Overview

A dollar today is worth more than a dollar tomorrow. Why? Because you can invest the dollar today and earn interest. This simple idea is the foundation of all finance.

Core Idea

Compounding: Interest on interest. Einstein called it the “eighth wonder of the world.” $$ FV = PV \times (1 + r)^n $$

  • $FV$: Future Value
  • $PV$: Present Value
  • $r$: Interest Rate
  • $n$: Number of periods

Formal Definition (if applicable)

Discounting: The process of determining the present value of a payment or a stream of payments that is to be received in the future. It’s the reverse of compounding.

Intuition

Would you rather have $100 now or $100 in 10 years? Obviously now. Would you rather have $100 now or $200 in 10 years? That depends on the interest rate. If you can earn 10% a year, $100 becomes $259 in 10 years. So take the $100 now.

Examples

  • Mortgage: You borrow $300k but pay back $600k over 30 years because of interest.
  • Retirement: Saving a little bit early is better than saving a lot late.
  • Lottery: Lump sum (PV) vs. Annuity (payments over time).

Common Misconceptions

  • “Interest is linear.” (No, it’s exponential. Small differences in rates make huge differences over time.)
  • “Inflation doesn’t matter.” (Real return = Nominal return - Inflation).
  • NPV (Net Present Value): The value of an investment minus its cost. If NPV > 0, do it.
  • IRR (Internal Rate of Return): The break-even interest rate.
  • Opportunity Cost: The money you could have earned elsewhere.

Applications

  • Valuation: How much is a company worth? (The sum of its future cash flows, discounted back to today).
  • Personal Finance: Should I pay off debt or invest?

Criticism / Limitations

Assumes a constant interest rate, which rarely happens in the real world.

Further Reading

  • Bodie, Kane, & Marcus, Investments
  • Malkiel, A Random Walk Down Wall Street