A capital gain (or loss) is the difference between the cost price and the selling price of a good or service.

## The Formula

Capital gain $= sale\hspace{0.1cm}price-cost\hspace{0.1cm}price$

#### Example 1

Rachel purchased a house two years ago for $390,000. She decides to sell her property and she gets$420,000 at the auction. At the time of her purchase, Rachel had solicitor’s fees, moving costs and duty which totalled $6,200. Her agent and solicitor have charged Rachel a combined cost of$6,800 to sell the property.

a) Calculate the capital gain (ignore the additional costs) and express this gain as a percentage of the purchase price correct to two decimal places.

Capital gain$= sale\hspace{0.1cm}price-cost\hspace{0.1cm}price$
Capital gain$=420,000-390,000$
Capital gain$=30,000$

Percentage gain$=\dfrac {capital\hspace{0.1cm}gain}{cost\hspace{0.1cm}price}\times 100$
Percentage gain$=\dfrac {30,000}{390,000}\times 100$
Percentage gain$=7.6923$

The capital gain is \$30,000 and the percentage gain is 7.69%.