# 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%` |