Compound interest calculator (UK)

How is compound interest calculated?

To see how compound interest is calculated, it’s best to use an example.

Let’s say you put £100 into a bank account earning 5% a year. After one year your balance would grow to £105.

After another year, though, your balance would not grow to £110, but £110.25. That extra 25p is earned because the 5% interest rate is applied to the balance of £105, not £100 – the £5 interest earned in your first year has had interest applied to it again in your second year.  

So far, so good.

But what the traditional explanation of compounding being “interest on interest” doesn’t capture, is that compounding doesn’t need reinvested income to work. A gold bar which pays no dividends or interest, but increases in value by 3% every year will also benefit from the effects of compounding, because the 3% growth rate will be applied to an ever-increasing value.

All that compounding needs to work is a positive growth rate and time.

Mathematically, compound interest is calculated by taking the value of a lump sum and using the following formula:

Where A = the future value, P = the value of the lump sum now, r is the interest rate, and n is the number of years being compounded over.

For example, the future value of a portfolio worth £100 earning 5% returns for 20 years would be calculated as follows:

£100 * (1 + 5%) ^ 20 = £265

It’s as simple as that.

For maths nerds, there’s a quick way to work out the future value of a periodic addition to a portfolio. Although it’s possible to use the formula above for every addition, it’s much faster to use the following formula:

So the value of £100 added each month for 20 years (240 months) at a 5% rate of return (0.42% per month) is calculated as:

£100 * ((1 + 0.42%) ^ 240 – 1) / 0.42% = £41,275

This formula works if the £100 payments are made at the end of the month.

If they’re made at the start of the month, you simply multiply the whole thing by another (1 + r) and you’re done.

By using the compound interest calculator above, you can play around with your own numbers.

After a while it’s clear that the length of time you stay invested for has an enormous impact on the future portfolio value. That’s because compounding grows the portfolio’s value exponentially.

It’s critical for investors to have a strong grasp of compounding, because it’s how we all generate wealth. The stock market is a compounding machine.

Despite its importance, compounding is constantly underestimated because we’re all terrible at visualising the exponential function. For example, figuring out 6*3 in your head is easy, but can you do 6³? Because it’s not something we grow up with an intuitive understanding of, or something which is internalised through maths lessons as kids, we all have an excellent grasp of linear functions, but a terrible grasp of exponentials.

So feel free to play around with the UK compound interest calculator above. If you’d like to have a longer read on the power of compounding, you can go and have a read of my post on the power of compound interest. Alternatively, Investopedia also does a great job of explaining compounding, and also has an article on the future value of compounded interest on periodic additions.