Understanding compound interest: a beginner’s guide

Did you know Albert Einstein called compound interest the eighth wonder of the world?

“He who understands it, earns it. He who doesn't, pays it,” he’s claimed to have said.

Understanding compound interest can transform your savings and give you a greater return on your deposits. It’s a straightforward concept that can have a significant impact on your account balance. We’ve put together this beginner’s guide, explaining what compound interest is and how it works.

What is compound interest?

Compound interest is a term regularly used when talking about savings and investments, but what does it mean?

Compound interest is the ability to earn interest on the interest itself. You not only earn interest on the money you put in your savings account, but also on the interest that money has already earned. So, as your savings increase over time, the rate at which they grow does too.

For example, imagine you have £10,000 in a savings account with a 5% annual interest rate.

Simple interest means you're earning interest only on the initial amount.

• After the first year, you'd earn £500 (5% of £10,000).
• After the second year, you'd again earn £500, and so on.

Compound interest means you’re earning interest on the initial amount and on the interest from previous years.

• After the first year, you'd still earn £500.
• However, in the second year, you'd earn 5% on the total amount, which is £10,500. So, you'd earn £525.
• In the third year, you'd earn 5% on £11,025, and so on.

This means the earlier you start saving, the more time you’ll have to earn compound interest. As you earn interest, it becomes part of the overall balance you’ll earn interest on for the next period.

If you’re looking to open a savings account, it can be worth checking how often your interest is paid. If you’re paid interest quarterly or monthly instead of annually, the total amount you’ll receive will be higher.

Look at our guide to interest rates for more information.

How is compound interest calculated?

To estimate the impact that compound interest could have on your savings balance, there’s a calculation you can use.

The formula for calculating compound interest is:

P = C (1 + r/n) nt

Let’s break this down:

• ‘C’ refers to the initial deposit
• ‘r’ is the interest rate
• ‘n’ is how regularly your interest is paid
• ‘t’ is how many years your money is invested for
• ‘P’ is the final value of your savings pot

Suppose you invest £5,000 (C) in a savings account that offers a 4.5% (r = 0.045) annual interest rate, compounded quarterly (n = 4), and you plan to leave the money invested for three years (t = 3). After three years, your initial deposit of £5,000 would grow to £5,718.37 (P) in this scenario.

If you’re not confident doing these calculations yourself, there are compound interest calculators online that can help you.

Why is compound interest so powerful?

Compound interest is a powerful tool that can significantly grow your savings over time.

Unlike simple interest, which is calculated only on your initial deposit, compound interest rewards you on your initial savings and the accumulated interest. So, if you commit to saving over a long period of time, the value of your savings pot can grow much faster than it would with simple interest.

Compound interest is most effective for long-term savers. The more time your deposit has to compound, the more you’ll be able to reap the rewards. This reiterates the power of long-term saving, or starting to save as early as possible, to maximise the benefits of compound interest.

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