Repeated Percentage Change

## Repeated Percentage Change

A percentage change to obtain a new value followed by another percentage change will give a different result to adding the two percentages together.

## Example 1

£100 is increased by 10%. The answer to that calculation is increased by 20%.

What is the difference between that calculation and simply increasing the amount by 30%?

The multiplier for the 10% increase is 1 + frac(10)(100) = 1.1

£100 x 1.1 = £110

The multiplier for the 20% increase is 1 + frac(20)(100) = 1.2

£110 x 1.2 = £132

The multiplier for the 30% increase is 1 + frac(30)(100) = 1.3

£100 x 1.3 = £130

The difference is £132 - 130 = £2

## Example 2

A shop reduces the price of a jacket by 30%. At the end of the sale, the shop increases the price of the jacket by 30% from its sale price.

Prove that the jacket is now cheaper.

The reason for the difference is that the original value before the sale was £100, and the percentage was based on that value.

After the sale, the original value was £70, and the percentage was based on that lower value.

Multiplier for sale price is 1 - frac(30)(100) = 0.7
Multiplier is now 1 + frac(30)(100) = 1.3