Mammoth Memory

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:

Girl looking in the mirror saying simply I'm pretty in the mirror mnemonic for 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%`

 

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