Compound interest explained: formula, examples and the rule of 72

Quick answer: Compound interest means you earn interest not only on the money you put in, but also on the interest it has already earned. The formula is A = P × (1 + r/n)^(n×t). At 7% a year, $10,000 becomes about $19,700 in 10 years, $38,700 in 20 and $76,100 in 30. The rule of 72 gives a quick estimate: divide 72 by the interest rate to find how many years it takes to double your money.

Key takeaways

• Time matters more than amount. Starting 10 years earlier can more than double your final total.
• The rate matters a lot: 72 ÷ 6% = 12 years to double; 72 ÷ 12% = 6 years.
• More frequent compounding (monthly vs yearly) helps, but only a little.
• Debt compounds too. Credit card interest at 24–40% a year grows against you very fast.
• Fees, taxes and inflation reduce your real compounding — keep them low.

Albert Einstein may never have called compound interest the "eighth wonder of the world" — but the maths behind the quote is real. This guide explains how compounding works in plain words, shows the formula with worked examples, and gives you practical ways to make it work for you (and stop it working against you).

#Simple interest vs compound interest

Example: You invest ₹1,00,000 at 8% for 20 years.

• With simple interest: ₹8,000 a year × 20 = ₹1,60,000 interest → ₹2,60,000 total.
• With yearly compound interest: ₹4,66,096 total.

Same money, same rate — compounding adds over ₹2 lakh extra.

#The compound interest formula

A = P × (1 + r/n)^(n × t)

• A = final amount
• P = principal (the starting amount)
• r = yearly interest rate as a decimal (7% = 0.07)
• n = how many times interest is added per year (1 = yearly, 12 = monthly)
• t = number of years

Worked example

$10,000 at 7%, compounded yearly, for 20 years:

A = 10,000 × (1 + 0.07)^20 = 10,000 × 3.87 = $38,697

Your money nearly quadruples, and $28,697 of it is interest.

#How compounding grows over time

$10,000 invested once at 7% a year:

Look at the last row: in the final 10 years, the money grows by about $73,600 — more than in the first 30 years combined. That's why compounding is often called a "snowball".

#Why starting early beats investing more

Three people each invest $200 a month at 7% until age 65:

The person who started at 25 put in only $24,000 more than the 35-year-old — but ends with more than double. Those extra 10 years let compounding do the heavy lifting.

Tip: Can't invest much now? Start with whatever you can — even small amounts — and increase it every year. A SIP or an automatic 401(k) contribution makes this automatic.

#The rule of 72

To estimate how long money takes to double, divide 72 by the yearly rate:

It also works for inflation: at 6% inflation, prices double in about 12 years, so your money buys half as much.

#Does compounding frequency matter?

$10,000 at 5% for 10 years:

More frequent compounding adds a little, but rate and time matter far more. When comparing savings accounts or deposits, look at the APY (US) or effective annual yield, which already includes compounding.

#When compounding works against you: debt

Credit cards compound interest on unpaid balances — often monthly, at rates of 20–30% a year in the US and 36–45% a year in India.

Warning: A $5,000 card balance at 24% APR, if you pay nothing, grows to about $6,340 in one year and roughly $10,000 in three years. Paying only the minimum keeps you in debt for years.

How to fight it:

• Pay the full statement balance every month.
• Pay off the highest-rate debt first (the "avalanche" method).
• Move expensive card debt to a lower-rate loan if you can, then stop using the card.
• Never take a new loan to pay an old one without a plan.

#What slows your compounding

• Fees: a 1% yearly fund fee on a 7% return cuts your 30-year result by roughly a quarter. Prefer low-cost index funds and direct mutual fund plans.
• Taxes: use tax-advantaged accounts — 401(k) and IRAs in the US, PPF and EPF in India.
• Inflation: a 7% return with 3% inflation is a 4% real return.
• Withdrawals: taking money out early resets the snowball.

#Practical ways to use compounding

1. Start now, even small.
2. Automate monthly investing on payday.
3. Reinvest dividends and interest (choose "growth" or "accumulation" options).
4. Increase contributions every year with your raise.
5. Keep costs low and avoid high-interest debt.
6. Stay invested through ups and downs; keep an emergency fund so you never have to sell in a crash.

Tip: Try your own numbers in the compound interest calculator or, for mutual fund SIPs, the SIP calculator.

#Frequently asked questions

What is compound interest in simple words?

It's interest earned on both your original money and the interest already added to it, so your money grows faster over time.

What is the formula for compound interest?

A = P × (1 + r/n)^(n×t), where P is the starting amount, r the yearly rate, n the compounding periods per year and t the number of years.

How does the rule of 72 work?

Divide 72 by the yearly interest rate. The answer is roughly how many years it takes to double your money.

Is compound interest good or bad?

Good when you save or invest; bad when you borrow, because your debt grows the same way.

Do stocks pay compound interest?

Stocks don't pay interest, but reinvested dividends and rising prices compound in a similar way over time.

How often is interest compounded in a savings account?

Many banks compound daily or monthly and pay monthly or quarterly. Check the APY or effective yield to compare.

What is the best way to benefit from compounding?

Start early, invest regularly, reinvest returns, keep fees low and stay invested for many years.

#Sources

• U.S. SEC Investor.gov — Compound interest calculator
• CFPB — What is a credit card interest rate (APR)?
• Federal Reserve Bank of St. Louis — Compound interest (education)