Teaching kids about compound interest: simple explanations that work

Compound interest is often called "the eighth wonder of the world" (the quote gets pinned on Einstein, though there's no good evidence he said it). Plenty of adults never quite get to grips with it, and few children are taught it at all. That's a shame, because the idea is simple once it clicks, and it's one of the most useful things a young person can understand about money.

Here are some ways to explain it to children that are easy to remember and fun to try at home.

Why teach children about compound interest?

1. Time is on their side. Children have decades ahead of them, and time is what makes growth build on growth.
2. Early habits stick. Understanding how money grows makes saving feel worthwhile rather than a chore.
3. It's a genuinely interesting idea. Told well, it catches children's imagination.
4. It lasts a lifetime. They'll use it for their first savings account, their first job's pension and everything after.

The snowball explanation (ages 7-10)

The idea: growing money is like a snowball rolling down a hill.

"Imagine you make a small snowball and roll it down a snowy hill. As it rolls, it picks up more snow and gets bigger. The bigger it gets, the more snow it picks up with each turn. Money can work the same way.

If you save £10 and it earns interest, you might get £1 extra. Now you have £11. Next year, you earn interest on all £11, not just the first £10. The longer you let it roll, the bigger it gets."

Try it:

• Use real snow if you have it, or modelling clay if you don't
• Start with a small ball
• For each "year", roll it down a small slope and add a little more
• Notice how the bigger ball picks up more each time

The penny doubling game (ages 10-14)

The idea: how fast things grow when growth builds on itself.

"I'm going to offer you two choices:

1. I give you £100 right now
2. I give you 1p today, 2p tomorrow, 4p the next day, 8p the day after, doubling every day for a month

Which would you choose?"

Most children pick the £100. Then show them this:

The reveal: by day 30 the total is over £10 million. Real investments don't double every day, of course (that's the point to make next), but it shows how growth speeds up once it starts building on itself.

The magic seeds story (ages 7-10)

The idea: plant early, harvest more.

"Imagine you have magic seeds. You plant one, and it grows into a tree that gives you 10 seeds next year. Each of those grows into a tree that gives 10 more."

• Year 1: plant 1 seed, get 10 seeds
• Year 2: plant 10 seeds, get 100 seeds
• Year 3: plant 100 seeds, get 1,000 seeds
• Year 5: 100,000 seeds

"Money doesn't grow that fast in real life. But the idea is the same: what grows can grow again. When family members save for you while you're young, they're planting seeds that have lots of years to grow."

Real money examples

These use 6% a year, a careful middle-of-the-road figure for long-term investing. It's for illustration only: real returns go up and down and aren't guaranteed.

Example 1: the birthday money choice

"Say your grandparents give you £100 every birthday from age 7 to 18. You have two choices.

Choice A: spend it each year

• You enjoy £1,200 over 12 years
• Amount at 18: £0

Choice B: invest it, growing at 6% a year

• You put in £1,200
• Amount at 18: about £1,690
• Nearly £500 of that is growth you didn't have to put in"

And if that money stayed invested until age 30, without adding anything more, it could be about £3,400. The same money, twice as big again, just from time.

Example 2: the £10 a month from birth

"Imagine your parents put £10 a month into an investment from the day you were born, and it grew by 6% a year. By your 18th birthday:

• They'd have put in £2,160 (£10 × 12 months × 18 years)
• It could be worth about £3,800
• That's around £1,650 of growth"

Activities to try

The cookie game

You'll need: real cookies, or drawings of cookies

The rules:

• Day 1: you have 1 cookie
• Each day, you get 50% more cookies than you had the day before
• You can never eat the cookies (that's like not taking money out)

Day by day:

• Day 1: 1 cookie
• Day 2: 1.5 cookies
• Day 3: 2.25 cookies
• Day 4: 3.38 cookies
• Day 7: 7.59 cookies
• Day 10: 17.09 cookies

"Look how it speeds up. The more you have, the more you get."

The Time Machine in the Squids-In app

The Squids-In app has a Time Machine made for children. They can:

• Enter an amount they've saved
• Slide forward to 18, 30 or 65
• See what time could do to it
• Set a goal and watch how close it gets

Why it helps: seeing the number change as they move the slider makes a slow, invisible process feel real.

Explanations for different ages

Ages 5-7: "money has babies"

"When you put money in a savings account, it's a bit like money having babies. If you have £10, it might have a £1 baby after a year. Now you have £11. Next year, all £11 can have babies. The more money there is, the more babies it can have."

Ages 8-12: interest

"Banks pay you interest for keeping money with them. It's like a thank-you payment. If you save £100 and the bank pays 5% interest, you get £5 after a year.

Next year, you earn interest on £105 (your £100 plus the £5). So you get £5.25. The year after, you earn interest on £110.25, and you get a little more again. It builds on itself."

Ages 13 and up: the formula

"Compound interest means you earn returns on your returns. Here's the formula:

A = P(1 + r)^t

Where:

• A = final amount
• P = starting amount
• r = yearly growth rate
• t = time in years

So £1,000 growing at 6% a year for 10 years: A = £1,000 × (1.06)^10 = about £1,790

That's nearly 80% more, just from waiting."

Questions children often ask

"Why doesn't everyone invest all their money if it grows?"

People need money for everyday life: food, a home, clothes. Investing is for money you won't need for a long time, so it has time to grow.

"What if I need the money before it's grown much?"

That's why it helps to keep money in different places. Money you'll want soon stays somewhere easy to reach. Money for the long term can be invested.

"Can I lose money?"

Yes, in the short term. Investments in companies go up and down, sometimes a lot. Over long periods, a spread of many companies has usually grown, but that isn't guaranteed. That's why investing is best for money you won't need for many years.

"How much should I save?"

A simple habit is to save a bit of any money you get, even 10%. Get £10, save £1 and spend £9. That £1 starts growing for your future.

Making it stick

1. Let them see real growth

If they have a Junior ISA or savings account, look at the balance together every so often, so they can see growth happening to their own money.

2. Draw a chart

Sketch how their savings could grow over time and pin it somewhere they'll see it.

3. Notice the growth, not just the saving

When you check the balance, point out the part they didn't add: "Look, your money grew by £5 this year without you doing anything."

4. The rule of 72

Older children (10 and up) can learn the rule of 72: divide 72 by the yearly growth rate to see roughly how many years it takes money to double.

• At 6%: 72 ÷ 6 = about 12 years to double
• At 4%: 72 ÷ 4 = about 18 years to double

It's a handy way to do the maths in your head.

5. Share your own story

If you have savings or investments, talk about how they've grown, and about the times they fell too. Real examples from someone they trust carry a lot of weight.

The one message to remember

"The younger you are when you start, the more years your money has to grow. Starting at 10 gives your money more time than starting at 20.

Time is the biggest help a young saver has. Lots of adults wish they'd had it."

Next steps

1. Pick the explanation that suits your child's age
2. Try one activity this week
3. Look at their savings together, if they have any
4. Try a visual tool, like our Junior ISA calculator or the Time Machine in the Squids-In app
5. Make it a game: can they guess how much it will have grown next time you look?

Conclusion

Compound interest doesn't have to be complicated. With a good story (snowballs, magic seeds, money having babies), something hands-on and a few real numbers, children can understand it.

Better still, they'll understand why saving matters, not just that they "should". When a child sees that birthday money invested at six could be worth about twice as much by the time they're 18, and far more if they leave it longer, saving starts to make sense on its own.