support - Testing Strategy

Learning Goal: Develop systematic validation and testing approaches for financial analysis.

🔍 Professional Prompt Sample A (Grade: A): “My analysis gives a required deposit of $18,532 today. I’ve validated it by checking: (1) $18,532 × (1.0045)^18 = $20,000 ✓, (2) PV < FV makes sense ✓, (3) seems reasonable for 18-month timeframe. I’m still uncertain about whether 5.4% APR is realistic for this type of account. What additional validation methods do finance professionals use for TVM calculations? How can I test whether my result passes the ‘common sense’ check?”

✨ Why This Shows Professional Validation Skills:

  • Multiple verification methods: Shows systematic approach

  • Mathematical confirmation: Demonstrates technical rigor

  • Reality testing: Applies common sense checks

  • Professional standards inquiry: Seeks industry best practices

🤦 Weak Prompt Sample (Grade: C): “Is my answer correct? How do I know if it’s right?”

💀 Why This Signals Amateur Status:

  • Zero validation effort: Shows no quality consciousness

  • Binary thinking: Misses nuanced analysis requirements

  • No methodology: Lacks systematic approach

  • Helpless dependency: Cannot self-validate work

🏅 Your Professional Credibility Challenge: Create a prompt that demonstrates the validation rigor that CFOs and portfolio managers demand from their teams.

Evolve: Pattern Recognition#

AI Learning Support - Pattern Recognition

🧩 Professional Prompt Sample A (Grade: A): “I just solved business funding using PV = FV/(1+r)^n for a single future payment. I can see this same logic applies to: loan payments (PV of payment stream), bond valuation (PV of interest + principal), stock valuation (PV of dividends). I’m wondering if this pattern extends to real estate analysis and capital budgeting decisions. What questions should I ask myself to test whether this PV framework transfers to other financial contexts I’ll encounter in my career?”

🎯 Why This Demonstrates Strategic Thinking:

  • Independent pattern recognition: Shows analytical intelligence

  • Cross-domain connections: Demonstrates broad understanding

  • Career-focused learning: Links to professional applications

  • Self-testing methodology: Seeks transferable frameworks

🙄 Weak Prompt Sample (Grade: D+): “Where else can I use this TVM stuff? Give me examples of other applications.”

📉 Why This Shows Limited Career Potential:

  • No intellectual work: Shows zero pattern analysis

  • Passive consumption: Expects to be fed information

  • Narrow thinking: Cannot make connections independently

  • Missed opportunities: Fails to build transferable skills

🌟 Your Strategic Excellence Challenge: Redesign this to showcase the pattern recognition and strategic thinking that separates senior analysts from junior staff.

Pattern Recognition:

Session 2:   PV = ? ---------> \$20,000 (single future payment)
             Today           18 months

Session 3:   PV = ? -----> Div₁ -----> Div₂ -----> Sale Price
             Today      Year 1     Year 2     Year 3
             (Stock Price = Present Value of ALL future cash flows)

Next week: “How much should you pay for Apple stock that pays future dividends and has a future sale price?” It’s identical PV logic—just multiple future payments instead of one. Same framework, bigger application.

Reflect: Learning Integration#

AI Learning Support - Learning Synthesis

Learning Goal: Consolidate learning and build connections to broader financial thinking.

🎓 Professional Prompt Sample A (Grade: A): “Through this DRIVER process, I learned that TVM is really about making money flows comparable across time periods. I struggled most with rate conversions (annual to monthly) and overcame this by always drawing out the timeline first. I think this analytical approach will help me with stock valuation (discounting dividends) and loan analysis (payment streams). What questions should I ask myself after each financial analysis to ensure I’m building transferable analytical skills rather than just solving individual problems?”

🚀 Why This Shows Professional Self-Awareness:

  • Concrete learning insights: Demonstrates deep understanding

  • Honest struggle assessment: Shows growth mindset

  • Solution-focused adaptation: Reveals problem-solving ability

  • Metacognitive development: Seeks learning frameworks

😴 Weak Prompt Sample (Grade: C-): “What did I learn from this session? How will this help me in my career?”

🛑 Why This Wastes Your Learning Investment:

  • No self-reflection work: Shows zero intellectual engagement

  • Delegates thinking: Misses personal growth opportunity

  • Generic questioning: Could apply to any subject

  • Passive learning: No ownership of development process

💎 Your Leadership Development Challenge: Create a reflection prompt that demonstrates the self-awareness and continuous improvement mindset that top performers cultivate.

Action: You’ve mastered the fundamental skill of finance: converting future cash flows into present value. This framework applies whenever money moves through time—from personal savings decisions to investment analysis to corporate strategy. Your next DRIVER opportunity: applying this exact framework to stock valuation, where future dividends get discounted to today’s value using identical logic.


