Middle Years

# 4.09 Simple interest

Lesson

It costs money to borrow money. The extra money that banks and other lenders charge us to borrow money is called interest. Interest may also refer to the additional money that is earned from investing money, such as into a savings account. There are different types of interest and in this lesson we are going to look at simple interest.

### What is simple interest?

Simple interest, or flat rate interest, describes a method of calculating interest where the interest amount is fixed (i.e. it doesn't change). The interest charge is always based on the original amount borrowed (or invested), and does not take into account any interest earned along the way (that is, interest on interest is not included).

Many financial institutions express their interest rates as a percentage "per annum", often abbreviated to "p.a.", which means "per year". For example, an interest rate might be given as $3%$3% p.a.

Simple interest

Simple interest is calculated as:

$I=PRT$I=PRT

• $P$P is the principal amount invested (or borrowed)
• $R$R is the interest rate per year expressed as a decimal or fraction
• $T$T is the time in years

The total total value of an investment or loan $A$A is then calculated as the principal plus interest:

$A=P+I$A=P+I

#### Worked example

##### example 1

An investment of $\$8580$$8580 is deposited at 2%2% p.a. flat rate for 44 years. (a) Find the interest earned in 11 year. Think: 2%2% interest is earned each year. So we need to find 2%2% of \8580$$8580. Can you see this in the same as using the formula with $P=\$8580$P=$8580, $R=2%$R=2% and $T=1$T=1 year? For the formula express $R$R as a decimal or fraction, thus $R=\frac{2}{100}$R=2100 or $0.02$0.02.

Do:

 $I$I $=$= $PRT$PRT $=$= $\$8580\times0.02\times1$$8580×0.02×1 == \171.60$$171.60 For financial questions give answers to $2$2 decimal places.

Thus, $\$171.60$$171.60 in interest would be earned in 11 year for this investment. (b) Find the interest earned in 44 years. Think: For simple interest the same amount is earned each year, so we could multiply the figure found in part (a) by 44. Can you see this is the same as using the formula with the values P=\8580P=8580, R=0.02R=0.02, T=4T=4 years? Do:  II == PRTPRT == 8580\times0.02\times48580×0.02×4 == \686.60$$686.60

(c) What is the total value of the investment after $4$4 years?

Think: The total value is the original investment plus the interest that has accrued over $4$4 years.

Do: