**Reverse Percentages **

You 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

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**Compound interest**

The 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 1^{st} year. This is your **principal**.

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

Principal after your 1^{st} year = £636

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

Principal after the 2^{nd} year = 674.16

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

So, principal after the 3^{rd} 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**.**