The purpose of business guidelines
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PERFORM FINANCIAL CALCULATIONS
FNSACC303A
Workbook
PERFORM FINANCIAL CALCULATIONS
Contents
Perform Financial Calculations 3
Part 1: Review Basic Arithmetic & Algebra 4
Part 2: Percentage Calculations in Accounting & Bookkeeping 41
Part 3: Simple Interest 58
Part 4: Compound Interest 62
Part 5: Income Tax 68
Part 6: Business Calculators, Software and Programs 74
Part 7: Common Computational Errors 77
Present Value and Future Value Tables 79
Perform Financial Calculations
|Unit descriptor |This unit covers the use of a common range of calculation methods and techniques for |
| |conducting routine financial calculations and transactions. |
|Application of the unit |This unit requires the application of literacy and numeracy skills to perform common |
| |computational tasks as part of an operational job role. |
|ELEMENT |PERFORMANCE CRITERIA |
|1. Obtain data and resources for |1.1. Input data is obtained and verified as relevant for workplace calculations |
|financial calculations |1.2. Outcomes of calculations are determined and confirmed from task specifications |
| |1.3. Relevant resources and equipment to perform the calculations effectively are acquired |
| |1.4. Simple spreadsheets are developed where necessary to perform calculations that may be |
| |repeated |
|2. Select appropriate methods and |2.1. Hand held calculators are primarily used for performing calculations with other equipment|
|carry out financial calculations |that may be required identified and obtained as necessary |
| |2.2. Calculations to complete the work requirements are performed using appropriate techniques|
| |2.3. Data used in calculations is rechecked against task specifications |
|3. Check calculations and record |3.1. Results are checked to ensure the calculations are accurate, meet the required outcomes |
|outcomes |with common computational errors recognised and corrected where required |
| |3.2. Calculation results are recorded to industry standards and enterprise requirements |
| |3.3. Calculation worksheets are stored or electronically filed for future use |
Unit Purpose
On successful completion of this unit you should have the skills & knowledge required to use a range of calculation methods and techniques for conducting routine financial calculations.
Specifically you should be able to:
• Apply basic mathematics
• Use & apply percentage calculations:
o Simple Profit & Loss
o Mark-Up
o Discounts
o Commission
o Depreciation & Appreciation
o Goods & Services Tax
• Calculate simple interest
• Calculate compound interest
• Work with income tax tables
• Gain an understanding of the use of business calculators, software and other programs that can be used to perform financial calculations
• Be able to identify and correct common computational errors.
Part 1: Review Basic Arithmetic & Algebra
Whole Numbers, Fractions & Decimals
In this section you will visit these numbers.
First, we look at the order in which we do the operations of addition, subtraction, multiplication and division of these numbers.
This work is followed by examples which use a mixture of these operations.
Next you will review how to add and subtract positive and negative numbers. Then we will look at multiplication and division of these directed numbers.
Then we will review the operations using fractions and decimals.
Also, you will use your calculator to check your operations.
Following this we will look at the role of pro-numerals in algebra.
Order of Operations
Sometimes in mathematics, you have to solve questions which have more than one operation. Take a look at the following example:
5 + 3 x 4
|How would you do this question? Write down your answer. |
|What did you get? |
Let’s work through the question and see the correct order of operations we must follow.
5 + 3 ( 4
= 5 + 12 (multiplication worked first)
= 17 (then addition is done)
For this example, we do the multiplication before the addition.
Grouping Symbols
Sometimes, grouping symbols (brackets, parentheses or braces) occur in ‘order of operations’ questions. Whatever occurs inside the grouping symbols must be done first.
Example 1 (14 – 2) ( 4
= 12 ( 4 (grouping symbols are worked first!)
= 48
Example 2 11 – (9 – 3)
= 11 – 6 (grouping symbols are worked first!)
= 5
|Now work through the following example. |
Example 3
Sometimes, more than one set of grouping symbols may occur in the same calculation. In this case, the inner grouping symbols are worked first.
3 + [10 – (4 + 3)] (inner grouping symbols worked first)
= 3 + [10 – 7] (other grouping symbols then worked)
= 3 + 3
= 6
Let’s now look at the steps you have followed. The way you work out an ‘order of operations’ question is shown here as a flowchart.
[pic]
Example 4
We work the ‘operations’ of each step from left to right.
14 – (10 – 2) ( 2 ( (5 – 2) + 4
Do step 1 = 14 – 8 ( 2 ( 3 + 4 (grouping symbols simplified)
Do step 2 = 14 – 4 ( 3 + 4 (division and
= 14 – 12 + 4 multiplication done)
Do step 3 = 2 + 4 subtraction and
= 6 addition done)
Activity 1
1 Using the correct order of operations answer the following:
(a) 8 – 4 + 2
(b) 13 + 5 – 6 + 3
(c) 7 x 2 – 4
(d) 18 ÷ 9 x 5
(e) 24 ÷ 2 ÷ 3 x 5
(f) 9 + 5 x 2
(g) 18 ÷ 3 – 1 x 4
(h) 10 – 12 ÷ 4 + 5 x 3
(i) 9 x (12 – 4) + 3
(j) (5 + 2) x (8 – 8)
2 For the following questions, are the answers correct? If not, what is the correct answer?
(a) 24 ÷ 6 + 6 ÷ 2 = 7
(b) 72 ÷ 8 – 1 x 6 = 48
(c) 5 + 2 x 1 – 7 = 0
(d) 16 ÷ 8 – 1 = 1
(e) 9 + 8 x 0 – 6 = 11
Fraction Bars
Sometimes a fraction bar occurs in a calculation. A fraction bar means division.
Example 5
[pic]eq14
Everything above a fraction bar is divided by everything below the fraction bar. When you re-write the fraction as a division, you must put grouping symbols where they are needed, as shown in the next two examples.
Example 6
[pic]eq15
Example 7
[pic]eq16
Another way!
You can do all the operations above the fraction bar then all the operations below and finally do the division.
Example 8
|[pic]eq17 |(do multiplications first) |
Another example:
Example 9
[pic]eq18
Activity 2
Solve the following:
[pic]eq19
Order of Operations and the Calculator
Most calculators have the ‘order of operations’ built-in, but you will need to check whether your calculator has this by doing the following questions.
9 + 1 ( 5
If you got 14 as your answer, your calculator does order of operations.
Note: To use your calculator to do Activity 2, you must first rewrite the question using brackets as shown above.
When a question contains large numbers, use your calculator. Try the following activity using your calculator.
Activity 3
1 A group of 143 students meet to see a hockey match. Four buses, each holding 32 passengers, took most of the students. The rest went by train. How many students went by train?
2 Sue and Paul are planning to marry. They have a quote from a caterer for $24 per head. Sue has estimated that there will be at least 44 people from her side of the family and Paul wants to invite a further 38 people.
(i) How many people will be attending Paul and Sue’s wedding?
(ii) Calculate the cost of catering for Sue and Paul’s wedding.
