TITLE: Unit 11 Earning and Spending: a Look at Percentages

Earning and spending

TITLE: Unit 11 Earning and spending: a look at percentages

Introduction to percentages 3

The meaning of percentage 3

Finding the percentage of a quantity 3

Using a calculator to find percentages 7

Percentages and wages 10

Percentages and spending 13

Percentages and banking 16

Suggested answers to activities 20

Introduction to percentages

This topic is devoted entirely to percentages, and the impact they have on our everyday earning and spending habits. Wage rises, sales assistants’ commissions, bank interest rates, mark downs and of course GST all rely onpercentages.

Before we look at some of these examples in detail, a quick review of the meaning of percentage is necessary.

The meaning of percentage

Remember that the important thing when dealing with percentages issimply to look at the word itself.

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Finding the percentage of a quantity

Most of the time, you will use a calculator to find a given percentage of an amount. We will explore the simplest way to do that shortly.

First, however, it is worth understanding that, because of the everyday nature of percentages, there are some which you should be able to calculate without the use of a calculator. These include 50% and 10%, and perhaps 5%, 20% and 25%.

This is how we can calculate simple percentages without a calculator.

Finding 50%

You will remember from Topic 4 that 50% is the same as ‘one half’. So 50% of an amount is just the same as half of it.

Examples

50% of $140 = $70
50% of 2600 m = 1300 m

Finding 10%

Remember 10% is the same as ‘one tenth’. So 10% of an amount is the same as dividing that amount by 10. You have learned that the simplest way to do this is to move the decimal point one place to the left or if there are zeros at the end of a whole number just leave one off.

Examples

10% of $140 = $14
10% of $135 000 = $13 500
10% of $2.80 = $0.28

Finding 5%

Obviously, 5% is half of 10%, so to find 5% of a quantity, first find 10%, then halve your answer.

Examples

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Finding 20%

This is also based on finding 10% first, but then you double your answer rather than halve it.

Examples

20% of $140 = double 10% of $140
= 2 ´ $14
= $28

Finding 25%

Do you remember that 25% is the same as ‘one quarter’ or ‘half of 50%’? So 25% of an amount is the same as dividing that amount by 4, or finding 50% then halving it.

Examples

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1 Complete the following table without a calculator, filling in the percentages shown. Use the diagram below to help you if you need to.

2 Perform these calculations without using a calculator:

(a) 10% of $75

(b) 20% of $510

(c) 5% of $800

(d) 25% of $1200

(e) 50% of $48

(f) 10% of $5.40

(g) 25% of $1800

(h) 20% of $145

(i) 10% of $52

(j) 50% of $16.90

Check your answers against those at the end of the topic.

Using a calculator to find percentages

What 10%, 20%, 25% and 50% all have in common is that they can all be expressed as simple fractions.

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These are the most commonly used percentages in shopping. However, in banking and finance it is more common to see numbers like 5.5% or 6.75% or 17%. These are not that easy to find without the aid of a calculator.

Remembering this makes it easy to find any percentage of any quantity.

Example 1

Find 17% of $3500

Answer:

Step 1: Translate:
% means ‘¸ 100’
‘of ’ means ‘times’ (´)

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Step 3: The answer is $595 or $595.00.

Example 2

Find 6.25% of $12 600

Answer:

Step 1: Translate:
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Step 3: The answer is $787.50.

Example 3

Find 12.5% of $275

Answer:

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Step 2: Using your calculator you will get $34.375

Step 3: The answer is $34.38.

In each example, the calculator steps should be shown as your working, because they demonstrate the arithmetic process used to obtain your answer. Did you notice that because each of these examples dealt with money, the answers need to be written with a $ sign? You may also need to round off some answers to two decimal places.

Use your calculator to find the quantities below. Remember to show your working for each one.

1 14% of $560

2 9% of $1250

3 30% of $8250

4 11% of $967

5 4.5% of $9800

6 1.5% of $66

7 13.5% of $775

8 99.9% of $100 000

9 130% of $200

10 6% of $25.90

Check your answers against those at the end of the topic.

Percentages and wages

Although most workers earn a set wage each week or fortnight, there are many reasons why the wage might be varied by a certain percentage. Here are some of them:

Wage rises

Junior employees (those under 21 years) might receive a rate rise for each birthday, or all workers in a certain industry might receive a general pay rise.

Loading and penalties

Employees working under certain dangerous conditions (eg at heights, or underground, or in dusty environments) sometimes are paid an extra loading, often expressed as a percentage oftheir normal hourly or weekly rate.

Holiday loading

loading, additional to their normal pay, for four weeks’ annual leave.

Commission

Salespersons, in particular, usually have part or all of their wage or salary determined by their volume of sales. This is called commission usually and is expressed as a percentage of total sales. It might range from 3% or 4% for sales people working in high-value sectors such as real estate, to 15% or 20% for those working in low-value sectors such as cosmetics.

Superannuation

All employers in Australia must pay superannuation (currently at the rate of 9%) on behalf of each employee. This means that employees not only receive their regular wage, but also have an additional 9% of its value set aside into a retirement savings fund on their behalf.

As you can see, workers need to be able to calculate percentages just to check their pay.

Example 1

Kelly is a stock-and-station agent who earns 4% commission on sales. Whatdoes she earn for arranging the sale of 100 sheep at $32/head?

