How Compound Interest Works: Simple Examples & Formula

Here is a short story with a big lesson. Two friends, Ana and Ben, both invest $200 a month at 7% a year. Ana starts at age 25 and stops after only 10 years, at 35. She never adds another dollar. Ben waits until age 35 and then invests every month for 30 years, until 65.

Who has more at 65? Ben put in $72,000. Ana put in $24,000. Yet Ana ends up with about $281,000, and Ben ends up with about $244,000. She put in a third as much money and still came out ahead. The reason is compound interest.

The quick answer

• Compound interest means you earn interest on your money, and then you earn interest on that interest.
• Simple interest is only paid on the original amount. It grows in a straight line. Compound interest grows in a curve that gets steeper.
• The three things that matter are the rate, the time and how much you add. Time usually matters most.
• It works against you too. A credit card compounds interest on what you owe.

Simple interest vs compound interest

Say you put $1,000 in an account that pays 7% a year.

• With simple interest, you earn $70 every year, always based on the original $1,000. After 30 years you have $3,100.
• With compound interest, the $70 from year one is added to your balance. In year two you earn 7% on $1,070. After 30 years you have about $7,612.

Same money, same rate, same 30 years. Compounding more than doubled the result.

Notice that the gap barely shows for the first 10 years. It explodes later. That is why compound interest feels slow and boring at the start, and magical at the end.

The compound interest formula

The formula looks scary, but it says something simple.

A = P x (1 + r / n) ^ (n x t)

• A = the amount you end up with
• P = the money you start with (the principal)
• r = the yearly interest rate, as a decimal (7% is 0.07)
• n = how many times a year interest is added
• t = the number of years

Try it: $1,000, 7%, once a year, 10 years. That is 1,000 x 1.07 ^ 10 = $1,967. You can skip the math with our compound interest calculator. It also handles monthly deposits, which the plain formula does not.

Does it matter how often interest is added?

A little. The more often interest is added (the compounding frequency), the more you earn, but the effect is small compared with the rate and the time. Here is $10,000 at 5% for 10 years:

Going from yearly to daily added under $200 over ten years. A one-point higher rate would add much more.

The Rule of 72: a mental shortcut

How long does it take to double your money? Divide 72 by the interest rate. That is the Rule of 72.

At 7%, money doubles in about 10 years (72 / 7 = 10.3). So $1,000 becomes $2,000 at 10, $4,000 at 20 and $8,000 at 30. It is a good estimate, and you can do it in your head. The rule works for debt too: at 24%, what you owe doubles in about three years if you do not pay.

Time beats money: the Ana and Ben story in detail

Let us come back to our two friends. Both earn 7% a year, with interest added monthly.

Chloe is the lesson. She started at 25 and never stopped. She put in $96,000 and ended with about $525,000. Of that, roughly $429,000 is interest. The money she earned is much bigger than the money she saved.

These numbers are examples, not promises. Real returns bounce up and down, and no one earns exactly 7% every year. But the pattern is real: start early, add steadily, leave it alone.

Which accounts use compound interest?

• Savings accounts and CDs. Interest is added daily or monthly. Rates are lower, but the money is safe and easy to reach.
• 401(k)s, IRAs and brokerage accounts. The "interest" comes as growth, dividends and gains that are reinvested. It is not guaranteed, and it can fall in bad years.
• Bonds. Interest paid out can be reinvested to compound.

Returns on stocks and funds are not guaranteed. They rise and fall, sometimes by a lot, so a real account will not climb in a smooth line like the examples above. Use a cautious rate when you plan, and try a few different rates side by side. To see what your savings could grow to by retirement, try our retirement savings calculator, and read how much retirement savings is enough.

Compound interest works against you on debt

The same force that builds savings can wreck a budget. Most credit cards add interest to your balance every day, as the Consumer Financial Protection Bureau explains. At a 22% APR, $1,000 that you leave alone for a year becomes about $1,246, a real cost of about 24.6% because the interest compounds. After three years, a $5,000 balance with no payments grows to nearly $9,700.

This is why paying off high-interest debt is a guaranteed "investment". Wiping out a card at 22% is like earning 22% with no risk. Read our guide on snowball vs avalanche debt payoff to decide the order.

Five ways to make compounding work for you

1. Start now. Even $25 a month is a start. Time is the part you cannot buy later.
2. Automate it. Money you never see is money you do not spend.
3. Raise it every year. Add 1% of your pay each year, or half of every raise.
4. Take free money. A 401(k) match is an instant return before any compounding begins.
5. Keep costs low and do not touch it. Fees compound too, and pulling money out stops the snowball.

Frequently asked questions

How does compound interest work in simple words?

You earn interest on your starting money. Then that interest is added to your balance, so next time you earn interest on a bigger amount. Repeat for years and the growth speeds up.

What is the compound interest formula?

A = P x (1 + r/n) ^ (n x t), where P is the starting amount, r is the yearly rate as a decimal, n is how many times a year interest is added, and t is the number of years.

How long does compound interest take to work?

It starts working on day one, but the effect only becomes obvious after many years. In the first table above, the gap is small at 10 years and large at 30. The longer you leave the money, the bigger the jump each year.

Can compound interest make you rich?

It can build real wealth over decades, but only if you keep adding money and leave it invested. It is a tool for steady people, not a way to get rich quickly.

What is the difference between APR and APY?

APR is the yearly rate without compounding. APY includes compounding, so it is higher. A 22% APR credit card that compounds daily has an APY of about 24.6%. For savings, compare APY.

Does the Rule of 72 include monthly deposits?

No. It only tells you how long a single lump sum takes to double. Use a calculator when you add money regularly.

The bottom line

Compound interest rewards patience more than skill. The best day to start was years ago, and the second best is today. Pick an amount you will not miss, set it to happen on its own, and let time do the heavy lifting. For official, beginner-friendly explanations and a free calculator, see Investor.gov's compound interest calculator.

Sources

• Compound interest calculator, Investor.gov (U.S. Securities and Exchange Commission)
• How does my credit card company calculate the amount of interest I owe?, Consumer Financial Protection Bureau
• Appendix A to Part 1030: Annual percentage yield calculation (Regulation DD), Consumer Financial Protection Bureau

Every dollar figure is calculated by script from the compound interest formula shown, with monthly deposits at the end of each month. Real returns vary and are not guaranteed. Last reviewed October 13, 2026.