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 =50,000×0.05×1year
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% |
| 50,000x | = | 1005 |
Multiply by x to get x on its own.
x×50,000x=100×x5
50,000=20x
Divide both sides by 20 to get x on its own.
| 50,00020 | = | 20x20 |
| x | = | 50,00020 |
| 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 =6,000×0.075×3year
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% |
| 6,000x | = | 1007.5 |
Multiply by x to get x on its own.
x×6,000x=100×x7.5
6,000=100x7.5
Multiply both sides by 7.5 to get x on its own.
| 6,000×7.5 | = | 100x×7.57.5 |
| 6,000×7.5 | = | 100x |
Divide both sides by 100 to get x on its own.
| 6,000×7.5100 | = | 100x100 |
| x | = | 6,000×7.5100 |
| x | = | 60×7.5 |
| x | = | £450 (This is for one year) |
For 3 years: £450×3=£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 =420×0.03×4years
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% |
| 420x | = | 1003 |
Multiply both sides by x to get x on its own.
x×420x=100×x3
420=100x3
Multiply both sides by 3 to get x on its own.
| 420×3 | = | 100x×33 |
| 420×3 | = | 100x |
Divide both sides by 100 to get x on its own.
| 420×3100 | = | 100x100 |
| x | = | 420×3100 |
| x | = | 4.2×3 |
| x | = | £12.60 (for one year) |
For four years this =4×£12.60=£50.40
Example 4
A bank lent £1,400 for 4 years at a simple interest rate. Monique paid £150 in interest, what was her interest rate?
Simple interest =prt
| £150 | = | 1400×r×4years |
| 150 | = | 1400×r×4 |
| 150 | = | 5600×r |
| r | = | 1505600 |
| r | = | 0.027 |
If 100%=1
x=0.027
(you need our work on percentages to work this out)
| 100x | = | 10.027 |
| x | = | 100×0.027 |
| x | = | 2.7% |