Section 5: Assignment - Time Value of Money Analysis#

Assignment Overview#

Analyze a retirement savings decision from the perspective of a financial advisor. Your client, age 22, has just graduated from university with an annual salary of $65,000. The client plans to retire at age 65 and intends to save 30% of annual income at each year-end. Your analysis must account for inflation (2% annually), salary growth (3% annually), and a portfolio allocation of 60% stocks (expected 8% return) and 40% bonds (expected 4% return).

Required Analysis:

  1. Calculate total accumulated wealth at age 65

  2. Determine present value of this future amount

  3. Develop and justify an alternative savings plan with supporting calculations

  4. Analyze the impact of an additional $1,000 annual contribution


DRIVER Framework Requirement#

DRIVER is your analytical work process, not a documentation format.

You must use DRIVER to conduct your analysis, not to describe completed work retrospectively. This means beginning your analytical work with the Define & Discover stage and completing both D and R stages before proceeding to implementation.

Work Process Requirements:

  • Begin your analytical work with the Define & Discover stage

  • Complete the Represent stage to plan your analytical approach

  • Proceed to Implementation only after D and R stages are documented

  • Document your process as you work through each stage sequentially

Submission Requirements:

All submissions must include:

  1. DRIVER Analysis Document demonstrating sequential stage completion

  2. Video presentation covering all six DRIVER stages in order: D → R → I → V → E → R

  3. Code repository with executable analysis

Your documentation must reflect chronological progression through the analytical process, not retrospective justification of completed work.

Critical Requirement: Assignments submitted without adequate Define & Discover stage documentation completed before implementation will receive a grade of zero without further evaluation.

Refer to DRIVER Framework: Assignment Guidelines for complete requirements and grading criteria.


Specific Requirements#

Financial Analysis Requirements#

Your analysis must include:

  1. Time Value of Money Calculations

    • Future value of variable contribution stream

    • Present value determination with appropriate discount rate

    • Compound interest effects across 43-year time horizon

    • Portfolio-weighted return calculations

  2. Scenario Analysis

    • Base case: Standard 30% savings rate

    • Alternative case: Modified savings strategy with justification

    • Sensitivity analysis: Impact of additional $1,000 annual contribution

    • Comparison of outcomes across scenarios

  3. Financial Planning Assessment

    • Retirement income adequacy evaluation

    • Inflation-adjusted purchasing power analysis

    • Risk-return tradeoff consideration

    • Professional recommendation with supporting rationale

Technical Requirements#

  1. Python implementation for multi-period cash flow calculations

  2. Variable contribution modeling with salary growth

  3. Portfolio return calculations with mixed asset allocation

  4. Present and future value computations

  5. Scenario comparison automation

Deliverables#

1. DRIVER Analysis Document

  • Format: Markdown, PDF, or Jupyter Notebook section

  • Structure: All six DRIVER stages as specified in framework guidelines

  • Content: Demonstrates systematic progression through analytical process

2. Video Presentation

  • Content: All six DRIVER stages with code demonstration

  • Delivery: Clear explanation suitable for finance professionals

  • Technical: Screen recording showing working code execution

3. Code Repository

  • Platform: Google Colab, Jupyter Notebook, or GitHub repository

  • Requirements: Executable code without errors, comprehensive documentation

  • Includes: README explaining DRIVER application and assumptions


Learning Objectives Alignment#

This assignment assesses your ability to:

  • Apply time value of money principles to multi-period problems

  • Model complex cash flow streams with growth rates

  • Calculate portfolio-weighted returns

  • Evaluate financial planning alternatives systematically

  • Apply the DRIVER framework to financial advisory scenarios

  • Integrate financial theory with technical implementation

  • Communicate analytical findings effectively


Assessment#

Your work will be evaluated according to the grading structure specified in DRIVER Framework: Assignment Guidelines:

Total: 100 points

1. Financial Concepts Accuracy (50 points)#

Your understanding will be assessed on the following session-specific financial concepts:

  • Time value of money principle: Why money today is worth more than money tomorrow

  • Present value and future value concepts: PV and FV calculations for single cash flows

  • Interest rates and compounding: Annual rates, compounding frequency, effective vs. nominal rates

  • Number of periods: Understanding time horizon effects on value

  • Annuities: Present and future value of ordinary annuities with equal payments

  • Variable cash flow streams: Valuing cash flows that grow over time

  • Portfolio-weighted returns: Calculating expected returns from mixed asset allocations

  • Real vs. nominal returns: Inflation adjustment and purchasing power

  • Discount rate selection: Choosing appropriate rates for different types of cash flows

2. Technical Implementation (10 points)#

  • Code execution for multi-period cash flow calculations

  • Variable contribution modeling with growth rates

  • Portfolio return calculations with mixed assets

  • Scenario comparison automation

  • Code organization and financial logic documentation

3. Integration of Finance and Technology (20 points)#

  • Automation of complex TVM calculations

  • Scenario analysis capabilities beyond manual computation

  • Visualization of cash flow growth and accumulation

  • Demonstrates understanding of how technology enables long-term financial planning

4. Following the DRIVER Framework (10 points)#

  • Define & Discover: Clear problem understanding and retirement planning objectives completed before implementation

  • Represent: Quality logic mapping for multi-period cash flow analysis

  • Implement: Systematic execution of TVM calculations

  • Validate: Verification against retirement calculators and reasonableness checks

  • Evolve: Alternative savings strategies and scenario analysis

  • Reflect: Learning insights about long-term wealth accumulation

Critical Gate: Assignments without adequate Define & Discover documentation before implementation receive zero.

