Compound Interest and the Rule of 72, Explained With Real Numbers

Compound interest is often described as interest on interest. True, but it undersells the effect. Over long periods compounding does most of the work, and a few small choices (the rate, how often interest is added, and how long you leave it) change the outcome far more than people expect.

Simple interest vs compound interest

Put ₹1,00,000 away at 8% a year for 10 years.

• Simple interest pays 8% of the original ₹1 lakh every year: ₹8,000 × 10 = ₹80,000 interest, so you end with ₹1,80,000.
• Compound interest adds each year’s interest to the balance, so next year’s 8% is earned on a bigger amount. After 10 years you have ₹2,15,892.

The extra ₹35,892 is the interest earned on earlier interest. Stretch the period to 20 or 30 years and that gap becomes most of the final amount.

The formula

A = P × (1 + r ÷ n)^{n × t}

P is the starting amount, r the yearly rate as a decimal, n how many times a year interest is added, and t the number of years. For the example above with yearly compounding: 1,00,000 × 1.08¹⁰ = ₹2,15,892.50.

Does compounding frequency matter?

A little. The same 8% compounded monthly instead of yearly gives about ₹2,21,964 after 10 years, roughly ₹6,000 more. The more often interest is added, the higher the effective yearly rate, but the jump from monthly to daily is tiny. When comparing deposits, look at the annual yield or effective rate, not just the headline rate.

The rule of 72

A quick way to estimate how long money takes to double: divide 72 by the yearly percentage rate.

• At 8%: 72 ÷ 8 ≈ 9 years (the exact answer is 9.01 years)
• At 6%: about 12 years
• At 12%: about 6 years

It works in reverse too. Inflation of 6% halves the buying power of cash in about 12 years. The rule is accurate for rates between roughly 4% and 15%; for very high rates, use the calculator.

Real returns: compounding after inflation

If a deposit earns 7% and inflation runs at 5%, your money grows in buying power by only about 2% a year. By the rule of 72, that real value takes around 36 years to double, not 10. When you compare investments over long periods, think in real (inflation-adjusted) returns, and use the Inflation Calculator to see what a future sum is worth today.

Three practical takeaways

• Start early. Ten extra years at the beginning add more than a bigger amount added later.
• Watch the fees. A 1% yearly fee on an investment compounds against you in exactly the same way returns compound for you.
• Debt compounds too. Credit card balances at 36–42% a year double in about two years. Clearing high-interest debt is usually the best “return” available.

To see how regular deposits grow, try the Savings Calculator; to measure the yearly growth rate of an investment you already hold, use the CAGR Calculator.

Frequently asked questions