Description of Percentage Calculation with examples

Percentage calculation is certainly known to you, you will find it almost daily in your life. On this page some examples are described.

Starting point for the percentage calculation is the following formula

\(\displaystyle\frac{W}{G}=\frac{P}{100}\)

\(W\) is the percent value

\(G\) is the basic value

\(P\) is the percentage

The first example calculates an increase of \(3\) percent. Whether it is a wage increase or rent increase does not matter and is left to your optimism or pessimism.

he percentage is given \(P = 3\). Let be the base value \(1000\), then \(G = 1000\).

We are looking for the percentage value \(W\).

The formula \(\displaystyle\frac{W}{G}=\frac{P}{100}\) is changed to the percentage value \(W\).

The calculation is \(\displaystyle W=\frac{G·P}{100}=\frac{1000 · 3}{100}=30\)

\(30\) are added to the base value. \(30 + 1000 = 1030\) is the new amount

Consider a package of shares worth \(1000$\) and calculate the value of the shares when the price falls to \(85\%\).

This means the percentage \(P = 85\) with a base value \(G\) of \(1000\).

To calculate the percent value \(W\) lautet die Formel \(\displaystyle W=\frac{G·P}{100}=\frac{1000·85}{100}=850\)

The value of the shares is now \(850$\)

Suppose the stock price rises again by \(15\%\), then we expect a base value of \(G = 850\) and a percentage \(P = 15\).

The calculation is then \(\displaystyle W=\frac{G·P}{100}=\frac{850·15}{100} = 127.50\)

The new value of the shares package is \(850 + 127 = 977.50$\). That's \(22.50$\) below the original value.

The difference is due to the fact that we assumed a base value of \(G = 1000\) when calculating the loss by \(15\%\). When calculating the profit of \(15\%\) we assumed a base value \(G = 850\).

This example calculates what percentage of the stock value in the example above should have risen to reach the starting level of \(1000$\).

The basic value \(G = 850\) and the percentage \(W = 1000\) are known.

The formula is changed to \(\displaystyle P=\frac{W·100}{G}=\frac{1000·100}{850}=117.65\)

The percentage of \(1000$\) is therefore \(117.65\) percent of the initial value of \(850$\). An increase of \(117.65 - 100 = 17.65\%\) is needed to reach the old starting value of \(1000$\).

Let's say you buy a product that is reduced by \(60\%\) for \(120$\)and want to calculate the starting price. Thus, the percentage of \(40\% (100 - 60)\) hat corresponds to a percent value of \(120$\) is known.

We are looking for the basic value \(\displaystyle G=\frac{W·100}{P}=\frac{120·100}{40}=300\)

Note the wording. The goods were reduced by \(60\%\); that means the remaining percentage is \(40\%\). If the goods were reduced to \(60\%\), the percentage would be \(60\%\).