Interest is......

If you put £100 in cash in a deposit account at 3% per year you will get back £103 after one year. The extra £3 is called 'the interest on the account' or just 'interest'. 3% is the 'interest rate', and may be described as 'annual interest' or '3% per annum' - 'per annum' meaning the same as 'per year'.

Interest over shorter periods

It may be that interest is paid on the account each 6 months. In that case it might be described as 'interest at 1.5% half-yearly'.

Note that the word 'interest' does not mean anything without a time period attached. If no period is mentioned it is assumed to be annual.

Simple interest

'Simple' here does not mean 'easy'. It is a technical term describing how interest is added to an account.

On your £100 deposit, 3% simple interest adds £3 to the account after one year, another £3 (making a total of six) after two years......a total of £15 after five years, £18 after six years........£30 after 10 years, and so on. The total in the account after 10 years is £130 - £100 (the 'principal') + £30 interest.

Simple interest is almost never used outside exams in Arithmetic. It's just a precursor to...

Compound interest

In real life, the £3 you earn on your £100 account is added to the balance to give an opening balance of £103 at the start of year 2. Your friendly bank will then calculate your 3% interest in year 2 on £103, giving £6.09. The interest you have earned over two years is not £6 but £6.09. This is described as '3% compound interest' or 'interest at 3% compounded annually’.

At this stage we are only explaining the terms, not delving into how they work. We leave that to Compounding Effect. But …….. (the next paragraph is voluntary):

We can tell you that;

• 4% simple interest over 20 years gives you 80% - (£180 from an initial £100).

• 4% compound interest over 20 years gives you 119% - (£219 from an initial £100).

So compound is better. And over long periods a lot better:

• 4% simple interest over 40 years gives you 160% - (£260 from an initial £100).

• 4% compound interest over 40 years gives you 380%- (£480 from an initial £100).