Compound interest is calculated on a given balance which includes previous payments made.

## The Formula

Compound interest is calculated by adding the interest to the principal at the end of a period which then creates a new balance that interest is calculated upon in the next period.

$A=PR^{nt}$

Where:

$A=$ Total amount ($P+I$)
$P=$ Principal
$R=1+\frac r{100}$
$n=$ Number of compound per year
$t=$ Time in years

Given this, the amount of interest can be found by subtracting the principal from the total amount ($I=A-P$).

### Example 1

Luke won a football tipping competition and received $1,000 prize money. Luke decides to invest this at 6% p.a. compounding quarterly for two years. How much money will be in Luke’s account at the end of the two years? Write down the information given. $P=1,000$ $R=1+\frac 6{100}=1.06$ $n=4$ $t=2$ $A=PR^{nt}$ $A=1,000(1.06)^{4\times 2}$ $A=PR^{nt}$ $A=1,593.848$ Write the answer including the dollar sign and correct to two decimal places (as we are referring to money). Luke will have$1,593.85 after two years.

## Use of Calculator

Although you should know how to use this formula, the easiest way to calculate the answer to most questions is to use the TVM solver on your calculator. When doing this, double check that you have entered the correct values. Bad data in = bad data out!