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'. 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.

Return

A cash deposit is quite a simple investment. For more complicated investments we use the word 'return' instead of the word 'interest'. So ‘return’ on an asset is the annual interest rate, compounded, that measures the benefit to the investor on a purchase and subsequent sale over a specific time period. Note that ‘return ‘ is meaningless unless it is tied to a period.