Everything Maths Grade 10

With an opening balance of R 1000 at the start of the year, the closing balance at the end of the year will
therefore be:

Closing balance=Opening balance+Interest

=R 1000+R 50

=R 1050

The opening balance in financial calculations is often called the principal, denoted asP(R 1000 in the exam-
ple). The interest rate is usually labelledi(5% p.a. in the example and “p.a.” means per annum or per year).
The interest amount is labelledI(R 50 in the example).

So we can see that:
I=Pi

and:

Closing balance =Opening balance+Interest

=P+I

=P+Pi

=P(1 +i)

The above calculations give a good idea of what the simple interest formula looks like. However, the example
shows an investment that lasts for only one year. If the investment or loan is over a longer period, we need to
take this into account. We use the symbolnto indicate time period, which must be given in years.

The general formula for calculating simple interest is

A=P(1 +in)

Where:

A= accumulated amount (final)

P= principal amount (initial)

i=interest written as decimal

n=number of years

Worked example 1: Calculating interest on a deposit

QUESTION

Carine deposits R 1000 into a special bank account which pays a simple interest rate of 7% p.a. for 3 years.

How much will be in her account at the end of the investment term?

SOLUTION

Step 1: Write down known values

P= 1000

i=0,07

n= 3

Chapter 9. Finance and growth 331