How Compound Interest Works, With a Simple Example

Compound interest is one of the quiet forces behind both growing savings and growing debt, so it pays to understand how it works.

Compound interest sounds like a math class topic. But the idea is simple, and once you see it, you will notice it everywhere: in savings accounts, retirement accounts, student loans and credit cards.

In short, compound interest means you earn interest not only on the money you put in, but also on the interest you already earned. The Federal Reserve Bank of St. Louis calls it "interest on interest." Over time, that small twist can make a big difference.

Simple interest vs. compound interest

Let's start with two terms.

• Principal is the money you start with. If you deposit $1,000, your principal is $1,000.
• Interest is what a bank pays you for keeping your money there, or what a lender charges you for borrowing. It is usually shown as a yearly percentage, called a rate.

With simple interest, you earn interest only on the principal. If you have $1,000 earning 5% simple interest, you earn $50 every year. After three years, you have $1,150. The $50 never changes.

With compound interest, each year's interest is added to your balance. Next year, you earn interest on that bigger balance. The amount you earn grows a little every year, even though the rate stays the same.

A worked example: $1,000 at 5% a year

Say you put $1,000 into an account that pays 5% interest, compounded once a year. You never add more money and never take any out.

Year 1: $1,000 × 5% = $50 in interest. New balance: $1,050.

Year 2: Now the 5% applies to $1,050, not $1,000. $1,050 × 5% = $52.50. New balance: $1,102.50.

Year 3: $1,102.50 × 5% = about $55.13. New balance: about $1,157.63.

Compare that with simple interest, where you would have $1,150 after three years. The gap is only $7.63. That does not sound like much, and in the short run, it isn't.

But watch what happens when you give it more time. Here is the same $1,000 at 5%, compounded yearly, with nothing added:

• Years: 1 — Simple interest: $1,050.00; Compound interest: $1,050.00
• Years: 10 — Simple interest: $1,500.00; Compound interest: $1,628.89
• Years: 20 — Simple interest: $2,000.00; Compound interest: $2,653.30
• Years: 30 — Simple interest: $2,500.00; Compound interest: $4,321.94

After 30 years, compound interest turns $1,000 into about $4,322. Simple interest gets you $2,500. The difference, about $1,822, is all "interest on interest."

The math behind the table is one formula: balance = principal × (1 + rate) ^ years. For 30 years, that is $1,000 × 1.05 ^ 30, which is about $4,321.94.

This example uses a steady 5% to keep things simple. Real investments, such as stocks and stock funds, do not earn a steady rate. Their value goes up and down, and you could lose money. Savings accounts pay interest, but their rates can change over time.

Three things that make compounding stronger

1. Time. Time is the biggest driver. In the table, the balance grew about $629 in the first 10 years but about $1,669 in the last 10 years. The St. Louis Fed makes the same point: starting early gives compounding more years to work.

2. The rate. A higher rate grows money faster. A handy shortcut called the Rule of 72 gives you a rough idea of how long it takes money to double. Divide 72 by the interest rate. At 8%, money doubles in about 9 years (72 ÷ 8). At 2%, it takes about 36 years. It is only an estimate. At 5%, the rule says about 14.4 years, while the exact answer is about 14.2 years.

3. How often interest compounds. Some accounts add interest once a year. Others do it monthly or even daily. The more often interest is added, the slightly faster your balance grows. That is why savings accounts show an APY, or annual percentage yield. APY is the rate you actually earn in a year once compounding is counted. For example, a 5% rate that compounds monthly works out to an APY of about 5.12%. When you compare savings accounts, comparing APYs lets you compare apples to apples.

Adding money regularly helps too. Each new deposit becomes principal that starts earning its own interest.

The flip side: compound interest on debt

Compounding works the same way when you owe money. If you carry a balance on a credit card, unpaid interest can be added to what you owe. Then you are charged interest on that interest.

The Consumer Financial Protection Bureau (CFPB) explains that many credit cards figure interest daily. The card adds each day's interest to the balance, so interest compounds on a daily basis.

That is why a balance that seems manageable can grow fast if you only make small payments. The same force that helps savers can work against borrowers. Paying more than the minimum, and paying high-interest debt first, can help you keep compounding on your side.

How to put compounding to work

You do not need a lot of money to use compound interest. A few habits may help:

• Start where you are. Even small amounts get the benefit of time. A little now can matter more than a lot later.
• Automate saving. Setting up an automatic transfer on payday makes regular deposits easier.
• Leave earnings alone. Compounding only works if the interest stays in the account.
• Compare APYs when choosing a savings account, and check that the bank is FDIC insured or the credit union is NCUA insured.
• Watch your debt. Paying credit card balances in full each month can help you avoid paying interest at all.
• Use a calculator. Free tools, like the compound interest calculator on investor.gov, let you test different amounts, rates and timelines.

This article is for education only and is not financial advice. Everyone's situation is different.