What is compound interest? A simple guide for families

In short: compound interest means you earn interest on your interest as well as on the money you started with. Left alone, the growth builds on itself, slowly at first and then faster. It also works against you when you borrow. Time matters more than the amount.

Albert Einstein is often quoted calling compound interest “the eighth wonder of the world.” There is no reliable evidence he said it, but the idea behind the quote is real, and it is one of the most useful things a young person can understand about money. This guide explains it with numbers you can check on a calculator.

Simple interest first

Suppose you put £100 in an account that pays 5% a year in simple interest. Each year you earn 5% of the original £100, which is £5. After 10 years you have earned £50 and your total is £150. The growth is a straight line.

Now add compounding

With compound interest, each year’s interest is added to the pot, and next year’s interest is calculated on the bigger total.

• Year 1: £100 earns 5%, which is £5.00, so you have £105.00.
• Year 2: £105 earns 5%, which is £5.25, so you have £110.25.
• Year 3: £110.25 earns 5%, which is £5.51, so you have about £115.76.

The extra 25p in year 2 is interest on interest. It looks tiny, but watch what happens over longer periods.

After 30 years the compound pot is worth over £180 more than the simple one, from the same £100 and the same rate. The longer the time, the bigger the gap. The same maths works in dollars.

The formula, if your teenager wants it

The standard formula is:

A = P × (1 + r)^t

where P is the amount you start with, r is the interest rate each year as a decimal (5% is 0.05), t is the number of years, and A is what you end up with. For £100 at 5% for 10 years, that is 100 × 1.05¹⁰ = £162.89. Interest is sometimes added monthly or daily, which makes the result slightly higher.

The rule of 72

Here is a quick mental shortcut. Divide 72 by the interest rate to estimate how many years it takes money to double.

• At 4%: 72 ÷ 4 = about 18 years.
• At 6%: 72 ÷ 6 = about 12 years.
• At 9%: 72 ÷ 9 = about 8 years.

It is an approximation, but a good one for ordinary rates. At 5%, it gives 14.4 years, and the exact answer is a little over 14.2.

Why starting early beats saving more

Because compounding rewards time, a small amount saved early can matter more than a larger amount saved late. Here is a simple comparison, assuming a steady 5% a year, which no real investment can promise:

• Saving £50 a month for 20 years means paying in £12,000. At a steady 5% a year, it would grow to roughly £20,500.
• Saving £25 a month for 40 years means paying in £12,000 as well. At the same steady 5%, it would grow to roughly £38,000.

Both people paid in the same total, but the one who started 20 years earlier ends up with far more, even though they saved half as much each month. These figures are illustrations, not forecasts. Real returns vary, may be lower, and, for investments, can be negative in some years.

Compounding works against borrowers too

The same effect makes debt expensive. If you owe £1,000 on a credit card charging 20% a year and make no payments, the debt grows to about £1,200 after one year and about £1,440 after two. The interest is calculated on the bigger balance, just as with savings.

That is why paying only the minimum on a card can take years and cost a lot more than the original purchase. A teenager who understands this is better protected against the pull of “buy now, pay later.”

Three things that reduce the magic

1. Inflation. Prices rise over time, so £162.89 in ten years will not buy what £162.89 buys today. What matters is the rate of return after inflation.
2. Fees and tax. Charges on funds and tax on gains or interest are deducted from growth. Small annual fees compound against you too. Rules differ between the UK and the US and change over time.
3. Real returns are not smooth. A savings account rate can change, and the value of investments goes up and down. A rate of 5% a year is an average, not a promise.

Ways to teach it

• Use a calculator or spreadsheet. Type in a starting amount and a rate and let your teenager change the years. Watching the curve steepen sticks in the memory.
• Try the rice on a chessboard story. One grain on the first square, doubling on each of 64 squares, ends up as a vast number. It is an extreme example of doubling, but memorable.
• Look at a real savings account. Find the advertised rate and ask how much a certain deposit would earn in one year, and in ten.
• Use a game analogy. Imagine a game where the points you earn also earn points. Most teens quickly see why that snowballs.

Where to go next

Once the idea of compounding clicks, the next conversation is how investing differs from saving, which our guide to explaining investing to a teenager covers. If your child is younger, our guide to pocket money is a good place to give saving a real purpose.

General information for families, not financial, tax or legal advice. Rules, rates and limits change and differ between the UK, the US and elsewhere, so check official sources (such as gov.uk or irs.gov) or speak to a qualified adviser before making decisions with real money. We make InvestiKid, so we have an interest in it; the advice in this guide stands without it.