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Compound Interest Explained

The term ‘compound interest’ gets thrown around a lot and the usual response is to nod along politely and smile. But actually, it’s pretty easy to get your head around. Once you’ve got that knowledge stored away, the idea of interest starts to make a lot more sense.

You don’t need a solid understanding of interest. You also don’t need to watch an entire series on Netflix in one sitting. But some things you just do anyway, and some things you do because it can just be pretty helpful in the long run.

Understanding compound interest can be helpful from working out the best deals on a loan, to knowing which savings account is going to bring you the most profit. It’s generally some handy knowledge to have so we thought we’d do the right thing and share it for everyone.

Interest

We can’t explain compound interest without first touching on ‘interest’ itself.

If you already know what interest is, then great. But if you don’t, then think of interest as the cost of borrowing. You take out a loan, you agree to pay interest on top of that. That interest on top of the original balance is like a price tag - that’s how much the loan will cost you to borrow.

Alternatively, if you’re looking at a savings account, then you can think of the interest as your money growing. If you put your funds in a pot and return to it a year later, you’ll find more than when you started.

What is simple interest?

But both those explanations are too basic, so let’s go a bit further.

Interest is a percentage of the balance. Let’s say you borrowed a loan of £1,000 and agreed to pay a flat rate of 20% interest. 20% of £1,000 is £200, so altogether you’re paying back £1,200.

That’s ‘simple interest’, which is sort of like interest in its purest form. But as you might expect, it wouldn’t have been necessary to write a guide breaking it down if it were always that straightforward.

The reality is that it’s very rare for anyone to calculate their interest as a flat rate from the beginning of the term, whether that’s for a loan, credit card, or savings account. Which leads us onto the subject of compound interest.

What is compound interest?

Compound interest is interest that accrues on top of what’s accrued already, or ‘interest on interest’. That sounds a bit complicated, so we’ll use an example to show how it works.

Example 1

We’ll use our £1,000 loan as an example again, this time with an annual 20% interest rate. 

Year 1 - £1,000 + 20% (£200) = £1,200

Year 2 - £1,200 + 20% (£240) = £1,440

Year 3 - £1,440 + 20% (£288) = £1,728

See how the amount of interest is going up each year? That’s because it’s not calculated against the £1,000 that was initially borrowed, but against the current balance at the time. So after Year 1, the balance has risen to £1,200. In Year 2, the interest is calculated against this new balance of £1,200, meaning that 20% interest works out as £240.

That ‘interest on interest’ is what is known as compound interest.

This is still quite a simplified example. Chances are that you’re also making payments to your loan to reduce the balance, or if it’s a savings account, adding or taking funds throughout the year. How does that affect the compound interest?

Example 2

We’ll use the same loan term for this example, but this time we’ll assume we’re also making a payment of £400 once a year.

Year 1 - £1,000 + 20% (£200) = £1,200

Year 2 - (£1,200 - £400 = £800) + 20% (£160) = £960

Year 3 - (£960 - £400 = £560) + 20% (£112) = £672

Now the amount of interest accruing each year is reducing, even though the compound interest is still being applied. That’s because the annual payments are reducing the total balance faster than the interest is increasing the balance.

So the lower the balance of the loan, the less interest accruing. This is why you’ll generally see more interest accruing at the start of a loan term, while the balance is higher.

Compounding frequency

Again, the above is just a basic example to demonstrate the difference between simple interest and compound interest, and to show how payments can affect your balance. But it’s rare that interest will be calculated annually in that way, or that you’d only be making one payment a year.

For instance, at Amigo Loans, we calculate our interest daily while customers make their payments monthly. We think calculating interest daily is best for our customers as it means they only need to pay interest for the exact period of time they have their loan. If they want to settle after three months, they only pay three months of interest.

The frequency that interest is applied to a balance is what is known as ‘compounding frequency’. Though calculating interest daily is slightly more complicated than if it was yearly, the idea is still exactly the same:

We’ll use a very basic example. Let’s say you have a loan (the exact balance doesn’t matter). On Day 1, £1 is added to the balance from the interest. On Day 2, another £1 will be added, as well as a further £0.10 from the compound interest (for a total of £1.10). On Day 3, there will be £1.22 in interest, because it’s on top of the interest from both Day 1 and Day 2.

Day 1 = £1.00

Day 2 = £1.10

Day 3 = £1.22

On Day 30, let’s say you make a payment of £50 to reduce the balance. Now there will be less interest accruing because of the reduced balance. This takes into account all the interest that accrued the month previously (the compound interest) as well as the payment.

As we mentioned, this is a very generalised example (and not based on Amigo’s figures), but it shows how daily interest can work out throughout the month. It’s not necessary to know the exact calculations in this much detail, but once you get your head around the basics, then credit can start to make a lot more sense.

Other uses for compound interest

All our examples have so far looked at loans (we’re a loan company, sorry), but we’ve tried to touch on other uses too.

Compound interest is also key to bank accounts and savings. Just like with a loan, the longer you leave the funds in your savings account, the more the compound interest will grow. That’s why it’s always a good idea to leave your savings as long as you can without touching it.

To make the most of compounding interest for your savings account, it’s best to go for an account that compounds more frequently. An account that compounds its interest quarterly 

or even monthly will start earning ‘interest on interest’ sooner than an account that compounds yearly. Basically, you’ll earn more interest in the long run. For more tips on the best savings accounts, check out this guide.

If you’re using an ISA, it’s also worth bearing in mind that your bank may have certain rules in place about withdrawing funds that could impact your balance. Though it won’t necessarily affect the interest itself, fees and charges could undo all the interest you’ve built up.

For any help in forecasting how compound interest could boost your savings, we’d also recommend checking out The Calculator Site where they’ll do all the hard work for you.

The bottom line

So that’s the basics of compound interest explained, and while we could go further, there’s not really any need. If you’re looking for the exact mathematical formulas of compound interest then you can check them out here, but for most people the basics are more than enough to get by.

Here’s a summary of what we’ve covered:

  • Interest - think of it like a price tag. You borrow some money and pay for the service of being able to return it over time.
  • Simple interest - this is calculated as a percentage of the balance. On a balance of £1,000, 20% would be £200. Simple.
  • Compound interest - this is where interest starts accruing on top of previous interest. In Year 1, 20% of £1,000 is £200. In Year 2, you’ll base the 20% interest on the new balance of £1,200. So, 20% of £1,200 = £240.
  • Compounding frequency - this is how often the interest is applied to the balance. If it’s applied more often, then it’s also compounding more frequently.
  • Uses of compound interest - understanding how interest works is relevant to all forms of credit, whether that’s a loan, a credit card, or even a mortgage. It’s also a huge factor for savings accounts, and knowing how it works can help you choose the best product for your circumstances.