Fractions
A fraction has a numerator (top line) and a denominator (bottom line) expressed as:
Example 10
[pic]eq25
Equivalent Fractions
Equivalent fractions are fractions which represent exactly the same number
[pic]eq26
Example 11: fill in the missing space
[pic]eq27
| |[pic]uf02 |
|Here’s how it’s done | |
It doesn’t matter whether we want to find the numerator or the denominator of our equivalent fraction—we can use the same method.
|Now, try this one: |
[pic]eq28
What should replace the question mark?
Did you decide it should be 20?
| |[pic]uf03 |
|Here’s how it’s done: | |
Activity 4
Convert these fractions to their equivalent fractions by filling in the missing numbers:
[pic]eq29
More Equivalent Fractions
Now we will look at the following equivalent fractions.
|What do you think you would do to the numerator so that these fractions would be equivalent? |
|[pic]eq33 |
Did you notice that the denominator, 8 can be reduced to 4 by dividing by 2?
[pic]uf06
So we must divide the numerator by 2 as well.
[pic]uf07
| |[pic]uf08 |
|Here’s the complete procedure: | |
Example 12
|[pic]eq34 |
|The numerator, 12 can be reduced to 4 by dividing by 3. |
[pic]uf09
What would you do to the denominator?
Divide the denominator by 3 as well.
[pic]uf10
[pic]eq35
Activity 5
Convert these fractions to their equivalent fractions by filling in the missing numbers:
[pic]eq36
Simplify Fractions
Whenever you work with fractions, you are often expected to simplify them—or to reduce them to their lowest terms. This means you have to find an equivalent fraction that has no common factors in its numerator and denominator. The easiest way to simplify a fraction is to divide the numerator and denominator by the highest common factor.
[pic]eq40
The factors of 45 are: 1, 3, 5, 9, 15, 45
The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The highest common factor is 15
[pic]uf13
However, if you are not sure of the highest common factor, you can keep dividing the numerator and the denominator by different factors until you get the simplest terms. This is a little slower, but will give you the correct answer.
[pic]eq41
| |[pic]uf14 |
|First step: | |
At this point you can see that 3 can also be divided into both the numerator and the denominator.
| |[pic]uf15 |
|Second step: | |
[pic]eq42
|Whenever you simplify fractions, always check to see if your answer can be simplified further. |
|A fraction is not completely in its simplest form until the numerator and the denominator have no common |
|factors. |
Activity 6
Write each of these fractions in their simplest terms.
[pic]eq43
Addition and Subtraction of Fractions
We have looked at similar fractions which are fractions with the same denominator. We can add and subtract similar fractions.
[pic]eq90
we can add these fractions:
[pic]eq91
[pic]eq92
[pic]eq93
First, you need to make these two fractions into similar fractions.
[pic]eq94
[pic]eq95
If one denominator is not a multiple of the other, we obtain similar fractions by multiplying each fraction by the other denominator.
Example 13
[pic]eq96
Example 14
[pic]eq97
Activity 7
Find the values of:
[pic]eq98
Adding Mixed Numbers
Example 15
[pic]eq101
You can see that we add the whole number parts first.
[pic]eq100
Subtracting Mixed Numbers
Is most easily done by changing all fractions into improper fractions.
Example 16
[pic]eq102
[pic]
eq103
Activity 8
Find the value of:
[pic]eq104
Multiplying Fractions
When multiplying fractions, we simply multiply the denominators together, and the numerators together.
Example 17
[pic]eq106
[pic]eq107
[pic]eq108
[pic]eq109
Note: You are not allowed to multiply the whole numbers first—they must be changed to improper fractions.
Dividing Fractions
You will remember from earlier modules, that when dividing by a fraction we need only invert the fraction, and then multiply.
Example 18
[pic]eq110
[pic]eq111
[pic]eq112
[pic]eq113
[pic]eq114
Activity 9
[pic]eq115
Decimals
Decimals are forms of fractions in which the denominator is always 10, 100, 1000 or a greater multiple of ten.
Instead of writing the fraction with a denominator, we write only the numerator part and use a decimal point to show where the fraction starts. Here are some examples:
[pic]eq132
|So decimals are just an extension of the ‘place value’ system that you have already seen in our number system. |
|Part of this system can be seen in the table below: |
[pic] uf30
Here are a couple of points to remember:
|When we write a positive fraction with a value less than 1 as a decimal, we always place a zero in the units column. The zero is there |
|to ‘hold the place’ and to make sure that the decimal point is not missed. |
|In a number like 0.001, there are no units, no tenths and no hundredths. We put zeros in these places in order to keep the 1 in the |
|thousandth place. We read 0.001 as ‘zero point zero zero one’. |
Now look at these examples.
Example 19
The number 287.648 is made up of
|2 hundreds |(2 ( 100) |200 |
|8 tens |(8 ( 10) |80 |
|7 units |(7 ( 1) |7 |
|6 tenths |[pic]eq133 |.6 |
|4 hundredths |[pic]eq134 |.04 |
|8 thousandths |[pic]eq135 |.008 |
| | |287.648 |
Example 20
[pic]eq136
Example 21
[pic]eq137
Decimals and Fractions
Decimals are just a different way of writing fractions with a multiple of ten in the denominator. So these fractions can easily be turned into decimals:
Example 22
[pic]eq138
Activity 10
Write these fractions as decimal numbers:
[pic]eq139
When the Denominator is Not a Multiple of 10
What if the denominator of the fraction is not 10, 100, 1000 or a greater multiple of ten?
Can we change any fraction into a decimal?
[pic]eq140
But there is another way.
[pic]eq141
First, we will look at division of a decimal number by a whole number to help you change any fraction into a decimal.
Let’s try the division of 3 by 4.
[pic]eq142
We can rewrite 3 as 3.00 without changing its value. (You can add as many zeros as you like.)
Now try 3.00 ( 4
[pic]eq143
[pic]eq144
Activity 11
Convert the following fractions to decimals:
[pic]eq145
Reversing the Process: Changing Decimals to Fractions
Since any decimal is just a form of a fraction with some particular multiple of ten in the denominator, we can change the decimal into a fraction very easily.
Example 23
[pic]eq159
Activity 12
Write these decimals as fractions.
|(a) |0.7 |(f) |5.001 |
|(b) |0.99 |(g) |0.009 |
|(c) |0.01 |(h) |3.9 |
|(d) |0.573 |(i) |0.31 |
|(e) |2.11 |(j) |5.113 |
Remember that the fraction you write is the equivalent fraction that is written in its ‘lowest terms’. When you turn a decimal into a fraction, you are expected to reduce it to its lowest terms.
Sometimes you find it already in its lowest terms;
[pic]eq161
[pic]eq162
[pic]eq163
|Whenever you convert a decimal to a fraction, you should always check to see if you can simplify it further. |
Activity 13
Convert these decimals to fractions and simplify, if necessary.
|(a) |0.6 |(d) |1.2 |
|(b) |0.25 |(e) |5.46 |
|(c) |0.625 |(f) |2.585 |
Directed Numbers
We can use the idea of a reference point to draw a number line.
This number line is marked in ‘ones’. 0 is the reference point.
[pic] uf33
Numbers to the right of 0 are positive (+)
and those to the left are negative (–).
|Write in values along the line. Then mark in these points: |
|+9, +12, –6, –1, +2, –4. |
|What numbers occupy the positions A, B and C? |
Did you find that A is –11, B is –9 and C is 5?
