Comprehensive Guide • Investing & Wealth

How Compound Interest Works: Formula, Frequencies & Rule of 72

✍️ Author: AG World Tools Editorial Team ⚖️ Reviewed by: Verified by AG World Tools Technical & Financial Review Board 📅 Last Reviewed: 2026-11-01

Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods, creating an exponential growth trajectory described by the formula $A = P \left(1 + \frac{r}{n}\right)^{nt}$. Unlike simple interest, which grows linearly by adding the same fixed percentage of principal each cycle, compounding earns "interest on interest."

The more frequently interest is compounded — whether annually, quarterly, monthly, or daily — the higher the effective annual yield (APY) earned by the saver.

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The Mathematical Formula Explained

$$\mathbf{A = P \left(1 + \frac{r}{n}\right)^{nt}}$$

Where:

  • $A$ = Final accumulated amount (Principal + Total Interest)

  • $P$ = Initial principal balance

  • $r$ = Annual nominal interest rate (in decimal, e.g., 8% = 0.08)

  • $n$ = Compounding frequency per year ($n=1$ for annual, $n=4$ for quarterly, $n=12$ for monthly)

  • $t$ = Number of years the money is invested

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    Worked Example: ₹1,00,000 at 8% for 5 Years Across Compounding Frequencies

    Let us observe the tangible impact of compounding frequency on an initial investment of ₹1,00,000 at 8.00% annual interest over 5 years:

  • Simple Interest (Linear):

    • $$\text{Interest} = ₹1,00,000 \times 0.08 \times 5 = \mathbf{₹40,000} \implies \text{Total} = \mathbf{₹1,40,000}$$
  • Annually Compounded ($n=1$):

    • $$A = 1,00,000 \times (1 + 0.08)^5 = \mathbf{₹1,46,933}$$ (Gain over Simple Interest: ₹6,933)
  • Quarterly Compounded ($n=4$ - Standard Indian Bank FD):

    • $$A = 1,00,000 \times \left(1 + \frac{0.08}{4}\right)^{20} = 1,00,000 \times (1.02)^{20} = \mathbf{₹1,48,595}$$ (Gain: ₹8,595)
  • Monthly Compounded ($n=12$):

    • $$A = 1,00,000 \times \left(1 + \frac{0.08}{12}\right)^{60} = \mathbf{₹1,48,985}$$ (Gain: ₹8,985)

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    The Rule of 72: Instant Mental Math

    The Rule of 72 is a fast heuristic used to approximate the number of years required to double your money at a fixed annual compound rate:

    $$\mathbf{\text{Years to Double}} \approx \frac{72}{\text{Annual Interest Rate (\%) prénom}}$$

  • At 6% interest: $72 / 6 = \mathbf{12\text{ years}}$ to double.

  • At 8% interest: $72 / 8 = \mathbf{9\text{ years}}$ to double.

  • At 12% equity return: $72 / 12 = \mathbf{6\text{ years}}$ to double.

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    Frequently Asked Questions

    Why do Indian fixed deposits compound quarterly?

    Most Indian public and private commercial banks compound fixed deposit interest on a quarterly basis in accordance with Reserve Bank of India (RBI) operating circulars. This provides a slightly higher effective annual yield than nominal stated rates.

    How does inflation affect compounding?

    While compound interest expands your nominal account balance exponentially, inflation erodes the purchasing power of each rupee. Your true economic wealth growth depends on the real rate of return (Nominal Interest Rate minus Inflation Rate).

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    Official Sources & Statutory References