Chapter 3: Time Value Of Money

Concept:
- Money now is more valuable than money later.
- Reason:
- Money can be used to generate more money.
- Ways to Generate Money:
- Running a business.
- Buying and selling items for a profit.
- Saving money in a bank to earn interest.

Definition:
- Compound interest is the interest paid on interest, or the reinvestment of interest paid on an investment’s principal.
- Principal: The face value of the deposit or debt instrument.

Example: Compound Interest at 6% Over Time
- Initial Investment: $100 (Present Value, PV)
- Interest Rate: 6% (denoted as 'i')
- First Year:
- Future Value (FV) after 1 year = $100 + ($100 * 0.06) = $106.
- After 10 Years:
- Future Value = $179.08.
- Total interest earned = $79.08.
- Reference: Keown/Personal Finance, 9th Ed - CH 3 Figure 3.3

Scenario: Using Calculator.net for Compound Interest at 6%
- Initial Investment: $100 (PV)
- First Year: FV = $106.
- After 10 Years:
- Future Value = $179.08, earning $79.08 interest.

Periodic Deposits at End of Compound Period:
- Strategy: Deposit an additional $100 annually for 10 years
- Total Amount After 10 Years:
- Future Value = $1,497.16
- Total interest earned = $397.16.
Periodic Deposits at Beginning of Compound Period:
- Strategy: Same additional deposits
- Total Amount After 10 Years:
- Future Value = $1,497.16
- Total interest earned = $476.25.
- Conclusion: Deposits made earlier yield higher interest payouts.

Example Calculation with 10% Interest:
- Present Value: $1,000
- Calculation:
- $1,000 x 0.10 = $100 (first year interest)
- Balance after 1 year = $1,000 + $100 = $1,100 (FV)
- Growth Over Years:
  - Year 2: $1,100 x 1.10 = $1,210
  - Year 3: $1,210 x 1.10 = $1,331
  - Year 4: $1,331 x 1.10 = $1,464.10
  - Year 5: $1,464.10 x 1.10 = $1,610.51
- Formula:
  - Future Value = Present Value x (1 + r)^n
  - $1,000 x (1.10)^5 = $1,610.51

Future Value Formula:
- Using letters:
- FV = PV x (1 + r)^n
  - Where:
  - PV = Present Value
  - r = Interest Rate
  - n = Number of Periods
Present Value Formula:
- Using letters:
- PV = FV ÷ (1 + r)^n
  - Where:
  - FV = Future Value
  - r = Interest Rate
  - n = Number of Periods

Present Value:
- Answers the question: What is it worth in today's dollars?
Future Value:
- Answers the question: If I invest X amount today at a certain interest rate, how much will I have in the future?

Scenario:
- Selma and Patty saving for retirement over 35 years.
- Selma invests $2,000 annually for 10 years.
- Patty waits 10 years to start investing the same amount.

Investment of $2,400:
- One-time deposit at varying annual interest rates, adding another $2,400 yearly:
- 0.42% for 40 years
- 1% for 40 years
- 5% for 40 years

Objective: Need $5,000,000 in 40 Years
At 5%:
- Required investment = $710,228.41
At 10%:
- Required investment = $110,474.64
- Significance:
- Emphasizes the importance of early investment.

Purpose: Estimate doubling time of an investment.
Formula:
- Years to double = 72 ÷ interest rate
- Example:
- 9% annual growth = 72 ÷ 9 = 8 years to double.

Interest rate is crucial in determining how much an investment grows.
Quote:
- “Compound interest is the eighth wonder of the world.” - Warren Buffet.

1¢ at 100% Compounded Daily:
- Day 1: $0.01
- Day 2: $0.02
- Day 3: $0.04
- Day 4: $0.08
- Progression:
- 5 days: $0.16
- 6 days: $0.32
- 31 days: $10,737,418.24, demonstrating the power of compounding.

Available on Canvas:
- Hypothetical Savings Plan
- Article: "No Matter How Old You Are, You Can Retire with $1M"