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

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.

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.

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.

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.*

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.

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.