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Percentages

Increasing a number by a percentage

 

To increase a number by a percentage you must first find the percentage of the number you want to increase it by and then add it to the original amount.  

 

Example 

 

Increase £76 by 14%

  • First, we would find what 14% of 76 is

  • 76/100 = 0.76, 0.76 x 14 = 10.64

  • 76 + 10.64 = 86.64

  • So the answer is £86.64

 

Decreasing a number by a percentage

 

To decrease a number by a percentage we do the opposite of increasing it, instead of adding the percentage amount to the original number, we subtract it.

 

Example 

 

Decrease £76 by 14%

  • First, we would find what 14% of 76 is again 

  • 76/100 = 0.76, 0.76 x 14 = 10.64

  • 76 - 10.64 = 63.36

  • So the answer is £63.36

 

Finding a percentage 

 

A percentage is a proportion that shows a number as parts per hundred. To find a percentage of a number we can treat the percentage as a proportion of a number out of 100. E.g 23% is the same as 23/100 of a number.

 

Example 

 

What is 27% of 80?

  • 27% = 27/100 of 80 

  • 27/100 = 0.27 

  • 0.27 x 80 = 21.6

  • So 27% of 80 is 21.6

 

Percentage change

 

Percentage change is the percentage that a number has increased/decreased by. 

To calculate percentage change you divide the difference by the original amount.

 

Example 

  • A shopkeeper buys a TV for £160 and sells it for £280, what is the percentage change.

  • 280-160 = 120

  • 120/160 = 0.75 

  • 0.75 = 75%

  • So the percentage change is 75%

 

Reverse percentages

 

Reverse percentages help us work out the original cost of something. for example, if a TV is increased by 24%, reverse percentages would allow us to work out the original cost of the TV.

 

Example

 

A TV has been increased by 17% to the price of £643, work out the original cost.

  • We can imagine that 643 is %117 of the original cost

  • This means we can find 1% by dividing it by 117 

  • 643/117 = 5.4957...

  • Now we can find 100% of the original cost, which is the original cost

  • 5.4957 x 100 = £549.57..

  • So the original cost was £549.57

 

Interest

 

There are two types of interest, compound, and simple interest.

 

Simple interest is calculated by finding the percentage amount and multiplying it by the number of time periods it is invested for.

 

Example of simple interest

 

£1200 is invested over 3 years (simple) with an interest rate of 2.5%. Calculate the amount at the end of the 3 years.

  • First we calculate 2.5% of 1200

  • 1200/100 = 12, 12 x 2.5 = 30 

  • 30 x 3 = 90 

  • 1200 + 90 = 1290

  • So the amount at the end of the 3 years is £1290

 

Compound interest is where each time interest is added onto an amount, the interest added also receives interest.

 

Example of compound interest.

 

£1200 is invested over 3 years (compound) with an interest rate of 2.5%. Calculate the amount at the end of the 3 years

  • First, we work out 2.5% of 1200 again which is 30

  • We then add 30 to 1200 making 1230. 

  • After the first year, the amount is now at 1230 so now the extra 30 gets interest also.

  • Now we work out what 2.5% of 1230 is which is 30.75

  • We add 30.75 to 1230 which is 1260.75. So after the second year, the amount is at 1260.75.

  • For the third year, we calculate what 2.5% of 1260.75 is which is 31.51875 and add that to the amount 

  • 1260.75 + 31.51875 = 1292.26875

  • After 3 years the amount is at £1292.27

As you can see this is a long method and luckily there is a shorter way.

 

Multiplier method 

 

The multiplier method is a much simpler way of calculating compound interest. To do it we use the percentage to find a multiplier and use the time period as a power 

 

Example 

 

£1200 is invested over 3 years with an interest rate of 2.5%. Calculate the amount at the end of the 3 years.

  • First, find the multiplier. A 2.5% increase would be 102.5% which is the same as 1.025, this is our multiplier.

  • 1200 x 1.025 x  x 1.025 x 1.025 = 1292.27

  • That's it!

  • There is another way to write this also. (1200 x 1.025)^3 would give the same answer.