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iGCSE (2021 Edition)

16.02 Financial applications of percentages

Lesson

Percentage increase and decrease

There are many financial applications for percentages, including the value of something either increasing or decreasing.

A common example of a percentage decrease is in retail, when an item is advertised as being on sale. If an item is advertised as $20%$20% off, calculations can be made to find the new price of the item when given the original value. Or vice versa, the original price when given only the sale price.

When applying a percentage decrease $%$%

decrease in value  = $\frac{%}{100}\times$%100× original value

new value = original value - decrease in value

                      = original value $\times\left(100-decrease\right)%$×(100decrease)%

An item can also increase in value. This is sometimes referred to as a mark-up, where the value of an item is increased by a certain percentage. A restaurant, for example, may introduce a $15%$15% surcharge on Sundays, meaning that the total bill is increased by $15%$15%.

When applying a percentage increase $%$%

increase in value$\frac{%}{100}\times$%100× original value

new value = original valueincrease in value

                  = original value $\times\left(100+increase\right)%$×(100+increase)%

 

Practice questions

QUESTION 1

We want to increase $1300$1300 by $40%$40% by following the steps outlined below.

  1. First find $40%$40% of $1300$1300.

  2. Add the percentage increase to the original amount to find the amount after the increase.

  3. Calculate $140%$140% of $1300$1300.

  4. Is increasing an amount by $40%$40% equivalent to finding $140%$140% of that amount?

    Yes

    A

    No

    B

QUESTION 2

We want to decrease $1500$1500 by $15%$15% by following the steps outlined below.

  1. First find $15%$15% of $1500$1500

  2. Subtract the percentage decrease from the original amount to find the amount after the decrease.

  3. Calculate $85%$85% of $1500$1500

  4. Is decreasing an amount by $15%$15% equivalent to finding $85%$85% of that amount?

    Yes

    A

    No

    B

Percentage change

Percentage can be useful when comparing a change in values. For example the cost of bread at a store may have increased due to drought from $\$2.00$$2.00 to $\$2.30$$2.30. To compare this increase to another store it is useful to use percentage rather than dollars. The bread has increased by $30$30 cents. Comparing this increase to the starting value:

$\frac{0.30}{2.00}=0.15$0.302.00=0.15

By converting this to a percentage we can say the bread has increased by $15%$15%

To find the percentage change

Percentage change $=\frac{new\ value-\ original\ value}{original\ value}\times100$=new value original valueoriginal value×100 %

Practice question

QUESTION 3

A holiday resort in Tasmania reduced its overnight rates from $\$320$$320 to $\$120$$120.

  1. Find the amount that Beth would save if she is to take advantage of the sale.

  2. Express this amount saved as a percentage discount.

    Make sure to give your answer as a percentage, correct to two decimal places.

Calculating original value

The original value of an item can be calculated when given a new amount and a percentage change (increase or decrease).

For example, the original value of an item when given a new amount of $\$63$$63 and a percentage increase or decrease of $3$3 %.

Finding original value given new amount (percentage increase)

original value = new value $\times\frac{100}{100-%\ change}$×100100% change

Finding original value given new amount (percentage decrease)

original value = new value $\times\frac{100}{100+%\ change}$×100100+% change

Practice question

QUESTION 4

There is a $12%$12% off sale in store. With this discount in place, a particular item sells for $\$2992.00$$2992.00.

Calculate the regular price of this item, to the nearest dollar.

Goods and services tax (GST)

Goods and services tax (GST) is a  tax of $10%$10% on most goods, services and other items sold or consumed in Australia. Businesses charge the customer an additional $10%$10% of the original price as a GST amount. For example, if the original price of an item was $\$20$$20, the GST on this item would be $\$2$$2 since $10%$10% of $\$20$$20 is $\$2$$2. The total price then charged would be $\$22$$22 .

For tax reasons, businesses need to keep track of how much GST they pay and receive, so it is important to be able to calculate prices before and after GST, as well as the amount and rate of GST.

Calculations including GST

cost including GST $=\cos t\ including\ GST\times1.1$=cost including GST×1.1

amount of GST  $=\frac{\cos t\ including\ GST}{11}$=cost including GST11

Calculations excluding GST

cost excluding GST $=\frac{\cos t\ including\ GST}{1.1}$=cost including GST1.1

amount of GST  $=\frac{\cos t\ excluding\ GST}{10}$=cost excluding GST10

 

Practice question

Question 5

The sales price of an item, including GST, is $\$40$$40. Calculate the price of the item without GST.

  1. Round your answer to the nearest cent.

Shares, dividends and yields

A popular method of investing is through buying shares.

  • the expectation that over time the value of the company (and thus the value of each share) will increase, meaning a small piece of the company is now worth more. 
  • Dividends are paid to shareholders when a company makes a profit.

Price-to-earnings ratio (P/E ratio)

As a shareholder we are interested in calculating the amount of profit and how this profit compared to the amount invested in the company.

Calculating the price-to-earnings ratio allows investors to compare different companies or different dividends. The lower the price-to-earnings ratio the better the result for an investor as it shows that they have invested less for each dollar of profit.

Price-to-earnings ratio

P/E ratio$=\frac{current\ share\ price}{dividend\ per\ share}$=current share pricedividend per share

Practice question

QUESTION 6

The annual earnings per share is $\$1.25$$1.25 and the market price of the share is $\$12.25$$12.25.

Calculate the price-to-earnings ratio.

Dividends

Companies share their profits with their shareholders by paying out dividends either as

  • a dollar value per share or
  • a percentage of current price of the share which is known as a dividend yield.

Dividends and yields

Dividend per share $=\frac{company\ profit}{total\ number\ of\ shares}$=company profittotal number of shares

Dividend yield $=\frac{dividend\ per\ share}{current\ share\ price}\times\frac{100}{1}$=dividend per sharecurrent share price×1001 %

Practice questions

Question 7

Calculate the dividend per share when a company's net profit of $\$373520$$373520 is to be distributed evenly among its $128800$128800 shares.

Question 8

Calculate the dividend yield (correct to one decimal place) when a firm with a share price of $\$38.20$$38.20 pays a dividend of $\$1.38$$1.38 per share.

Outcomes

0580C1.16A

Use given data to solve problems on personal and household finance involving earnings.

0580E1.16A

Use given data to solve problems on personal and household finance involving earnings.

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