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

> Compound interest earns interest on your interest. The formula, how compounding frequency matters, the rule of 72, real examples in $ and ₹, and how debt compounds against you.

- URL: https://2search.in/knowledge/articles/oct-26/compound-interest-explained
- Genre: Personal finance
- Country: Everywhere
- Published: 2026-10-27
- Updated: 2026-10-27
- Publisher: 2search (https://2search.in)

> **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).



![Compound interest explained: formula, examples and the rule of 72 Breakdown & Visual Guide](/images/articles/compound-interest-explained/diagram.svg)

## Simple interest vs compound interest

| | **Simple interest** | **Compound interest** |
| --- | --- | --- |
| Interest is earned on | Only the original amount | Original amount **plus** past interest |
| Growth | Straight line | Curve that gets steeper over time |
| Formula | P × r × t | P × (1 + r/n)^(n×t) |
| Common in | Some short loans, car loans in some countries | Savings, FDs, mutual funds, PPF, credit cards |

> **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**:

| Years | Value | Of which interest |
| --- | --- | --- |
| 10 | $19,672 | $9,672 |
| 20 | $38,697 | $28,697 |
| 30 | $76,123 | $66,123 |
| 40 | $149,745 | $139,745 |

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:

| Starts at age | Total put in | Value at 65 |
| --- | --- | --- |
| **25** | $96,000 | **~$525,000** |
| 35 | $72,000 | ~$244,000 |
| 45 | $48,000 | ~$104,000 |

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](/sip-vs-lump-sum) or an automatic [401(k)](/401k-ira-contribution-limits-2026) contribution makes this automatic.

## The rule of 72

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

| Rate | Years to double (72 ÷ rate) |
| --- | --- |
| 4% | 18 years |
| 6% | 12 years |
| 7.1% (India's PPF) | ~10 years |
| 8% | 9 years |
| 10% | 7.2 years |
| 12% | 6 years |
| 24% (a typical credit card) | **3 years** — for your debt |

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:

| Compounded | Final amount |
| --- | --- |
| Yearly | $16,289 |
| Monthly | $16,470 |
| Daily | $16,487 |

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](/roth-vs-traditional-ira) in the US, [PPF](/ppf-interest-rate-rules) 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](/emergency-fund-how-much) so you never have to sell in a crash.

> **Tip:** Try your own numbers in the [compound interest calculator](/tools/compound-interest-calculator) or, for mutual fund SIPs, the [SIP calculator](/tools/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](https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator)
- [CFPB — What is a credit card interest rate (APR)?](https://www.consumerfinance.gov/ask-cfpb/what-is-a-credit-card-interest-rate-what-does-apr-mean-en-44/)
- [Federal Reserve Bank of St. Louis — Compound interest (education)](https://www.stlouisfed.org/education)