# 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.

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.