Check your line with this one.
[pic] uf34
All values are equally spaced along the line.
+9, +12 and +2 all lie to the right of 0, as they are
positive numbers.
–6, –1, and –4 all lie to the left of 0, as they are
negative numbers.
Positive numbers may be written as +4, (+4) or 4.
Similarly, negative numbers may be written as –8 or (–8).
Each number to the right of another is greater than
the one before, thus:
+5 is greater than +3
+1 is greater than –2
–1 is greater than –5
Alternatively, each number to the left of another is less than
the one before, thus:
+1 is less than +3
–2 is less than 0
–7 is less than –5
When you add a number, you move that many places to the right.
Example 24
3 + 2
| |
[pic] uf36
Activity 14
Calculate the following. Use a number line if you find that it helps you.
(a) +3 + (+4) =
(b) –3 + (+8) =
(c) –12 + (+8) =
(d) –6 + (+2) + (+5) =
Subtracting Directed Numbers
The addition of a negative number is the same as subtraction.
50 + (–30) = 20
Look at this on the following number line.
[pic] uf41
Start at +50 and, since you are adding a negative number, count 30 to the left. You will end up at 20.
–30 is the number that has the opposite direction to +30. Subtraction is really addition of the same size number with the opposite direction.
–30 + (+30) = 0
+30 + (–30) = 0
|Draw a number line and use it to calculate 13 – 9. |
[pic]uf42
When you add a negative number, you draw your arrow in the opposite direction to the way when you add a positive number.
|Use a number line to calculate +4 + (+3) and +4 + (–3). |
|Did your number line look like this? |
[pic] uf43
NB: If a number does not have a sign in front of it, it is assumed to be positive. That is, 4 = +4.
More on Subtraction
Subtraction reverses the normal direction of a number.
5 – (+ 3)
+ 3 would normally move 3 places to the right, but the – (+3) reverses this to move 3 places to the left.
-3
| |
Activity 15
Calculate the following:
1 (a) 8 – (–2) = 8 + 2 =
(b) 6 – (–8) =
(c) –2 – (–9) = –2 + 9 =
(d) +2 – (–2) =
(e) (–6) – (–3) =
(f) (–5) – (–5) =
(g) 0 – (–3) =
(h) 11 – (–7) – (–1) =
2 (a) 5 + 6 =
(b) (–2) – (+7) =
(c) – 2 – (+3) =
(d) – 5 – 6 + 3 =
(e) 0 – (–5) =
(f) +4 + (–9) =
(g) 8 – 5 + 6 – 2 =
(h) 12 – (–10) =
3 (a) At Thredbo the temperature was –7°C and then rose by 10°C. What is the new temperature?
(b) What is the difference in temperature between 38°C and –9°C?
4 How many years were there between:
(a) 1215 AD and 1994 AD?
(b) 55 BC and 1215 AD?
5 If your bank balance was –$42 and you deposited a cheque for $97, what would your new balance be?
Multiplying and Dividing Directed Numbers
Multiplying Directed Numbers
Multiplication is just repeated addition.
That is: 3 [pic] 2 means 2 + 2 + 2, or three lots of 2
and, 4 [pic] (–1) means (–1) + (–1) + (–1 ) + (–1), or four lots of –1
Example 26
3 ( (–2) = (–2) + (–2) + (–2)
= –6
or 3 ( (–2) = –6
also –3 ( 2 = – (+2) + – (+ 2) – (+ 2)
= –6
So a positive number times a negative number (in any order) gives a negative number.
What does –3 ( –4 mean?
–3 ( –4 = – (–4) + – (–4) + – (–4)
= 4 + 4 + 4
= 12
So remember
|– a ( – b = + ab |
Again: –2 [pic] (+3) gives –6
+2 [pic] (–3) gives –6
but: –2 [pic] –3 gives +6
|Multiplying two numbers with the same sign gives a positive answer, while multiplying numbers with different |
|signs gives a negative answer. |
|Examples: |
|+4 [pic] (+3) = +12 |
|–4 [pic] (–3) = +12 |
|+4 [pic] (–2) = –8 |
|–2 [pic] (+4) = –8 |
Try these examples:
|+4 [pic] (–2 )[pic] (+5) |This expression has multiplication only. |
|=[+4 [pic] (–2)] [pic] (+5) |The product of +4 and –2 is –8. |
|= –8 [pic] (+5) |This is then multiplied by +5. |
|= –40 | |
|–3 [pic] (+4) [pic] (–6) |This expression has multiplication only. |
|= [–3 [pic] (+4)] [pic] (–6) |The product of –3 and +4 is –12. |
|= –12 [pic] (–6) |This is then multiplied by –6. |
|= +72 | |
Activity 16
Work out these products:
(a) (–2) [pic] (+8) =
(b) (–3) [pic] (–3) =
(c) 3 [pic] 4 =
(d) 6 [pic] (–5) =
(e) 2 [pic] 2 [pic] (–3) =
(f) (–4) [pic] 5 [pic] (–5) =
(g) (–4) [pic] 11 =
(h) 3 [pic] (–8) [pic] (+2) =
Division of Directed Numbers
As you have seen, division is the opposite of multiplication.
|What would you expect the answers of these divisions to be? |
|–20 ÷ 4 = .............. |
|–20 ÷ (–5) = .............. |
Since 4 [pic] (–5) = –20, then –20 ÷ 4 = –5
Also, since (–5) × 4 = –20, then –20 ÷ (–5) = 4
Written another way, these expressions are:
[pic]eq169
The same rules about negative and positive numbers apply to both multiplication and division.
|Dividing two numbers of the same sign gives a positive answer. |
|For example: |+16 ÷ (+4) = +4 |
| |–16 ÷ (–4) = +4 |
|Dividing two numbers with different signs gives a negative result. |
|For example: |–15 ÷ (+3) = –5 |
| |+15 ÷ (–3) = –5 |
Activity 17
Work out the value of:
[pic]eq170
‘Order of Operations’ with Directed Numbers
Do you remember learning about ‘order of operations’?
The following examples use all four number operations.
| |
|Work through these examples. |
|3 [pic] (–2) + (+4) = –6 + (+4) Multiplication first |
|= –2 |
|3 – [(–12) ÷ (+4)] = 3 – (–3) Brackets first |
|= 3 + 3 |
|= 6 |
What about these?
[pic]eq171
What did you have to do first?
Did you notice that each expression above and below the fraction line must be worked before the division takes place?
Activity 18
Calculate the following:
[pic]
eq172
Part 2: Percentage Calculations in Accounting & Bookkeeping
Understanding & Working With Percentages
Writing Percentages as Fractions
A per cent (%) is just a common fraction, which has a denominator of 100. Since you know the bottom line is always 100, you don’t need to write it, so you just put the % sign.
‘Per cent’ actually means ‘out of 100’ in Latin.
So, 50% just means a fraction with a top line of 50, and bottom line of 100:
50% = [pic]
You can of course cancel this to [pic].
Examples
1 25% = [pic] = [pic] after cancelling.
To enter 25% just enter 25[pic]100[pic] and the display is [pic].
2 2% = [pic] = [pic]
2[pic]100[pic] and the answer is [pic].