Answer:

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Example 2

Sharman earns a weekly wage of $612 as a storeman. He is going to take three weeks of his annual leave and will be paid his usual wage plus 17.5% holiday loading.

(a) How much extra pay will he receive for the three weeks?

(b) What will be his total pay for the three weeks of his holiday?

Answer:

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Sharman will receive $321.30 extra for his three-week holiday period.

(b) Total pay = $1836 + $321.30
= $2157.30

1 Mick’s normal hourly rate as a window cleaner is $13.40, but he is paid a ‘height loading’ of 14% when he works on scaffolding.

(a) Calculate Mick’s hourly rate when working on scaffolding.

(b) What does Mick earn for working two eight-hour days on scaffolding?

2 Heather is a computer operator earning $36,710 per year. Her employer is required to pay 9% of her annual salary into a superannuation fund on her behalf. How much is this each year?

3 Giang is a real estate salesman who earns 5% commission on all sales of up to $100000 value, and 3.5% on sales valued at more than $100,000 but less than $250000. Find Giang’s commission for:

(a) selling a one-bedroom unit in Wollongong at $94,950

(b) selling a three-bedroom house in Parramatta for $235,500.

4 Wendy is an Avon lady who earns 15% commission on all her sales. Last week, shesold cosmetics to three friends for $37, $118 and $64.50 respectively. How much commission did Wendy earn that week?

5 Dimitra earns $412 per week as a junior typist at a local business. She is about to take four weeks’ annual holiday, and will be paid her usual wage plus 17.5% holiday loading for the period. Calculate the total amount of her holiday pay-packet.

6 Richard runs a small produce store in a country town, employing two adult staff, eachof whom earns $680 per week, and one junior hand on $552 per week.

(a) Calculate Richard’s total wages bill for the year (52 weeks).

(b) The National Wage case determines that all employees are to be given a 5.5% increase. What will be Richard’s new annual wages bill, after the increase takes effect?

(c) According to the usual conditions of employment, Richard must also pay an additional 9% superannuation for each employee, and 17.5% holiday loading forfour weeks for each employee.

(i) Find the total amount paid in superannuation each year for the threeemployees, after the wage rise.

(ii) Find the total amount paid in holiday loading for the three employees, after the wage rise.

(iii) By adding wages, superannuation and holiday loading, calculate the total annual cost of Richard’s payroll.

Check your answers against those at the end of the topic.

Percentages and spending

There are two main ways that you will see percentages used when making purchases:

·  Discounts: A store might have an advertised sale, or perhaps you are entitled to a trade discount or employee discount.

·  GST: From July 1, 2000, most purchases of goods (from a cup of coffee to a new car) and services (from plumbing to legal matters) became subject to a 10% GST (Good and Services Tax). You don’t usually need to calculate the GST yourself when shopping, however, as, unlike some other countries where the price of goods are displayed ‘ex-tax’, prices in Australia are required by law to be shown inclusive of GST.

If you run a small business and are registered to collect GST, there are two main types of calculations you will be required to make every day. Theseare:

·  adding the 10% GST on to the value of every product or service you sell

·  calculating the value of GST included in the cost of every item you purchase for your business. (This calculation is made so that you can claim back this cost from the Tax Office).

Let’s look at some everyday examples.

Example 1

Sally’s favourite jewellery store is advertising 25% off every item in the store! How much should she pay for a necklace marked at $129.50?

Answer:

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Example 2

Rossco’s lawn-mowing business is registered for GST. If his labour is costed at $36/hr, what price does he charge a customer for a three-hour job?

Answer:

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As with all similar money problems, remember to set your work out clearly using words and showing working.

1 W-mart stores advertised a ‘15% off all appliances’ sale. What will be the saving on a blender which normally sells at $134.99?

2 Leo buys a pair of jeans, normally priced at $89, at a ‘20% off’ sale. What will he pay for the jeans?

3 Stan is a builder who obtains a 12.5% trade discount on all his timber purchases at Oliver’s Timber Supplies. If the normal price of Oregon is $2.65 per metre, what price must Stan pay for a six-metre length?

4 Essential Cleaners are registered for GST. If the labour is charged at $35 per hour, how much GST would need to be added to the cost of a four-hour job?

5 Before GST was introduced, Joe’s favourite Auto magazine used to cost him $5.80. What does it cost him now (assuming there have been no other price rises)?

6 The recommended retail price of a particular CD is $34.95. If Sam’s Sounds has a sale offering 15% discount on all CDs, and Dave’s Discounts regularly sells them for $29.95, which store is offering the better discount?

7 Dino, the auto electrician, charges $40 per hour, plus parts, plus GST for all jobs. What does he charge a customer for a job which takes two hours labour and which uses $5.80 worth of parts?

8 Swee is shopping for a VCR. The first store she visits has the model she wants with a marked price of $390, but they are having a sale and all items are marked down by 15%. The second store she visits has exactly the same model with a marked price of $360 and will give her a 5% discount if she buys the VCR today. Which store is offering the best deal?

Check your answers against those at the end of the topic.

Percentages and banking

A bank interest rate is always quoted as a percentage.

·  If you have savings, the bank will pay you interest on the amount held in your account, The rate can vary from a very small rate such as 0.25%p.a. (per annum, or per year) on, say, a simple passbook savings account, to around 8% p.a. on certain types of investment accounts.