It costs money to borrow money. The extra money that banks and other lenders charge us to borrow money is called interest. On the other hand, interest may also refer to additional money you earn from lending or depositing money, such as in a savings account. There are different types of interest and here we are going to learn about simple interest.
Simple interest is a method where the interest amount is fixed (i.e. it doesn't change). This fixed interest charge is based on the original amount, which is called the principal. Simple interest is calculated using the formula:
$I=Prt$I=Prt
where $P$P is the principal (the initial amount borrowed)
$r$r is the interest rate per time period, expressed as a decimal or fraction
$t$t is the number of time periods (the duration of the loan)
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. Note that $r$r needs to be a decimal or fraction, so an interest rate given as a percentage needs to be converted into a decimal or fraction.
Practice question
Question 1
Calculate the simple interest on a loan of $\$8000$$8000 at $8%$8% p.a. for $6$6 years.
Give the answer to the nearest dollar.
The unit of time used for $t$t must match the unit of time used in the interest rate $r$r. Sometimes this means a conversion is required. For example, we might need to convert a number of days into a number (or fraction) of years.
Practice question
Question 2
Calculate the simple interest earned on an investment of $\$5440$$5440 at $6%$6% p.a. for $566$566 days.
Assume that a year has $365$365 days and write your answer to the nearest cent.
Sometimes banks will describe interest rates in terms of days, months, quarters (quarter years), or half years (semi-annual). In this case a conversion may again be required to ensure $r$r and $t$t are in the same unit of time.
Practice questions
Question 3
Calculate the simple interest earned on an investment of $\$7000$$7000 at $1.8%$1.8% per quarter for $9$9 years.
Give your answer to the nearest cent.