3 37% = [pic] (we can’t cancel).
37[pic]100[pic] and the answer is [pic].
100% means [pic] or 1!
So, any percentage larger than 100 represents a number larger than 1.
4 130% = [pic] = 1[pic]
130[pic]100[pic] and the answer 1[pic].
5 280% = [pic] = 2[pic]. Use your calculator to cancel [pic] down.
6 112.5% = [pic] = 1[pic] (using the calculator).
Writing Percentages as Decimals
Percentages can be easily turned into decimals:
50% = [pic] = 0.5
Remember—when dividing by 100, you just move the decimal point two places to the left.
Examples
7 23% = [pic] = 0.23
On the calculator, 23[pic]100[pic][pic] gives 0.23
Actually, it’s easier to do 23[pic]100[pic] which also gives 0.23
8 140% = [pic] = 1.4
140[pic]100[pic] and the answer is 1.4
9 17.25% = 17[pic] = 0.1725
Activity 1
1 Change these percentages to fractions in their simplest form (cancelled down):
(a) 80% __________ (b) 74% __________
(c) 12.5% __________ (d) 175% __________
(e) 387.5% __________ (f) 0.16% __________
2 Change these percentages to decimals.
(a) 60% __________ (b) 37.5% __________
(c) 213% __________ (d) 0.45% __________
Changing Fractions to Percentages
You can also easily change fractions to percentages. All you need to do is to use equivalent fractions to turn the denominator to 100.
Examples
10 To change [pic] to a percentage, multiply top and bottom by 20:
[pic]s4_eqn17
There is a simpler way to get the same answer. Just multiply the fraction by 100 and add a % sign. We use the calculator for this:
[pic] = [pic] × 100% = 80%
4[pic]5[pic]100[pic] and the display is 80.
11 Change [pic] to a percentage.
[pic] = [pic] × 100% = 75%
3[pic]4[pic]100[pic] which displays 75.
12 Change [pic] to a percentage.
[pic] = [pic] × 100% = 8.[pic]%
1[pic]12[pic]100[pic] and the display is 8.333333333333
13 Change 3[pic] to a percentage.
3[pic] = 3[pic] × 100% = 362[pic] %
3[pic]5[pic]8[pic]100[pic] and the display is 362[pic]1[pic]2.
Changing Decimals to Percentages
To change decimals to a percentage, you also just need to multiply by 100 and add a % sign:
0.4 = 0.4 × 100% = 40%
Examples
14 0.23 = 0.23 × 100% = 23%
15 2.07 = 2.07 × 100% = 207%
16 1.0671 = 1.0671 × 100% = 106.71%
Activity 2
Convert the following to percentages.
1 [pic] __________ 2 [pic] __________
3 [pic] __________ 4 3[pic] __________
5 0.7 __________ 6 1.8 __________
7 2.075 __________ 8 5.6775 __________
Percentages of Amounts
Percentages are most often used to represent a fraction of a given amount; for example, a store may offer 20% off all items.
You will now look at how to find the percentage of an amount.
Examples
17 Find 20% of $55.
First, we convert the percent to a fraction, then replace the ‘of’ with ‘×’:
20% of $55 = [pic] × 55
20[pic]100[pic]55[pic] Answer is $11.
or 20[pic]100[pic]55[pic] Answer is $11.
18 Find 18% of 350 mm.
18% of 350 = [pic]× 350
18[pic]100[pic]350[pic] Answer is 63 mm.
19 Find 135% of $20.
135% of 20 = [pic] × 20
135[pic]100[pic]20[pic] Answer $27.
20 Find 12.5% of $512.
12.5% of 512 = [pic] × 512
12.5[pic]100[pic]512 [=] Answer is $64.
Expressing an Amount as a Percentage of Another Amount
You may want to know what percentage one value is of another.
Examples
21 What percentage is 30 cm of 150 cm?
Here, you can write the first value as a fraction of the second, then convert to a percentage by multiplying by 100.
The percentage 30 cm is of 150cm is [pic] × 100%.
30[pic]150[pic]100[pic] and the answer is 20%.
22 What percentage is $15 of $300?
Remember, you write the first value as a fraction of the second, then convert to a percentage.
The percentage $15 is of $300 is [pic] × 100%.
15[pic]300[pic]100[pic] and the answer is 5%.
Activity 3
1 Find:
(a) 50% of $300 ________ (b) 25% of $180 ________
(c) 15% of 600 mm ________ (d) 27% of 60 kg ________
(e) 140% of 8 litres ________ (f) 12.5% of $80 ________
2 What percentage is:
(a) 15 cm of 120 cm? __________ (b) $20 of $25? __________
(c) 30 mins of 2[pic] hours? (Hint: Convert both measurements to mins.) __________
(d) $21.25 of $85?__________
Percentages are used in an endless variety of situations in the business world, as well as in everyday situations. A few of these applications are shown in the sections that follow:
• Simple Profit and Loss
• Mark-Up
• Discounts
• Commission
• Depreciation & Appreciation
• Goods & Services Tax
Simple Profit and Loss
In business the principal aim of buying and selling goods is to make a profit, by selling goods for more than they cost. In simple terms:
Profit = Selling Price - Cost Price.
Sometimes (for a variety of economic reasons) goods need to be sold for less than what they cost, and so a loss is incurred:
Loss = Cost Price - Selling Price.
The percentage profit (or percentage loss) is, in general, the profit or loss expressed as a percentage of the selling price.
Percentage Profit/(Loss) = Profit x 100
Selling Price
|Example 23 |
|A heater that cost a retailer $64.50 and was sold for $95. What percentage profit does the retailer make? |
|Solution |
|Cost Price = $64.50, Selling Price = $95 |
|Profit = $95 - $64.50 = $30.50 |
| |
|Percentage Profit/(Loss) = Profit x 100 |
|Selling Price |
|= 30.50/95.00 x 100 |
|= 32.10526 |
|= 32% (nearest percent) |
| |
| |
| |
| |
| |
|Example 24 |
|Michael bought a second-hand car for $4,000 and a year later sold it for $3,200. What is the percentage loss? |
|Solution |
|Cost Price = $4,000, Selling Price = $3,200 |
|Loss = $3,200 – $4,000 = $800 |
| |
|Percentage Profit/(Loss) = Loss x 100 |
|Selling Price |
|= 800/3,200 x 100 |
|= 25% |
| |
| |
Mark-Up
Percentage Mark-up = Sales Price – Cost Price x 100
Cost Price
As you can see this formula is just an alternative to the above formula. “Profit” is replaced by “Sales Price – Cost Price”.
|Example 25 |
|A heater that cost a retailer $64.50 and was sold for $95. What is the mark-up?? |
|Solution |
|Cost Price = $64.50, Selling Price = $95 |
| |
|Percentage Mark-up = SP - CP x 100 |
|CP |
|= 30.50/64.50 x 100 |
|= 47.2868 |
|47% (nearest percent) |
| |
|Example 26 |
|A retailer marks up all his outdoor goods by 45%. If he bought a tent for $680, what will the selling price be? |
|Solution |
|100% + 45% = 145% |
|145% of $680 = 145 x 680 = $986, so the selling price is $986. |
|100 |
| |
| |
Discounts
There are many times when we come across percentages in real life. Shops often advertise a sale with a given percentage off the regular price. The amount taken off the regular price is called the discount.
