Compound Interest Explained: How Money Snowballs (and How Debt Does Too)

Put £10,000 somewhere that grows by 6% a year and leave it alone. After 10 years you have about £17,900. After 30 years you have about £57,400, even though you never added another penny. Most of that extra money came from growth on earlier growth.

That snowball effect is compound interest. It is the reason starting early matters so much for savers, and the reason a credit card balance can run away from you. The maths is the same in both directions, so once you understand it, you can spot when it is working for you and when it is working against you.

What compound interest actually is

The Federal Reserve Bank of St. Louis puts it simply: compound interest means earning interest on your original money plus on the interest it has already generated, which is why it is often called “interest on interest”.

Simple interest is the opposite. You only ever earn on the amount you started with. At 6% simple interest, £10,000 earns £600 every year, no more and no less.

Here is how the two compare on £10,000 at an illustrative 6% a year, with interest added once a year:

• After 10 years: £16,000 with simple interest, £17,908 with compound interest.
• After 20 years: £22,000 simple, £32,071 compound.
• After 30 years: £28,000 simple, £57,435 compound.

The gap starts small, then widens fast, because each year’s 6% is calculated on a bigger pile. Compounding rewards time above everything.

A quick caution about every number in this article. The rates are examples chosen to make the maths easy to follow. Real investments do not grow by a smooth 6% a year, and their value can fall as well as rise. Savings rates change too.

Why starting early matters so much

Imagine two people who each save £200 a month into an account that grows at an example rate of 6% a year, compounded monthly, until they turn 65.

• Alex starts at 25. Over 40 years Alex pays in £96,000 and ends up with about £398,300.
• Sam starts at 35. Over 30 years Sam pays in £72,000 and ends up with about £200,900.

Sam saved 75% as much money as Alex but finished with only about half as much. Those first ten years were worth far more than £24,000, because that money had the longest time to snowball.

Now try a third saver, Jo, who puts in £200 a month from 25 to 35 and then stops completely, leaving the pot to grow until 65. Jo pays in just £24,000 and ends up with roughly £197,400. That is almost the same as Sam, who paid in three times as much but started a decade later.

These figures assume deposits at the end of each month and a rate that never changes, so treat them as a picture of how compounding behaves, not a forecast. You can test your own numbers with the SEC’s free compound interest calculator on Investor.gov, which lets you set a starting sum, a monthly contribution, a rate and how often interest is compounded.

How often interest is added

Interest can be added yearly, quarterly, monthly or even daily. The more often it is added, the sooner each slice starts earning interest of its own.

Take £10,000 at an example rate of 5% for one year:

• Added once a year: £10,500.00
• Added quarterly: £10,509.45
• Added monthly: £10,511.62
• Added daily: £10,512.67

That is about £12 in a year. Over 30 years the gap grows to about £1,600 (£43,219 yearly against £44,812 daily). Frequency matters, but far less than the rate or the time.

APR, APY and AER: reading the label

Because compounding frequency changes the result, banks use standard measures so you can compare accounts fairly.

In the US, savings accounts quote an APY (annual percentage yield). Federal rules define it as a rate reflecting the total interest paid on an account, based on the interest rate and the frequency of compounding for a 365-day period.

In the UK, savings adverts quote an AER (annual equivalent rate). Industry guidance from UK Finance and the Building Societies Association describes it as showing what the interest rate would be if interest was paid and compounded once each year. If two accounts pay the same gross rate but one compounds more often, that one will show a higher AER.

The 5% compounded monthly in the example above works out to an APY or AER of about 5.12%. When you compare savings accounts, compare the APY or AER, not the headline rate.

APR (annual percentage rate) is the borrowing-side figure. On a US credit card it is the yearly rate the daily rate is worked out from, so daily compounding comes on top of it. That matters a lot, as the next section shows.

The Rule of 72

There is a neat shortcut for estimating how long money takes to double: divide 72 by the annual rate. The St. Louis Fed gives the example that at 2%, it would take 36 years to double your money, and stresses that the rule is an approximation.

