Simple interest formula


In this lesson, you'll learn how to use the simple interest formula.


What is simple interest?


It's interest calculated only on the principal - the original amount of money borrowed or invested.


Here's a formula to help you work out simple interest



where

  • p = principal
  • r = interest rate per period (expressed as a percentage %)
  • n = number of periods


A typical interest rate is per year and the principal's usually borrowed or invested (and interest accrues) over a number of years.


However, we'll also consider the effects of simple interest on money borrowed or invested for less than a year.


Some examples of how to calculate simple interest


William borrows $1000 from his bank over a period of 2 years at an annual simple interest rate of 5%


Simple interest

= prn

= 1000  x  5%  x  2

= $100


Your calculator key strokes are 1000, multiply sign (x), 5, percentage sign (%), multiply sign (x), 2, equals sign (=). You may need to press a shift or 2nd function button to access %


In addition to the $1000 he originally borrowed, William will have to pay back $100 simple interest.


What if the same amount of money is borrowed over 6 months at the same rate of interest?


There are 12 months in a year, therefore


Simple interest

= prn

= 1000  x  5%  x  6/12

= $25


On your calculator enter 1000, multiply sign (x), 5, percentage sign (%), multiply sign (x), 6, divide sign (÷), 12, equals sign (=)


William will need to pay back $25 simple interest plus the principal $1000.


And if $1000 is borrowed over 90 days at 5% simple interest rate?


There are 365 days in a year, so


Simple interest

= prn

= 1000  x  5%  x  90/365

= $12.33 (rounded up to the nearest cent)


See if you get this figure using your calculator - the key entries are the same as the last calculation only enter 90 instead of 6, and 365 instead of 12.


That's a total of $1012.33 payable to the bank (original loan $1000 plus simple interest $12.33).


In reality, of course, loans are usually paid back gradually rather than at the end of the loan term. This reduces the overall amount of interest payable.


Further practice using the simple interest formula


Emma invests $200 in a savings account with an annual simple interest rate of 3%.


Try and calculate how much simple interest she'll earn over

  • 5 years
  • 9 months
  • 13 weeks


Here are the workings out/answers in order


Simple interest

= prn

= 200  x  3%  x  5

= $30


Emma will accrue $30 over 5 years on the $200 she originally invested.


Simple interest

= prn

= 200  x  3%  x  9/12   (12 months in a year)

= $4.50


The amount of simple interest Emma will earn over 9 months is $4.50.


Simple interest

= prn

= 200  x  3%  x  13/52   (52 weeks in a year)

= $1.50


That's interest of $1.50 over 13 weeks.


But can't you accumulate interest on interest?


Yes! This is known as compound interest.


If you'd like to learn more about this type of interest and how it differs from simple interest click here.


Back to top


› Simple interest formula