Year 9 Interactive Maths - Second Edition

## Simple Interest

If you have extra money you can invest it in a bank, building society or government bonds, for example, and this investment will earn money for you.

The sum of money invested is called the principal.  We often denote the principal by P.  The money earned by the principal is called the interest and it is earned at a rate known as the interest rate.  Interest is often represented by I and the interest rate by r.

There are many ways in which interest is calculated and paid.  We will be looking at the simplest of the methods used.  It is called simple interest.

Let us consider an example of an investment on simple interest terms of \$100 invested for 3 years at 10% per annum (p.a).

Each year the investor will receive interest equal to 10% of the principal.  That is:

The investor also gets the principal of \$100 back at the end of the third year.

Note that we could have calculated the interest I, as follows:

###### In general:

If \$P is invested at the rate of r per annum for t years, then the total (simple) interest, \$I, earned is given by

I = Prt

#### Example 15

##### Solution:

So, the total interest earned is \$65.63.

###### Note:

Both r and t need to be expressed in the same units.  So, if the rate is measured in per cent per annum (i.e. annually), then the time needs to be measured in years.