So how good is it? Here is the shortcut against the exact answer (with interest added once a year):

• 2%: rule says 36 years, exact answer 35.0 years.
• 4%: rule says 18 years, exact 17.7.
• 6%: rule says 12 years, exact 11.9.
• 8%: rule says 9 years, exact 9.0.
• 12%: rule says 6 years, exact 6.1.
• 24%: rule says 3 years, exact 3.2.

It is remarkably close between about 4% and 12%, and almost perfect around 8%. At very low or very high rates it drifts by a few months to a year or so, which is still fine for a back-of-the-envelope check.

The rule also works in reverse. If prices rise by 3% a year, they double in roughly 24 years, which means your cash buys about half as much.

When compounding works against you

Credit card debt runs on exactly the same maths, but now the snowball is rolling towards you.

In the CFPB’s model credit card agreement, the daily periodic rate is the APR divided by 365, and each day’s interest is added into the next day’s balance, which the agreement says “causes interest to compound daily”. Individual card agreements vary, so check yours.

Take a £3,000 balance at an example APR of 24%:

• The daily rate is about 0.066%, roughly £1.97 of interest on the first day.
• Because that interest compounds daily, the effective yearly cost is about 27.1%, higher than the 24% on the label.
• With no payments at all, the balance would pass £3,800 within a year and double in under three years.

Repayment speed changes everything. Using the same example:

• Paying a fixed £150 a month clears it in about 26 months, with roughly £3,880 paid in total.
• Paying a fixed £75 a month takes about 83 months (almost seven years), with roughly £6,190 paid.
• Paying only a shrinking minimum of 2.5% of the balance (or £25, whichever is higher) takes about 24 years and costs around £11,660.

Real minimum-payment formulas vary, but small payments on a high-rate balance mostly feed the interest.

The CFPB notes that on most cards you can avoid interest on purchases by paying the full balance by the due date each month, and that because interest is worked out daily, paying earlier in the cycle reduces what you are charged.

What quietly eats your returns

Fees

A fee of 1% a year sounds tiny. But it comes off your balance every year, so it compounds too, just in the wrong direction.

The SEC shows this with a $100,000 investment growing 4% a year for 20 years. With a 0.25% annual fee it ends up worth about $208,000; with a 1% fee, about $179,000. That 0.75% difference costs nearly $30,000.

Go back to Alex, saving £200 a month for 40 years. If a 1% yearly fee cuts the growth rate from 6% to 5% (a simplified way to model it), the final pot drops from about £398,300 to about £305,200. That single percentage point takes about £93,000, or nearly a quarter of the final value.

Inflation

Inflation compounds as well. The US Federal Reserve aims for inflation of 2 percent over the longer run. Even at that modest target, £100 today would buy only about £82 worth of goods after 10 years, and about £55 worth after 30.

What matters is your real return: growth after inflation. A 6% return with 2% inflation is a real return of about 3.9%. And if a savings account pays less than inflation, your balance grows on paper while what it can buy shrinks. Our explainer on what inflation is and why prices keep rising covers how it is measured and what drives it.

It also helps to know what a fund actually holds. Broad index funds weight companies by size, so a few giants make up a big slice of them. Our explainer on Jensen Huang stepping down at Nvidia shows how news about one company reaches an ordinary S&P 500 fund.

Practical takeaways

• Start as early as you can, even with small amounts. Time does more of the heavy lifting than the size of each deposit.
• Compare savings using APY or AER, because it bakes in how often interest is added.
• Treat high-interest debt as an emergency. Paying down a 24% card balance is like earning a guaranteed 24% return, which no ordinary savings account comes close to.
• Pay credit cards in full when you can, and pay early in the cycle when you cannot.
• Look hard at fees. A percentage point a year can cost a large slice of a long-term pot.
• Think in real terms. Ask what your money will buy, not just what the number says.
• Keep the accounts themselves safe. If you manage money online, keep your browser patched against zero-day attacks and check which old accounts still use your username.

This article explains how the maths works and is not personal financial advice. For decisions about your own savings, investments or debts, a regulated adviser or a free government-backed guidance service can help you weigh your options.