What compound interest actually is

Compound interest is interest paid on your original money and on the interest it has already earned. That second part is the whole point. With simple interest you earn a return only on the amount you put in. With compound interest, last year's interest joins the pile, and next year you earn interest on the larger total. The balance does not grow in a straight line, it curves upward, and the curve gets steeper the longer you leave it alone.

A worked example

Say you put 1,000 dollars into an account paying 5 percent a year.

• After year one you have 1,050 dollars.
• In year two you earn 5 percent on 1,050, not on 1,000, so you add 52.50 and reach 1,102.50.
• In year three you earn 5 percent on that, and so on.

After 10 years you have about 1,629 dollars. With simple interest, earning a flat 50 dollars a year, you would have only 1,500. The extra 129 is interest that earned its own interest. Stretch the same money to 30 years and the gap becomes enormous.

The formula, in plain terms

The standard formula is A = P(1 + r/n) raised to the power nt, where P is the principal you start with, r is the annual rate as a decimal (5 percent is 0.05), n is how many times a year interest is added, and t is the number of years. You do not need to run this by hand: the US Securities and Exchange Commission publishes a free compound interest calculator that does it for you.

Why time matters more than the rate

Here is the part that surprises people. Because compounding builds on itself, the years at the end do the heaviest lifting. A dollar invested in your twenties has decades to compound; the same dollar invested in your fifties has only a few years. That is why starting early, even with small amounts, often beats saving larger sums later. Time is the one input you cannot buy back.

How often it compounds

The more often interest is added, the faster the total grows, though the effect is smaller than people expect. Daily compounding beats annual compounding on the same rate, but the difference over a year is modest. The rate and the time matter far more than the frequency.

It works on debt too

Compound interest is not only a saver's friend. On a credit card, unpaid interest is added to the balance, and the next month's interest is charged on the larger figure. That is why a card quoted at a given annual rate can cost more than the number suggests, and why clearing high-interest debt is often the best return available anywhere.

How to put it to work

• Start now, not when you have more. Time is the input you cannot buy back.
• Leave it alone. Withdrawing resets the compounding.
• Mind the real return. Inflation eats into growth, so compare your rate against it; our explainer on what inflation does to your money covers that.
• Check where it compounds. A maintained list of current savings and bond rates sits in our rates and returns tracker, and the glossary defines the terms.

The bottom line

Compound interest is the closest thing investing has to a free lunch, but it is paid in patience. The mechanism is simple, interest earning interest, yet over decades it does most of the work in a portfolio. Understanding it is the first step to using it, whether you are growing savings or trying to escape debt. For where to put money to compound, see stocks vs bonds.