Welcome back to class! Today we are wrapping up Chapter 4: Personal Finance by diving into Section 4.5. This section moves beyond savings and loans to look at the broader economic factors that affect your wallet: Inflation, Taxes, and Stocks.

Understanding these concepts isn't just for the final exam; it is crucial for navigating your financial future. Below are the key takeaways from today's lecture notes and the video assignment.

1. Understanding Inflation and the CPI

How do we know if life is getting more expensive? We use the Consumer Price Index (CPI), which measures the average price paid by consumers for a standard "market basket" of goods and services. When the CPI goes up, we have inflation.

To calculate the rate of inflation, we look at the percentage change in the CPI:

$$\text{Rate of Inflation} = \frac{\text{Change in CPI}}{\text{Previous CPI}} \times 100\%$$

The Buying Power Trap: It is important to note that if inflation is $5\%$, the buying power of your dollar does not decrease by exactly $5\%$. Because the cost of goods has risen, your dollar buys a smaller fraction of those goods. We use the Buying Power Formula to find the actual percentage decrease:

$$ \text{Percent Decrease in Buying Power} = \frac{100i}{100 + i} $$

Where $i$ is the inflation rate as a percent. For example, if inflation is $5\%$, the purchasing power drops by roughly $4.8\%$.

2. Taxes: Deductions vs. Credits

In our review of the tax tables (see the Betty vs. Carol example in the notes), we discovered a major difference between two ways to lower your taxes:

  • Tax Deductions: This lowers your taxable income. It saves you money based on your tax bracket percentage.
  • Tax Credits: This lowers your tax bill dollar-for-dollar.

Key Insight: As we saw in the notes, even though Betty had a larger deduction ($10,000$) compared to Carol ($9,000$), Carol ended up paying less tax because she had a $1,000$ tax credit. Credits are generally more powerful than deductions!

3. The Stock Market (DJIA)

We also looked at the Dow Jones Industrial Average (DJIA). It represents a collection of major stocks. A key multiplier to remember for the DJIA is roughly 7.56.

For every $1 move in any Dow company’s stock price, the DJIA changes by about 7.56 points. So, if a stock like Walt Disney increases by $3$ per share, the Dow jumps by:

$$ 3 \times 7.56 = 22.68 \text{ points} $$

4. Video: The Trillion Dollar Bet

Please ensure you watch the assigned video, The Trillion Dollar Bet. This documentary connects our math concepts to the real world by exploring the Black-Scholes formula. It tells the story of Long-Term Capital Management (LTCM), a hedge fund run by Nobel Prize-winning economists. It serves as a fascinating (and cautionary) tale about what happens when mathematical models of the market meet the unpredictability of human behavior.

Action Items

  • Review: Go over the Chapter 4 Summary slides (slides 12-13) to refresh your memory on simple vs. compound interest formulas before the quiz.
  • Quiz: Complete the Section 4-5 Quiz.
  • Final Project: Please submit your topic for the Final Project this week.

Study hard, and see you in the next class!