What is compound interest? How does it work?

At a glance

• Compound interest occurs when you earn interest on top of interest already earned on your original savings deposit.
• It can be a great way to maximise the returns from your savings.
• Bear in mind that it can apply to borrowing too, so it’s important to understand how it works.

When we earn interest on our savings, we get a little extra added to our savings pot. We may choose to have this interest “paid away” to another account – perhaps if we wanted to earn an income from our savings – but more often, it stays in the same account and is added to the savings we already have.

This means we can benefit from compound interest – the chance to earn interest on top of interest we’ve already accrued, and it works on both ISAs and standard savings accounts.

How does compound interest work?

When you earn interest on your savings, the interest you earn is can be added to your savings pot. Then the next time you earn interest, you not only earn it on your original savings amount, but also on the interest you have previously accrued – in other words, your interest is compounded.

With compound interest, your savings have the chance to grow and snowball, and the more you save and the longer you leave it untouched, the larger your nest egg will become. Let’s take a look at an example:

Vera has £1,000 to save. She decides on an account paying an interest rate of 4.00% annually.
At the end of year one she receives £40 in interest (£1,000 x 4% = £40).

This £40 is added to her original £1,000 savings, making a new total of £1,040.

At the end of year two she’s earned £41.60 (£1,040 x 4% = £41.60) because she’s not only been paid interest on her original £1,000, but also on the £40 interest she earned in year one.

The £41.60 is then added to her £1,040 to make a new total of £1,081.60.

The cycle then repeats again and again, so that by the end of year 10, her savings have grown to £1,480.24.

The table below shows how much she’d earn in interest each year.

Note that the above example applies to interest being earned annually. Interest can be paid at different frequencies – such as monthly or quarterly – but the same compounding rules apply.

Watch your savings grow

Want to see how much interest you could earn on your savings? Our lump sum investment calculator shows how much your investment will be worth at the end of your chosen savings period thanks to compound interest.

You can also visit our charts to view the latest savings and ISA rates.

Compound interest vs. simple interest

Whereas compound interest takes the interest you’ve already earned into account, simple interest does not – it focuses solely on the original amount you invested.

So, using the above example, all we’d have to do it multiply the original investment (£1,000) by the interest rate (4%) to give us the amount earned in interest each year (£40). This is then multiplied by the number of years the money is invested (over 10 years = £400).

Simple interest calculations are rarely used when it comes to savings, and are only really useful if the saver has the interest paid away from the account. In the above scenario, if Vera had paid the interest into another account she’d only ever earn £40 a year in interest, as she’d only be earning interest on £1,000.

So, whereas with the interest compounded she would earn £480.24 over a 10-year period, with the interest paid away (and using a simple interest calculation) she would only earn £400.00.

Using savings as income

If you’re opting to use your savings as an income, you’ll have the interest paid into a different account and will always be earning “simple” interest as you won’t get the compounding effect. Just bear in mind that because your savings pot never gets a chance to grow, the amount you can buy with it will become less over time, due to the effects of inflation.

How to calculate compound interest

You can calculate compound interest using the basic principle above – take the initial deposit amount and multiply it by the interest rate. Then take that amount, add it to the initial investment, and multiply it by the interest rate again. Continue this for the number of years you’re investing for.

There is a formula you can use: A = P(1 + r/n)^nt.

• A is the total balance you’ll have at the end of the investment period.
• P is the original (or principal) amount of money deposited.
• r is the annual interest rate.
• n is the number of times interest is calculated in a year (e.g. if it’s annually it would be 1, quarterly would be 4 and monthly would be 12).
• t is the time (in years) the money is invested for.

If you’d rather keep it simple, we’ve got a compound interest calculator you can use instead that does the hard work for you.

Note that when comparing the best savings accounts, you should always go by the AER, or the annual equivalent rate. This is the rate that takes compound interest into account, to show exactly how much interest you’ll earn over the course of the year. You can find out more about AER, gross and net rate in our guide.

Compounding and investments

The effects of compounding can be seen even more clearly when it comes to investments, thanks to both the larger amounts that are often deposited and the length of time these investments are left to mature.

This is because the more that is invested, and the longer it remains invested for, the bigger the compounding effect will be, and ultimately the more interest you’ll generate. This can be particularly the case with things like pensions, which are designed to be left untouched for decades for the snowballing effect to really pay off and generate impressive returns.

Compound interest on borrowing

It’s important to remember that the principles of compounding can apply to borrowing too. For example, if you only ever pay the minimum amount on your credit card, interest will be added to the balance each month, and thanks to compounding this means the amount you owe will continue to increase over time. It’s a similar story with overdrafts, where interest is charged on the amount you’re overdrawn and therefore the amount you owe will continue to rise until you repay it.

So, while compounding can be incredibly beneficial for savings and investments, it’s certainly less so when it comes to borrowing, and is why this kind of credit should only be used sparingly and provided you can manage it effectively. Read our guide to see if you should get a credit card so you know if it’ll be worthwhile or not.