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GCSE Maths : Decimals and Proportion

Reverse Percentages and Compound Interest (Higher Tier)

Reverse Percentages and Compound Interest (Higher Tier)

Reverse Percentages

MathsYou might  be given a price that has been increased or decreased and have to work backwards to figure out what the original price was.

For example, a stall owner buys a load of toasters in bulk. He sells them at £24 after increasing the price by 20%. What was the cost price?


We say the cost price is 100%. The selling price was the cost price plus 20% which is then 120%

The selling price is £24.

So, now you need to figure out what 100% is, if 120% is £24.

First of all work out 1%:

120% = £24

1% = £24/120 = £0.2

The cost price is 100% so now you need to multiply your answer by 100:

Cost price = 0.2 x 100 = £20

Second example: a man has a bed  that he wants to sell over an online auction site. He sells it at 20% of its original value at £145. What did he originally buy the bed for?

The original price is 100%.

Second hand = 20% = £145

1% = £145 ÷ 20%

100% = 100 x 1% = 100 x (145 ÷ 20) = £725


Compound interest

MathsThe difference between simple and compound interest is that with compound interest you pay interest on the amount from the year before, whereas with simple it’s always on the same amount.

For example, let’s say you borrowed £600 for 4 years but this time from a bank that charged you 6% compound interest per year.


You start with £600 in your 1st year. This is your principal.

Interest your 1st year is 6/100 x 600 = £36

Principal after your 1st year = £636

Interest in your second year = 6/100 x 636 = 38.16

Principal after the 2nd year = 674.16

Then, interest in the 3rd year = 6/100 x 674.16 = 40.4496

So, principal after the 3rd year would be = 714. 6096 = 714.6

That means that the total interest charge is approximately £114.61

In your exam you might be asked to do one of the following:

      • - find the percentage of an amount
      • - find out the percentage when given two amounts
      • - find out a percentage increase or decrease
      • - find the cumulative change

Always make sure you read the question carefully so you know what you’re being asked.