|Example 27 |
|A shirt normally sells for $45 but is on sale for a discount of 20%. Calculate the new price. |
|Solution |
|20% of $45 = 20/100 x $45 |
|= 0.2 x $45 |
|= $9 |
|The discount is therefore $9. The new price is $45- $9 = $36. |
| |
|Another way of looking at the problem is to look at the discount price as being 80% of the original price (100% - 20% = 80%). |
|So the new discount price is 80% of $45 = 80/100 x $45 |
|= 0.8 x $45 |
|= $36 |
| |
|Example 28 |
|A personal computer was reduced from $1800 to $1350 in a sale. What was the percentage discount that was given? |
|Solution |
|Discount = $1800 - $1350 |
|= $450 |
|% Discount = 450/1800 x 100 |
|= 25% |
| |
| |
|Example 29 |
|At a sale advertising 15% off all items in the store, a jacket was marked down to $127.50. What was the original price of the jacket? |
|Solution |
|100% – 15% = 85% of the original price = $127.50 |
|$127.50 / 0.85 |
|= $150. |
| |
|Example 30 |
|Jack is a builder. At the hardware store he receives a trade discount of 7.5% on all purchases, plus a further 2.5% discount if he pays his |
|account within 30 days. Jack bought timber at the marked price of $1,200, and paid his account ten days later. How much did Jack pay? |
|Solution |
|Trade discount = 7.5% of $1,200 |
|= 0.075 x $1,200 |
|= $90 |
|Amount owing after trade discount = $1200 - $90 = $1,110 |
|Early payment discount = 2.5% of $1,110 |
|= 0.025 x $1,110 |
|= $27.75 |
|Amount owing after early payment discount = $1,110 - $27.75 = $1,082.25 |
|Hence Jack paid $1,082.25. |
|Note: We could have found 92.5% of $1,200, and then 97.5% of $1,110. |
| |
Commission
Some people, for example real estate agents and salesmen, earn their money by charging commission on the value of goods they sell. The agent acts on behalf of the seller, and the seller pays the agent a percentage of the sale price of the commodity, such as land or houses. The commission is usually a percentage of the selling price. Some salesmen are paid a retainer plus commission on the value of their sales.
| Example 31 |
|John is a car salesman. He is paid a commission of 2.5% on the value of sales he makes. Last month John sold cars to a value of $185,000. How |
|much commission did he earn for the month? |
|Solution |
|Commission = 2.5% of $185 000 |
|= 0.025 x $185 000 |
|= $4,625 |
| |
|Example 32 |
|Naomi is a real estate agent. He charges commission for sales as follows: 3% on the first $100,000, and 1.75% on any amount above $100,000. Last |
|week Naomi sold a house for a client for $485,000. How much commission did he charge on the sale? |
|Solution |
|Commission = 3% of $100,000 + 1.75% of $(485,000 – 100,000) |
|= 3% of $100,000 + 1.75% of $385,000 |
|= 0.03 x 100,000 + 0.0175 x 385,000 |
|= $3000 + $6737.50 |
|= $9737.50 |
|Naomi charged her client $9737.50 for the sale. |
| |
Depreciation & Appreciation
Over time, commodities tend to either decrease or increase in value. When a commodity (such as computers, cars, equipment) decreases in value, we say that it depreciates in value. When a commodity (such as antiques, land, houses) increases in value, we say that it appreciates in value. In most cases depreciation and appreciation over a number of years are calculated on the value of the commodity at the end of each year.
| Example 33 |
|Farmer Joe bought some new machinery for $46,000. In the first year it will depreciate in value by 15%. Find the value of the machinery after one|
|year. |
|Solution |
|Machinery decreases in value by 15%. 100% - 15% = 85% |
|Value after one year = 85% of $46,000 |
|= 0.85 x $46,000 |
|= $39,100 |
|After one year the machinery will be worth $39,100. |
| |
|Example 34 |
|Jan bought a block of land for $50,000. In the first year it increased in value by 4%, and in the second year it increased in value by 5%. What |
|was the value of the block of land after two years? |
|Solution |
|In the first year 4% was added to the value. 100% + 4% = 104% |
|Value at end of first year = 104% of $50,000 |
|= 1.04 x $50,000 |
|= $52,000 |
|In the second year 5% was added to the value. 100% + 5% = 105% |
|Value at end of second year = 105% of $52,000 |
|= 1.05 x $52,000 |
|= $54,600 |
| |
| |
Goods & Services Tax (GST)
Another situation where we often come across percentages is in the Australian Goods and Services Tax (GST). GST was introduced in Australia in the year 2000. The Australian Government charges a 10% tax on most goods and services.
|Example 35 |
|The charge for a double room at a motel is $130 per night, before GST has been added. |
|(a) Calculate the amount of GST (10%) to be added to the charge. |
|(b) Calculate the amount to be charged after GST has been added. |
|Solution |
|(a) GST = 10% of $130 |
|= 0.10 x $130 |
|= $13 |
|(b) Charge (including GST) = $130 + $13 |
|= $143 |
|Alternatively, to work out the charge including GST, we could simply find 110% of $130 (in other words, find 1.10 x $130). |
|Example 36 |
|Including 10% GST, Jim’s new suit cost him $385. |
|(a) What was the price of the suit before GST was added? |
|(b) How much GST was added? |
|Solution |
|(a) Price including GST = 100% + 10% |
|= 110% |
|110% of pre-GST price = $385 |
|= 385 / 1.10 |
|= $350 |
|The price of the suit before GST was added was $350. |
| |
|(b) Amount of GST = $385 - $350 |
|= $35 |
|Alternatively, to work out the 10% GST that was added, we could do these calculations: |
|385/110 x 10 = $35. |
|385 / 11 = 35 |
| |
Activity 4
1 At a ‘20% off’ sale, Susan bought a pair of slippers that normally retail for $25. What discount did she get, and how much did she have to pay for the slippers?
2 A store has a ‘45% off clearance’ sale on all electrical items. Jason bought a juicer (normal price $29) and a microwave oven (normal price $161). What was the total price he paid at the sale?
3 A used car salesman receives 2.5% commission on all the cars he sells. He sold one car for $8 500, another for $11 000, and another for $23 500. What was his total commission?
4 An art auction house retains 8% of all money gained at auction. A ‘Dobell’ was sold for $240 000. What was the commission?
5 A washing machine man came to fix my washer. The cost was $112 labour, and $28 parts. How much GST must be added?
6 A store offers a ‘20% off’ sale on all items. What is the discount on a $315 TV and a $42 picture frame?
7 At a ‘15% off’ sale, Dale bought an electric chainsaw, which normally retails for $140. What discount did he get, and how much did he have to pay for the saw?
8 A store has 12.5% off all women’s clothes. Saffron bought a top (normal price $45) and a skirt (normal price $35). What was the total price she paid?
9 Charlotte bought jeans, normally priced at $85, on sale for just $63.75. What was the percentage discount?
10 A used caravan salesman receives 5% commission on all the vans he sells. He sold one van for $12 500, and another for $14 000. What was his total commission?