5. Clear Communication and Explanation (10 points)#

  • Video clearly explains TVM analysis and retirement planning journey

  • Complex multi-period calculations explained simply

  • Logical flow from principles to practical retirement planning

  • Demonstrates genuine understanding of compound growth effects

Total: 100 points


Data Sources and Assumptions#

Required Assumptions:

  • Initial salary: $65,000 (age 22)

  • Retirement age: 65 (43-year time horizon)

  • Savings rate: 30% of annual income (year-end contributions)

  • Salary growth: 3% annually

  • Inflation rate: 2% annually

  • Stock return: 8% annually (60% portfolio weight)

  • Bond return: 4% annually (40% portfolio weight)

Verify calculation accuracy using online retirement calculators. Document any deviations from stated assumptions with justification.


Submission#

Submit all deliverables according to your instructor’s specified method and deadline.

Ensure your DRIVER Analysis Document clearly demonstrates that you completed the Define & Discover stage before proceeding to implementation. Your documentation should reflect progressive development through the analytical process, not retrospective justification.


Refer to DRIVER Framework: Assignment Guidelines for complete documentation requirements, grading criteria, and framework application guidance.


Section 6: Reflect & Connect - Financial Insights Discussion#

Individual Reflection#

Instructions: Answer in 1-2 sentences. Don’t use AI - this checks your understanding.

Question 1: Why is a dollar today worth more than a dollar next year? Question 2: What’s the difference between present value and future value? Question 3: When might TVM analysis NOT be very helpful for a financial decision? Question 4: Complete this statement: “The biggest misconception I had about interest and time was…”

AI Learning Support - Learning Synthesis

Learning Goal: Develop metacognitive awareness and reflection skills for continuous learning.

💡 Professional Prompt Sample A (Grade: A): “I’ve completed my first session on time value of money and applied the DRIVER framework to a business funding problem. I feel confident with single payment PV/FV but less sure about more complex compounding scenarios. Act as an experienced finance mentor and help me reflect: 1) What core TVM principles should I master before moving to stock valuation? 2) How can I test my readiness for multi-period cash flow analysis? 3) What self-assessment questions should I ask after each financial analysis session?”

🏆 Why This Accelerates Your Professional Growth:

  • Specific competency assessment: Shows honest self-evaluation

  • Forward-looking preparation: Links to upcoming challenges

  • Systematic improvement: Seeks reusable frameworks

  • Mentorship mindset: Values expert guidance

🤯 Weak Prompt Sample (Grade: D): “What did I learn today and how will it help my career?”

💸 Why This Wastes Your Tuition Investment:

  • Zero introspection: Shows no self-awareness

  • Vague and generic: Could apply to any class

  • No growth strategy: Misses skill development opportunity

  • Lazy engagement: Minimal intellectual effort

⭐ Your Excellence Development Mission: Design a reflection prompt that shows the self-awareness and continuous improvement drive that finance leaders possess.

Pair Discussion#

Share your reflection with a partner. Then discuss:

  • Which of today’s concepts will you actually use this semester?

  • How do you think the TVM framework will apply to stock valuation next week?

  • What’s still confusing that we should address next class?

Class Synthesis#

Three volunteers share one insight from their pair discussion that demonstrates the practical power of TVM thinking.


Section 7: Looking Ahead - From Time Value to Investment Analysis#

Session Preview#

The TVM framework you just mastered is the foundation for every major topic in this course:

Timeline of Course Applications:

Session 3 (Stocks):     Dividends -----> Dividends -----> Stock Price Today
                        Year 1          Year 2           (Present Value)

Session 4 (Bonds):      Interest -----> Interest -----> Principal + Interest
                        Year 1          Year 2          Year 3 (Maturity)
                        
Session 5 (Real Estate): Monthly Payment -> Monthly Payment -> ... (360 payments)
                         Month 1          Month 2              Month 360

Sessions 9-10 (Corporate): Project Cash Flow -> Project Cash Flow -> NPV Decision
                           Year 1             Year 5              Today
  • Session 3 (Stocks): “What’s Apple stock worth?” = “What are Apple’s future dividends worth today?”

  • Session 4 (Bonds): “Should I buy this Treasury bond?” = “Are these future interest payments worth the current price?”

  • Session 5 (Real Estate): “Can I afford this house?” = “What’s the present value of 30 years of mortgage payments?”

The Pattern: Every financial decision is ultimately a TVM problem. Master this, and you master finance.