# Interest

*Understand 'interest'. Then you can understand the vital concept of 'return'*

## 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 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 over two years'.

In case you are bored by this, we will tell you that;

- 3% simple interest over 20 years gives you 60% - £160 from every initial £100.
- 3% compound interest over 20 years gives you 81%- £181 from every initial £100.

So compound is better. In fact, at higher interest rates, a lot better. More on this later.

## Interest compounded over shorter periods

If interest is compounded half-yearly, the interest after 6 months is £1.50 and the interest in the second 6 months is 1.5% of £101.50, or £1.52. You can calculate that the interest in the third and fourth periods is £1.55 and £1.57 - a 2-year total of £6.14.

So more frequent compounding is better.

## Return

A cash deposit is quite a simple investment. For more complicated investments we use the word 'return' instead of the word 'interest'.