11 A real estate agent charges 1.8% commission on a house sale. What is the commission on a house which sold for $650 000?
12 What GST is charged on a refrigerator priced at $800?
13 I bought items costing for $45, $67, and $11. What total GST did I pay?
Part 3: Simple Interest
There are two main types of interest:
1) Simple Interest
The investment earns the same amount of interest each period based on the original amount of principal and the rate of interest charged.
2) Compound Interest
The investment earns a different amount of interest each period based on the accumulation of principal and interest at the time the interest is calculated.
At this point we will consider simple interest only.
Calculations Involving Simple Interest
This was the favoured type of interest rate in hire purchase and / or most other unsecured loans in motor trade and white goods retailing (e.g., refrigerators, washing machines).
Why was this so? The reasons are:
• Calculations were easy to make.
• Calculations were easy to understand.
• Simple interest earned more for the lender/finance company than compound interest.
Definitions
Here are some definitions to start with:
|principal |Amount of loan or investment deposit. |
|instalments |Dollar amount to be repaid per loan period: principal (part) and interest. |
|term |Agreed period or time the borrower has to repay all of the principal and attached interest OR period of |
| |investment. |
|interest rate |Represents the risk level associated with the loan or deposit—expressed as a percentage. |
|interest |The dollar amount charged by the lender on the basis of applying an interest rate to the principal or |
| |dollar amount received from a deposit. |
| |Income to depositor/lender and an expense to borrower. |
The idea of simple interest is that interest charged or paid on the initial loan or deposit remains the same for each and every period of the loan term. The interest dollar amount remains fixed.
Investing / Depositing Money at Simple Interest
If you are investing / depositing money at simple interest, provided interest is not paid during the deposit term, simple interest calculations do not recognise that the accumulating interest should attract interest itself. Note, the financial institution (bank, finance company etc) has the use of this interest by way of on-lending until the deposit term finishes and the principal is repaid.
Borrowing Money at Simple Interest
If you are borrowing money at simple interest, there is no recognition that the loan amount reduces over the period of the loan. The borrower pays the same amount of dollar interest in the first year of the loan period as is paid in the last repayment.
Symbols
Before we start making simple interest calculations, here are some symbols that are used to construct simple interest formulae and that you will need in order to solve simple interest problems.
|P |principal |
|I |interest |
|R |interest rate |
|T |term |
|A |future value (sometimes called ‘accumulated amount’) |
|N |number of loan repayments during the term |
|L r |dollar amount of each loan repayment |
Now the formulae:
(1) Principal
[pic]
eqn01
(2) Interest
I = (P × R × T )
(3) Rate
[pic]
The interest rate R is usually given as an annual percentage rate with the time in years. The time needs to be converted to the time measurement used in the problems
E.g.. if in months then:
[pic]eq5
Or if days:
[pic]eq6
eqn02
(4) Term
[pic]
eqn03
(5) Future value or accumulated amount
Use one of the formulae below:
A = P + [ 1 + ( R × T) ]
A = P + I
A = P + (P × R × T)
(6) To calculate loan repayments
[pic]
Activity 1
1. You have a bank deposit earning simple interest @ 6% per year that has grown to $3570 after three years.
(a) Calculate the amount of the original deposit. (P)
(b) Calculate the amount of interest earned over the three years. (I)
2. Alice earns $1500 interest over five years on a deposit of $9000.
Calculate the simple interest rate that was applied (R).
3. If a $6500 deposit grows to $8700 at a simple interest rate of 4.5 % per year, what period of time has this taken? (T)
4. Investment: Deposit $5000 @ 4% per year simple interest. How much do you have at the end of five years? (A)
5. This is a loan repayment: (Lr)
|Principal: |$5000 |
|Interest rate: |4% per year simple interest |
|Term: |5 years with monthly instalments/repayments |
|Instalments: |to be calculated |
Part 4: Compound Interest
Remember: Simple Interest is always calculated on the original amount of investment and a fixed amount of interest is earned each period.
Compound Interest is calculated on the value of the investment (principal plus interest) at the time the interest is charged. If you have invested an amount of money in a fixed bank deposit the original amount of the investment will increase as the interest earned is added to it. The interest is calculated on the increased investment and is said to be compounding. The investment earns a different amount of interest each period based on the accumulation of the investment amount and interest at the time the interest is calculated.
If you are paying back a loan amount you will be reducing the principal each time you make a repayment. The interest included in each payment will be calculated on the actual principal owing at the time. The amount of interest decreases in each payment made.
Formulas for Calculations of Compound Interest
Formulas for compound interest are summarised below. Where:
|PV |= |Present Value — the original investment amount or the amount |
| | |borrowed, or the present value of future cash flows |
|i |= |interest rate |
|n |= |number of periods over which the interest rate is compounded |
|FV |= |accumulated value at the end of the period or Future Value |
|I |= |Amount of interest |
|To calculate the FUTURE VALUE or accumulated value (FV)|[pic]eq9 |
N.B. The compound interest tables are based on the accumulation factor
[pic]
eq10
|To calculate the amount of interest earned or paid |[pic]eq11 |
|(I) | |
| |[pic]eq12 |
|Then: |[pic]eq13 |
|To calculate Present Value (PV) |[pic][pic]eq14 |
|To calculate the interest rate (i) |[pic]eq15 |
|Multiply both sides by 1/neqn14 |[pic]eq16 |
Example 1
You deposit $5000 at the beginning of Year 1 earning compound interest of 4% per year with a term of five years. How do we calculate the future amount?
We will set up a table to show how compound interest works.
Table 1: How compound interest works
|Year |Opening balance |Interest earned @ 4% |Closing balance |
|1 |5000.00 |200.00 |5200.00 |
|2 |5200.00 |208.00 |5408.00 |
|3 |5408.00 |216.32 |5624.32 |
|4 |5624.32 |224.97 |5849.29 |
|5 |5849.29 |233.97 |6083.26 |
The table is using the same data from Activity xx (4). Using simple interest the answer is a closing balance of $6000; and using the compound interest formula, the result will be a further $83.26 earned. This may not seem a large advantage, but on millions of dollars over long terms the benefit to depositors can be enormous.
Superannuation has this advantage, particularly for those who are able to contribute to a super fund from an early age. Imagine the benefit of leaving your contributions in a fund for thirty five years (from 25 years of age to 60 years).While annuities also play a major role, it is the compound interest concept that has the multiplier effect. It’s like a snowball gathering more snow as it rolls down a hill.
Compound interest is all about earning interest on your interest.
We are assisted by three procedures to make compound interest calculations quicker than using a table like the one above.
Future Value
Procedure 1: using a formula
This involves using a formula to calculate the Future Value (FV) of a single or lump sum.
FV = PV ( 1 + i ) ⁿ
Where:
|FV |= |Future value |
|PV |= |Present value |
|i |= |Interest rate |
|n |= |number of compounding periods raised to a power |
Example 2
We will use the data from the table in Example 1 so that you can compare the time taken to arrive at the same result.
FVIF
FV = 5000 (1 + .04 )ⁿ 5 = 5000 × 1.2167 = $6083.26
How did we calculate 1.2167? Future value interest factor (FVIF).
