In both the foundation and higher tiers of GCSE maths, interest questions come up fairly regularly. You will need to be able to apply two different types of interest – compound and simple. In this blog I will explain the difference between the two methods by way of an example.
What is interest?
We all know the meaning of the word interest (as in “I’m not interested in maths!”) but the word has a very different meaning in finance and mathematics.
Banks want you to give them your money to look after. So to incentivise you to give them your money, they will offer you interest. Interest is a small percentage of the money you have in your account. It means that all you need to do is deposit money into the savings account, and you’ll earn money doing so! You don’t even need to do anything. It’s easy money.
How to calculate simple interest
Let’s say I have £1,000 that I want to save for 4 years. Let’s say that the bank (which we’ll call the Simple Bank) is offering us a simple interest rate of 4% per year.
This means that each year I will earn 4% of my £1,000. So, to calculate how much money I will have in my account after the 4 years, all I need to do is find 4% of £1,000 and then add this on 4 times (for 4 years).
£1,000 × 4% = £40 (this is how much interest I earn each year)
£40 × 4 = £160 (this is how much interest I earn over 4 years)
£1,000 + £160 = £1,160 (this is how much money I will have at the end of the 4 years)
So that’s how you calculate simple interest. It’s, as the name suggests, very simple.
How to calculate compound interest
Compound interest is the method that most banks use to calculate interest. It is more beneficial to the saver.
Let’s say, again, that I have £1,000 and I want to save for 4 years. The bank (we’ll call this one the Compound Bank) is offering us a compound interest rate of 4% per year.
The difference between simple and compound interest is that while simple interest will only add 4% of the original amount each year, compound interest adds 4% of the previous year’s amount.
So, at the end of Year 1, I will add 4% of £1,000, and we will have the same as we would with simple interest.
£1,000 × 4% = £40
£1,000 + £40 = £1,040 at the end of Year 1
Then, at the end of Year 2, I will add 4% of £1,040 instead, which will be marginally higher than the equivalent stage with simple interest.
£1,040 × 4% = £41.60
£1,040 + £41.60 = £1,081.60 at the end of Year 2
Then, at the end of Year 3, I will add 4% of £1,081.60
£1,081.60 × 4% = £43.26
£1,081.60 + £43.26 = £1,124.86 at the end of Year 3
Then, at the end of Year 4, I will add 4% of £1,124.86
£1,124.86 × 4% = £44.99
£1,124.86 + £44.99 = £1,169.86 at the end of Year 4
As you can see, with simple interest, the gains each year are fixed, whereas with compound interest the gains each year increase (in Year 1 it was £40, in Year 2 it was £41.60, in Year 3 it was £43.26).
In the table below, you can see how the amount in our bank account changes each year with both the Simple Bank and the Compound Bank. Each year, the difference between compound and simple increases (albeit only marginally).
| Simple Bank | Compound Bank | Difference | |
| Year 1 | £1,040 | £1,040 | £0 |
| Year 2 | £1,080 | £1,081.60 | £1.60 |
| Year 3 | £1,120 | £1,124.86 | £4.86 |
| Year 4 | £1,160 | £1,169.86 | £9.86 |
It seems like calculating compound interest is much more time-consuming than simple interest, however there is a trick for quickly calculating compound interest which I will demonstrate in the next blog.
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