How exponential compounding (A = P(1 + r/n)^(nt)) turns regular savings into wealth.
The Power of Compounding
Simple interest earns returns only on initial principal; compound interest earns returns on both principal and all previously accumulated interest.
Compound Interest Formula: A = P(1 + r/n)^(n·t)
The Continuous Compounding Limit (Euler's Number e)
As the compounding frequency n approaches infinity (compounding every microsecond), the formula converges to the continuous exponential function.
Continuous Compounding: A = P · e^(r·t)
The Quick Rule of 72
To estimate how many years it takes for an investment to double at a fixed annual return 'r', divide 72 by r.
Rule of 72: Years to Double ≈ 72 / Annual_Interest_Rate (%)
Example: $10,000 Invested for 30 Years
At 8% annual compound return: 72 / 8 = 9 years to double. $10,000 doubles 3.3 times over 30 years to become over $100,626 without adding another penny.
Future Value: $10,000 × (1.08)³⁰ = $100,626.57
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