It costs money to borrow money from financial institutions (like banks). The extra money that these lenders charge is called interest. Interest can also refer to money earned from investing money, such as in a savings accounts.
The starting amount, either borrowed or invested, is called the principal. The interest is usually described as a rate (percentage) per annum. For example, an investment of $\$100$$100 at a rate of $3%$3% per annum. $3%$3% of $100$100 is $3$3 , so this investment produces $\$3$$3 every year.
Calculating simple interest
Simple, or straight line interest is a method where the interest amount is fixed (i.e. it doesn't change). The interest is based on the original principal.
It is calculated using the formula: $I=Prn$I=Prn, (or$I=PRT$I=PRT)
- where $I$I is the total interest earned
- $P$P is the principal (the initial amount borrowed/invested)
- $r$r (or $R$R) is the interest rate, expressed as a decimal or fraction.
- $n$n (or $T$T) is the number of time periods (the duration of the loan/investment)
The interest rate is often given as a percentage per time period. For example $4.5%$4.5% p.a. where "p.a." is an abbreviation of per annum, which means every year. However, the unit of time used for $n$n must match the unit of time used in the interest rate $r$r. Sometimes this means a conversion is required. For example, the time of a loan / investment may be given as a number of days, which would then need to be converted into a number (or fraction) of years.
Calculating principal, rate or time
Using any three known pieces of information from the simple interest formula it is possible to find the remaining unknown variable.
The formula can be rearranged to calculate the principle, the rate or the time. As long as you know the simple interest rule you don't need to remember all the variations but they are useful to see.
Rearranging the simple interest formula
To find the interest rate, $r$r%:
$r=\frac{I}{Pn}$r=IPn
To find the time, $n$n:
$n=\frac{I}{Pr}$n=IPr
To find the principal amount, $P$P:
$P=\frac{I}{rn}$P=IrnCalculating the amount of the loan / investment
For simple interest, once the interest is calculated, it can then be added to the principal amount to calculate the total amount of the loan / investment, represented by $A$A. This is found using the following formula:
$A=P+I$A=P+I
In some cases you may know the final amount of the investment $A$A, and not $I$I, the interest that has been earned. In this case use the formula: $P=\frac{A}{(1+rn)}.$P=A(1+rn).
Practice questions
Question 1
Calculate the simple interest on a loan of $\$8000$$8000 at $8%$8% p.a. for $6$6 years.
Give the answer to the nearest dollar.
Question 2
Question 3
For a simple interest rate of $6%$6% p.a. , calculate the number of years $T$T needed for an interest of $\$1174.20$$1174.20 to be earned on the investment $\$1957$$1957.
Give your answer as a whole number of years.
Enter each line of working as an equation.