How Compound Interest Works: The Mathematical Engine of Wealth

The Math of Compounding: Why Linear Thinking Fails

Humans intuitively think linearly: if ₹10,000 earns ₹1,000 in Year 1, our minds assume it will earn ₹10,000 over 10 years. But with compounding, your earnings become productive workers that earn their own earnings.

The classic compounding formula is: $$A = P \times \left(1 + \frac{r}{n}\right)^{n \times t}$$

Where: - $A$ = Final accumulated corpus - $P$ = Initial principal invested - $r$ = Annual interest / compounded return rate (decimal) - $n$ = Compounding frequency per year (e.g. 1 for annual, 4 for quarterly, 12 for monthly) - $t$ = Number of years invested

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The Hockey-Stick Effect: Patience is the Multiplier

In the first 5 to 7 years of investing, compounding feels disappointingly slow. Your account value barely looks different from your total contributions. However, between Year 10 and Year 25, the exponential curve turns vertical: - In Year 1 to 5: 80% of your portfolio value is your own deposited principal. - In Year 15 to 20: Over 70% to 80% of your portfolio value consists purely of accumulated compound returns!

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The Rule of 72: A Quick Mental Math Shortcut

To quickly estimate how many years it takes for your investment to double at a given annual return rate ($r$), divide 72 by the annual return rate: - At 12% CAGR (typical diversified Indian equity): $72 / 12 = \mathbf{6\text{ years to double}}$. - At 8% interest (Fixed Deposit / EPF): $72 / 8 = \mathbf{9\text{ years to double}}$. - At 4% interest (Savings Account): $72 / 4 = \mathbf{18\text{ years to double}}$.