Using the Sharp EL-735, the entries are:
|Enter |1 + 0.04 |
|" |2nd F |
|" |[CST] Yⁿ |
|" |5 |
|" |= 1.2167 |
Procedure 2: using tables
Tables have been constructed that produce future value interest factors (FVIF).
You will see it is headed up ‘Future Value of $1 at the End of n Periods FVIF = ( 1 + k )ⁿ’ or something similar.
The table’s vertical column is headed up ‘Period’.
Then spread across the table you will see %.
To find 1.2167, look down the Period column until you find 5. Then look across the top of the table until you see 4%. Where the row meets the column is 1.2167.
Tables have been supplied with this Workbook. Your teacher can give these to you or alternatively go to the following website:
So, if you know the interest rate and the number of compounding periods (the term), you can find the FVIF.
Procedure 3: using financial calculator
Using the Sharp calculator EL – 735:
|Enter |5000 |
|" |PV |
|" |4 |
|" |i |
|" |5 |
|" |n |
|" |comp |
|" |FV $6,083.26 |
Note: You will not need to purchase a financial calculator for this subject. Knowing how to use tables and ordinary calculator will suffice.
Present Value
The next step is to calculate the present value (PV) of a future lump sum (time value of money in action).
Procedure 1: using a formula
We can do this in two ways and get the same result.
Method 1
[pic]
Calculate the present value of a deposit that has grown to $9000 in four years, earning compound interest of 6% per year.
[pic]
Below is another way of calculating it.
Method 2
[pic]
eqn11
Procedure 2: using tables
Under the heading “Present Value of $1: PVIF” (or similar named table), look down the period column till you find 4 — and then across the page till you find 6%.
Where the row meets the column you find .7921 present value interest Factor (PVIF).
Procedure 3: using financial calculator
| | |
|Enter |9000 |
|" |FV |
|" |6 |
|" |i |
|" |4 |
|" |n |
|" |comp |
|" |PV |
| |$7128.84 |
Note: You will find minor differences in PV results when using the tables as compared to the Sharp calculator ($7,128.71 tables compared to $7,128.84 calculator). This happens because the tables are to four decimal places and the calculator has 10 decimal places.
Activity 1
1. You deposit $3,000 at the beginning of Year 1 earning compound interest of 3% per year with a term of 2 years. What is the future value?
2. You have inherited $12,000 and have decided to invest it in a term deposit for 5 years at an interest rate of 10%. How much will you have on maturity?
3. You hope to have $40,000 in 2 years time for a car. The current interest rate is 8%. How much do you need to invest today?
4. You are saving for a house and need a $150,000 deposit in 3 years time. The current interest rate is 3%. How much do you need to put into your bank account today?
Part 5: Income Tax
Income tax is a tax on the earnings of all income earners. It is deducted from the wages and salaries of workers throughout the year and is paid to the Federal Government. State governments receive a proportion of this personal income tax to fund spending on education, health services, and so on. The Australian Taxation Office (ATO) is the official tax-collecting agency of the Federal Government.
Activity 1
Go to the NSW State Government website: and research the ways in which the State Government spends taxes. List 5 areas below.
1. ___________________________________________________
2. ___________________________________________________
3. ___________________________________________________
4. ___________________________________________________
5. ___________________________________________________
Most wage and salary earners have PAYG tax (Pay As You Go tax) deducted from their pay according to a prescribed rate and the employer forwards this to the government. At the end of the financial year (June 30) all income earners are expected to fill out a tax return and lodge it with the Australian Taxation Office (ATO). Each employer sends a payment summary to the employee showing the employees earnings for the year and the amount of tax deducted by the employer
The purpose of the tax return is to make sure that the employee has paid the correct amount of tax. If an employee has paid more tax during the year than the ATO assesses, he or she will receive a refund. If less tax has been paid, he or she will be required to pay the difference.
The income on which tax is calculated is called the taxable income.
Some expenses are allowed as deductions. In general, a tax deduction is allowed for a necessary expense incurred by the taxpayer in the course of earning their income. For example, someone setting up a lawn-mowing business could claim a tax deduction for the cost of a lawn-mower and other gardening implements, and a vehicle. These allowable deductions are specified by the ATO for different jobs.
Taxable income = Gross income - Deductions
The amount of tax to be paid depends on how much is earned, with lower paid workers paying a smaller percentage of their gross earnings in tax. All tax calculations are based on annual income
The ATO provides a table from which the amount of tax that should be paid per year can be calculated. This is in a booklet called the Tax Pack, which contains instructions on how to complete a tax return. Alternatively, all this information can be found on the ATO website (.au).
Calculating Tax Payments
Income is taxed progressively: low-income earners pay a smaller percentage of their earnings than high-income earners. The ATO provides a table that gives the marginal rates of tax. The marginal rate is the percentage rate of tax to be paid on that part of the income that falls within a particular bracket. These are shown below for the financial year 2010/2011:
|Taxable income |Tax on this income |
|0 – $6,000 |Nil |
|$6,001 – $37,000 |15c for each $1 over $6,000 |
|$37,001 – $80,000 |$4,650 plus 30c for each $1 over $37,000 |
|$80,001 – $180,000 |$17,550 plus 37c for each $1 over $80,000 |
|$180,001 and over |$54,550 plus 45c for each $1 over $180,000 |
Suppose Helen has a taxable income of $100,000. The amount of tax payable could be calculated as follows.
$100,000 falls within the 80,001 – 180,000 tax bracket
Tax payable = 17,550 + 0.37 x (100,000 - 80,000)
= 17,550 + 0.37 x 20,000
= 17,550 + 7,400
= 24,950
| Example 1 |
|Using the income tax table for the 2010/2011 financial year calculate the tax payable on taxable incomes of: |
|(a) $17 000 (b) $5,500 |
|Solutions |
|(a) $17,000 is in the $6,001 - $37,000 tax bracket. |
|Tax payable = 0.15 x (17,000 - 6,000) |
|= 0.15 x 11,000 |
|= 1,650 |
| |
|(b) $5,500 is in the $0 - $6,000 tax bracket. |
|Tax payable = NIL |
|Example 2 |
|Last year Michelle’s gross income was $29,960. Her allowable deductions were $860. |
|(a) Find her taxable income |
|(b) Calculate the amount of tax due. |
|(c) Michelle’s employer deducted $205 each week in tax. How much will her refund be? |
|Solution |
|(a) Taxable income = Gross income - Allowable deductions |
|= $29,960 - $860 |
|= $29,100 |
|(b) Tax on $29 100 = 0.15 x (29,100 - 6,000) |
|= 0.15 x 23,100 |
|= 3,465 |
|(c) Tax already paid = 52 weeks x $205 = $10,660 |
|[pic]Refund = $10,660 – $3,465 |
|= $7,195 |
| |
Activity 2
Using the income tax tables for the financial year 2010/2011 calculate the tax payable on incomes of:
a) 32,900
b) 190,000
c) 26,000
Activity 3
Using the income tax tables for the financial year 2009/2010 calculate the tax payable on incomes of: (You will need to go to the following link on the ATO website for the 2009/2010 tax tables: ).
a) 15,500
b) 175,100
c) 6,100
PAYG Withholding Tax Tables
The Australian Taxation Office (ATO) publishes the PAYG withholding tax tables on its website (.au).
