Encyclopedia>Numbers and Quantities>Fractions and Percentages>Percentages>How to Find Relative Percent Change

Here you will learn about the calculation of percentage change. You might have heard that the prices of housing has risen by $20$ %, but what does it actually mean when people say that something has risen or fallen by a certain percentage?

This type of increase or decrease is called a percentage change. The answer to the question asked above is then: The price for housing at two different times are compared, and the change in price is converted to a percentage relative to the original price. This is what you will learn here.

You want to compare old value to new value and find the percentage change. Have a look at the formula written below.

Formula

$$\text{\%change}=\frac{\text{newvalue}-\text{oldvalue}}{\text{oldvalue}}$$ |

If you get a positive number, something has grown in value.

If you get a negative number, something has declined in value.

Example 1

**You bought a Playstation for $\text{\$}\text{}320\text{}$. You decided to sell it two years later. You sold it for $\text{\$}\text{}175\text{}$. What was the percentage change? **

The percentage change is: $$\begin{array}{llll}\hfill \frac{175-320}{320}& \approx -0.453\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =-45.3\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

This means that the change in value was $-45.3\phantom{\rule{0.17em}{0ex}}\text{\%}$. You got a negative percentage, meaning that the Playstation declined in value. It has fallen by $45.3\phantom{\rule{0.17em}{0ex}}\text{\%}$ in value.

Example 2

**You deposit $\text{\$}\text{}5000\text{}$ to the bank. A year later you find that this has grown to $\text{\$}\text{}5200\text{}$. What is the percentage change? **

The percentage change is: $$\begin{array}{llll}\hfill \frac{5200-5000}{5000}& =0.04\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =4\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

The percentage change is $4$ %. Since you found a positive number, the money you deposited has grown in value by $4$ %.

Example 3

**Four years ago a house cost $\text{\$}\text{}350\phantom{\rule{0.17em}{0ex}}000\text{}$, now the same house costs $\text{\$}\text{}420\phantom{\rule{0.17em}{0ex}}000\text{}$. How many percent has the house grown in value? **

You have to calculate the percentage change. $$\begin{array}{llll}\hfill \frac{420\phantom{\rule{0.17em}{0ex}}000-350\phantom{\rule{0.17em}{0ex}}000}{350\phantom{\rule{0.17em}{0ex}}000}& =0.20\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =20\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

In four years the value of the house has grown by $20$ %.

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