What is compound interest?

8 October 2026 · 12 minute read · Jump to the calculator

Compound interest is interest that earns more interest. The extra stays in each year, so each year you get a bit more than the last.

The US Securities and Exchange Commission puts it in one line: “Compound interest is the interest you earn on interest.” (Investor.gov)

How does compound interest work? M explains it with a jar of sweets

This is the picture from the film above. M is Rich's mother. She does the teaching. Rich is the pupil.

When Rich was ten, M gave him a jar of 10 sweets and a deal. For every ten sweets in the jar, she adds one. Every year. That extra sweet is called interest. You get it for leaving your sweets alone.

Rich ate the extra sweet. Every year, for 40 years. His jar still holds 10.

“The jar's still full. Ten. Not lost one.”Rich

M kept a second jar. Same 10 sweets, same deal. Nobody ate the extra one, so it stayed in. Eleven. Twelve. At twenty sweets, in year 10, the deal adds two a year. At fifty, in year 21, it adds five. The extra sweets are now getting extra sweets of their own. That is compound interest.

“It starts slow. Then it gets fast.”M

After 40 years the second jar holds 284 sweets and M is adding 25 a year. Rich's jar holds 10, and gets one.

Compound: the other jar. Simple: the ten sweets in Rich's jar plus his wrappers.

M says how it works. She never says what anyone should do about it.

Two jars: a compound interest calculator in sweets, biscuits or money

Two jars begin with the same amount and get the same yearly rate. In the first, each year's interest is worked out on the starting amount only. In the second, it is worked out on everything in the jar. The slider walks through the years, and the table under the jars lists every one.

Compound interest examples, worked by hand

£100.00 at 5% a year, for two years

Year one: 5% of £100.00 is £5.00, which makes £105.00. Year two: 5% of £105.00 is £5.25, which makes £110.25. With simple interest the second year would add £5.00 again and stop at £110.00. The extra 25p is interest on last year's interest. The US Securities and Exchange Commission uses the same sum, in dollars, on its classroom page and gets the same answer.

M's jar, year by year

The compound interest formula, and why M's jar gives a smaller number

The textbook formula is: amount after n years = start × (1 + rate)ⁿ. For 10 sweets at 10% for 40 years it gives 452.59. M's jar holds 284. Both are right. They follow different rules about small change.

The smaller the piece that can earn interest, the closer a real jar gets to the formula. A sweet is a big piece. A penny is a small one.

Once a year, or once a month?

Interest can be added more often than yearly. £100.00 at 12% added once a year becomes £112.00. The same 12% split into 1% a month, added twelve times, becomes £112.66. The extra 66p is interest that the first eleven months of interest earned.

What is the rule of 72?

The rule of 72 is a shortcut for doubling. Seventy-two divided by the yearly rate gives roughly the number of years a compound jar takes to double. It is arithmetic, not a promise: it says nothing about what any rate will be.

The shortcut is closest in the middle of the table. In M's jar of whole sweets, 10% takes 10 years to turn 10 into 20, not 7.3, because a part of a sweet is never paid. At today's UK Bank Rate of 3.75% the rule gives 19.2 years and the formula gives 18.8.

The rule is old. It appears in Luca Pacioli's Summa de arithmetica, printed in Venice in 1494, without any explanation, which suggests it was already in use.

How does compound interest work on a loan or a credit card?

The sum is the same. The jar belongs to the lender. When interest on a debt is not paid, it is added to what is owed, and the next interest is worked out on the larger figure.

In five years the interest alone comes to £1,488.32. With simple interest it would be £1,000.00. Many loans and cards work interest out monthly or daily, which is the once-a-month case above with a different jar. The agreement for each one says how.

If you are struggling with debt, free help is available from MoneyHelper and from debt charities.

What does a jar do at today's Bank Rate?

Bank Rate is set by the Bank of England, which describes it as the rate it pays to banks and building societies that hold money with it. It is not a rate anyone is offered on savings or charged on a loan. The CPI figure is how much dearer the things people buy were than a year before. Both are stored when this page is built and shown with their dates. Both will change.

Prices compound as well. A rise of a few percent is worked out on last year's prices, which already include the rise before. The last column is the calculator's second jar with the price figure typed in as the rate.

Sources: Bank of England Database, Official Bank Rate (series IUDBEDR) and Office for National Statistics, CPI annual rate (series D7G7), both under the Open Government Licence v3.0. Last read: 8 October 2026. The next CPI figure is due on 21 October 2026.

Where does compound interest come from?

Nobody is known to have invented it. A clay tablet from Babylon, about four thousand years old, may be the first written compound interest problem. Around 1340 the Florentine merchant Francesco Balducci Pegolotti put a table of it in his trading handbook. In 1613 Richard Witt, in London, published Arithmeticall Questions, a whole book on the subject. In 1683 the mathematician Jacob Bernoulli asked what happens if interest is added more and more often, and in answering it came close to the number now called e (MacTutor).

Did Einstein call it the eighth wonder of the world?

There is no good evidence that he did. Quote Investigator, which traces quotations to their first appearance, lists the “eighth wonder” line among several about compound interest that are pinned on him, and reports finding no significant evidence that he said the best known of them. The earliest version of that one it found is a 1916 advertisement, spoken by a made-up character. The earliest link to Einstein it found is from 1976. He died in 1955. This page does not repeat the line as his.

Scripted comedy. Rich and M are AI characters. Nothing here is advice. For decisions about your own money, speak to a regulated adviser or a free service like MoneyHelper (moneyhelper.org.uk).