# Simple interest

Simple interest is the amount of interest paid and it is simply the same every time.

SIMPLE INTEREST = SIMPLY THE SAME

Simple interest =prt

 Where: p= The beginning amount r= The interest rate (expressed as a decimal) t= Time (in years or time period)

To remember the formula of simple interest:

Simply I'm pretty

(Simple interest =prt)

Example 1

Mrs Jones borrows £50,000 from the bank for one year at a simple interest rate of 5%. How much interest does she pay?

Simple interest =prt

Simple interest =50,000times0.05times1year

Simple interest =£2,500

Answer: Mrs Jones pays £2,500 interest

NOTE:

An alternative to this is just to use logic.

(see our work on percentages to help)

 £50,000 = 100% x = 5% (50,000)/x = 100/5

Multiply by x to get x on its own.

(xtimes50,000)/x=(100timesx)/5

50,000=20x

Divide both sides by 20 to get x on its own.

 (50,000)/20 = (cancel20x)/cancel20 x = (50,000)/20 x = £2,500

Example 2

A loan is taken out for £6,000 for 3 years at 7.5% simple interest what is the total amount to pay back to the loan company?

First work out the simple interest

Simple interest =prt

Simple interest =6,000times0.075times3year

Simple interest =£1,350

The original sum borrowed =£6,000

Therefore the total to pay back =£1,350+£6,000

=£7,350

NOTE:

An alternative to this is just to use logic.

(see our work on percentages to help)

Work out interest for one year

 £6,000 = 100% x = 7.5% (6,000)/x = 100/7.5

Multiply by x to get x on its own.

(xtimes6,000)/x=(100timesx)/7.5

6,000=(100x)/7.5

Multiply both sides by 7.5 to get x on its own.

 6,000times7.5 = (100xtimescancel7.5)/cancel7.5 6,000times7.5 = 100x

Divide both sides by 100 to get x on its own.

 (6,000times7.5)/100 = (cancel100\x)/cancel100 x = (6,000times7.5)/100 x = 60times7.5 x = £450 (This is for one year)

For 3 years: £450times3=£1,350

The original sum borrowed was =£6,000

Therefore the total to pay back =£1,350+6,000=£7,350

Example 3

Bernard invests £420 into a simple interest account which gives 3% interest per annum. What is the interest Bernard earns in 4 years?

Simple interest =prt

Simple interest =420times0.03times4years

Simple interest =£50.40

Alternatively, we could work it out using simple logic.

(see our work on percentage to help)

Work out interest for one year

 £420 = 100% x = 3% 420/x = 100/3

Multiply both sides by x to get x on its own.

(cancelxtimes420)/cancelx=(100timesx)/3

420=(100x)/3

Multiply both sides by 3 to get x on its own.

 420times3 = (100xtimescancel3)/cancel3 420times3 = 100x

Divide both sides by 100 to get x on its own.

 (420times3)/3 = (cancel100\x)/cancel100 x = (420times3)/100 x = 4.2times3 x = £12.60 (for one year)

For four years this =4times£12.60=£50.40

Example 4

A bank lent £1,400 for 3 years at a simple interest rate. Monique paid £150 in interest, what was her interest rate?

Simple interest =prt

 £150 = 1400times\r\times4years 150 = 1400times\r\times4 150 = 5600timesr r = 150/5600 r = 0.027

If 100%=1

x=0.027

(you need our work on percentages to work this out)

 100/x = 1/0.027 x = 100times0.027 x = 2.7%