Master discounting and compounding and the rest of finance follows.
What you will learn
Explain present and future value
Apply the compound interest formula
Understand discounting as the inverse of compounding
The power of compounding
The power of compounding
Risk vs return
Risk vs return
A dollar today > a dollar tomorrow
Money has time value because a dollar today can be invested to earn more, and because inflation erodes future purchasing power. So $100 today is worth more than $100 in a year. This is the foundation of every valuation, loan, and investment decision.
💡 Future value
FV = PV × (1 + r)^n. Invest $1,000 at 7% for 20 years: 1,000 × 1.07^20 ≈ $3,870. The growth is exponential — most of it happens in the later years. This is why starting early matters more than earning a slightly higher rate.
Present value & discounting
Discounting is compounding in reverse: PV = FV / (1 + r)^n. It answers 'how much is a future cash flow worth today?' A $1,000 payment in 10 years, discounted at 8%, is worth only ~$463 today. Every asset price is the present value of its expected future cash flows.
The rule of 72
A quick mental shortcut: divide 72 by the annual return to estimate doubling time. At 7%, money doubles in ~10 years (72/7 ≈ 10.3). At 12%, ~6 years. At 2%, ~36 years. The rule makes the cost of low returns instantly visible.
💡 Small rate, huge difference
$10,000 for 40 years: at 6% → ~$103,000; at 8% → ~$217,000; at 10% → ~$453,000. Two percentage points more than doubled your outcome over four decades. Time is a multiplier of every rate decision.
Annuities & perpetuities
An annuity is a series of equal payments (a mortgage, a pension). A perpetuity pays forever — its value is simply Payment ÷ rate. These formulas price bonds, loans, and many income assets. The pattern: every cash-flow stream reduces to discounting.
❓ Quick check
At 7%, money doubles in about how many years (Rule of 72)?
A) 5 years
B) 10 years
C) 20 years
D) 72 years
72/7 ≈ 10.3 years.
(Knowledge check — full exam is next)
Key takeaways
Time value = the foundation of all valuation
FV = PV(1+r)^n; PV = FV/(1+r)^n
Rule of 72 estimates doubling time; time amplifies every rate
📝 Weekly Exam — pass with 80% to unlock next week
10 questions. Review the Deep Dive and courses before attempting.
1. A dollar today is worth more than a dollar tomorrow because:
Opportunity cost + inflation.
2. FV of $1,000 at 7% for 10 years is about:
1000 × 1.07^10 ≈ $1,967.
3. Discounting is:
PV = FV/(1+r)^n.
4. PV of $1,000 in 10 years at 8% is about:
1000 / 1.08^10 ≈ $463.
5. The Rule of 72 estimates:
72 ÷ rate ≈ years to double.
6. $10,000 at 8% for 40 years grows to about:
10000 × 1.08^40 ≈ $217,000.
7. A perpetuity's value equals:
PV = P / r for a perpetual payment.
8. The single biggest lever on long-term wealth is:
Time × rate dominates long-run outcomes.
9. An annuity is:
Repeated equal cash flows.
10. Why is 'start early' more powerful than 'earn more'?
Exponential growth rewards time most.
Your score: —
🛠 Weekly Project
Build a compounding table for your own goal.
1
Choose a savings goal and monthly contribution.
2
Compute the future value at 5%, 7%, and 9% over 10, 20, 30 years (use a spreadsheet or the Lab).
3
Find the doubling time for each rate (Rule of 72).
4
Write one sentence on how the rate and the time horizon each changed your outcome.