Compound interest definition

Compound interest is a means of calculating the potential return from an investment that takes the cumulative effect of interest into account.

How does compound interest work?

Compound interest works by factoring in the effect of compounding when calculating the potential return from a particular investment.

What that means in practice is that your return is not only based on your initial investment deposit, but on any interest accumulated with that deposit – which makes it different to simple interest, which only takes your original sum into account.

Calculated using simple interest

You’d make £1000 each year your capital is invested (10% of 10,000 = 1000). After ten years, you’d get your £10,000 back plus a total of £10,000 interest.

Calculated using compounding

You’d make £1000 in interest for the first year your capital is invested. Then in your second year, you’d get 10% of your original £10,000 plus 10% of the additional £1000 to make £1100.

In your third year, you’d get 10% of your original £10,000 plus 10% of all the interest you’d made so far: £1000 in your first year, and £1100 in your second. After ten years, you’d get back your original £10,000, but the effect of compounding would mean you’d make almost £16,000 interest.

As you can see from the graph, it is particularly important to consider compounding for longer term investments. If you’d kept your £10,000 capital invested for 30 years, for example, compound interest would see it grow to over £170,000.

Calculating compound interest

To calculate the potential impact of compound interest on any investment, you multiply your initial deposit by your interest rate, to the power of number of years you are invested (assuming your interest rate is calculated annually).

= Initial investment (interest rate)^{Years invested}

Compounding frequency

But compound interest isn’t always calculated annually, and the frequency of any compounding can also have a major effect on the final result. With a higher frequency of compounding, the total value of your investment would be even higher.

Say that instead of being calculated annually, your £10,000 is compounded every quarter - it still gets a 10% annual return, but that return is spread to 2.5% every three months. At the end of the first year, it would be worth £11,038, or £38 more than if it was compounded yearly. After ten years, it would be worth over £900 more.

Other uses for compounding

Compounding doesn’t just come into play when factoring in the return on investments. The interest on loans can also be calculated using compounding, meaning that you end up paying back a lot more if you keep your loan for an extended period of time.
And with investments, the fees you pay can also be subject to compounding. Take the above £10,000 as an example – if your portfolio charges you 1% in management fees compounded annually, then you’ll pay £100 in your first year but almost £260 in your tenth. Over the course of the ten years, your fees would total more than £1750.