5.1 Calculating a percentage of an amount
Working out the percentage of an amount requires a similar method to finding the fraction of an amount. Take a look at the examples below to increase your confidence.
Example: Finding 17% of 80
17% of 80 = of 80, so we do:
80 ÷ 100 × 17 = 13.6
Example: Finding 24% of 60
24% of 60 = of 60, so we do:
60 ÷ 100 × 24 = 14.4
Just as with fractions, you will often need to be able to work out the price of an item after it has been increased or decreased by a given percentage. The process for this is the same as with fractions; you simply work out the percentage of the amount and then add it to, or subtract it from, the original amount.
Activity 9: Percentages of amounts
You earn £1,500 per month. You get a 5% pay rise.
a.How much does your pay increase by?
b.How much do you now earn per month?
a.5% of £1,500 = of £1,500 = 1,500 ÷ 100 × 5 = £75.
b.£1,500 + £75 = £1,575 per month.
You buy a new car for £9,500. By the end of the year its value has decreased by 20%.
a.How much has the value of the car decreased by?
b.How much is the car worth now?
a.20% of £9,500 = - of £9,500 = £9,500 ÷ 100 × 20 = £1,900. The car has decreased by £1,900.
b.The car is now worth: £9,500 − £1,900 = £7,600.
You invest £800 in a building society account which offers fixed-rate interest at 4% per year.
a.How much interest do you earn in one year?
b.How much do you have in your account at the end of the year?
a.4% of £800 = of £800 = £800 ÷ 100 × 4 = £32 interest earned.
b.£800 + £32 = £832 in the account at the end of the year.
There are two other skills that relate to percentages that are very useful to know. The first is percentage change. This can be useful for working out the percentage profit (or loss) or finding out by what percentage an item has increased or decreased in value.