Go to the link to view the tax tables. Bookmark this website for future reference.
As you can see tax tables are prepared for different pay periods as well as different types of income earners. For example, you might have a weekly paid employee with 2 dependants who requires a Medicare levy adjustment. In this case you would use the tax table Medicare Levy Adjustment Weekly Tax Table (NAT1010).
It’s entertaining to see that there is a separate tax table for Actors, Variety Artists and Other Entertainers (NAT1023). Why do you think that would be so?
Activity 4
Go to the website and download the fortnightly tax table for regular payments (NAT1006).
a) How much tax would an employee pay who earns $496 per fortnight & no tax free threshold?
___________________________________________________________________
b) How much tax would an employee pay who earns $224 per fortnight & has a tax free threshold with leave loading?
___________________________________________________________________
c) How much tax would an employee pay who earns $980 per fortnight & has a tax free threshold with no leave loading?
___________________________________________________________________
Activity 5
Go to the website and download the weekly tax table for regular payments (NAT1005).
a) I am an employee with a tax free threshold. What is the maximum amount I can earn per week before I begin to pay tax?
___________________________________________________________________
b) I am an employee with no tax free threshold. What is the maximum amount I can earn per week before I begin to pay tax?
___________________________________________________________________
Part 6: Business Calculators, Software and Programs
Calculators and computers have taken away much of the need for manual and mental calculation. Whilst most of the activities you have done in this workbook have been manual there are more efficient ways of doing things. The introduction of technology and computer software has made complex calculations appear much simpler & faster. However, even though calculators & computers can “crunch the numbers” it is still important for you to be able to understand what the numbers mean.
Hand Held Calculators
Calculators perform many of the basic mathematical tasks that have been applied in this workbook. Calculators add, subtract, divide, multiply etc. Even a simple calculator can perform other functions such as calculating percentages, tax rates and even keep numbers in memory for future use.
You will need to have a basic inexpensive calculator for your course.
Financial calculators such as the popular Sharp EL735 perform more complex calculations such as calculating compound interest; annuities; amortising a loan; discounted cash flows. Refer to the calculator’s user manual on how to perform these calculations. You may be required to purchase a financial calculator later on in your course.
Statistical calculators will perform calculations such as measures of central tendency (mean) & measures of dispersion (standard deviation). Portfolio theory and correlation & regression are also additional examples of the types of calculations that can be performed by a scientific calculator.
Computers
Computers have made many time consuming tasks fast, accurate & timely. All sorts of programs are available to perform all sorts of calculations. For example, commercial financial software can be purchased to analyse shares & markets. Statistical packages such as SPSS make analysing statistics (almost) a breeze!
Spreadsheets
Spreadsheets such as Microsoft Excel take out the tedious nature of manual calculations which gives the developer more time to spend on analysing & interpreting the results.
On-Line Special Purpose Calculators
On-line special purpose calculators have been developed by organisations to assist their customers in making financial decisions.
For example, the Commonwealth Bank has developed a number of calculators and tools for their customers.
Go to the website to view the calculators & tools that they have developed. They cover everything from foreign exchange; personal loans; home loans; insurance & investments.
Activity 1
Give three advantages in using calculators, spreadsheets or other software for performing business calculations.
1. ________________________________________________________________
2. ________________________________________________________________
3. ________________________________________________________________
Give three disadvantages in using calculators, spreadsheets or other software for performing business calculations.
1. ________________________________________________________________
2. ________________________________________________________________
3. ________________________________________________________________
Activity 2
Go to the Commonwealth Bank website .
Click on the “How Much Can I Borrow” calculator. Enter the details required.
How much were you able to borrow based on your information?
________________________________________________________________
________________________________________________________________
________________________________________________________________
Activity 3
Go to the Commonwealth Bank website .
Click on the “Risk Profile” calculator. Enter the details required.
What is your risk profile?
________________________________________________________________
________________________________________________________________
________________________________________________________________
Part 7: Common Computational Errors
To err is human! We all make mistakes. Errors in business calculations can have dire consequences if they are not picked up. For example, if there is an error in a breakeven calculation a company may be making business decisions on incorrect information.
Most errors can be picked up if we have a “gut feel” for what the answer should be or if the information makes sense. This is one reason why it is so important to have an understanding of what the numbers mean. Once numbers have been calculated it is important to analyse and interpret their business meaning. If it does not make sense then one of the many things that can be looked at is if there were any errors in calculations.
Let’s have a look at some common computational errors.
Input / Transcription Errors
Incorrect amounts may have been keyed into a computer program or spreadsheet. For example, the hours worked for an employee should have been entered as 40 but were accidently entered as 4. What do you think would be the consequence of this?
In a transcription error I have reversed the numbers. A general journal to write off an advertising expense was entered as $19 instead of $91. What do you think would be the consequence of this error? Has the net profit ultimately been overstated or understated?
Wrong Spreadsheet Function or Formula
Incorrect formulas, functions or cell referencing etc. will all result in errors. For example, you may have a spreadsheet that you have prepared that shows your budgeted production over the next 12 months. If any of the formulas or cell referencing is incorrect you will be making business decisions on incorrect information.
Incorrect Methodology
Using an incorrect method will also result in errors. Accidently using present value instead of future value would affect the viability of a business decision.
Other Mathematical Errors
Other mathematical errors include:
1. Wrong computational sign – for example, should have added not subtracted
2. Incorrect order of operations – amounts in brackets are calculated first;
3. Incorrect positioning of decimal points and brackets in equations – for example amount should have been 20.1 not 2.01.
Activity 1
1. Are the following correct (C) or not correct (NC)?
a. 40 + 5 – 13 = 14 C or NC
b. 10 x (12 – 2) = 118 C or NC
c. 10 x (12 – 2) = 100 C or NC
d. 2/5 = 0.04 C or NC
e. 4/8 = 0.50 C or NC
Activity 2
What three things could you do to help prevent errors in business calculations?
1. ______________________________________________________________________________________________________________________________________
2. ______________________________________________________________________________________________________________________________________
3. ______________________________________________________________________________________________________________________________________
Present Value and Future Value Tables
Table A-1 Future Value Interest Factors for One Dollar Compounded at k Percent for n Periods: FVIF k,n = (1 + k)
Period |1% |2% |3% |4% |5% |6% |7% |8% |9% |10% |11% |12% |13% |14% |15% |16% |20% |24% |25% |30% | |1 |1.0100 |1.0200 |1.0300 |1.0400 |1.0500 |1.0600 |1.0700 |1.0800 |1.0900 |1.1000 |1.1100 |1.1200 |1.1300 |1.1400 |1.1500 |1.1600 |1.2000 |1.2400 |1.2500 |1.3000 | |2 |1.0201 |1.0404 |1.0609 |1.0816 |1.1025 |1.1236 |1.1449 |1.1664 |1.1881 |1.2100 |1.2321 |1.2544 |1.2769 |1.2996 |1.3225 |1.3456 |1.4400 |1.5376 |1.5625 |1.6900 | |3 |1.0303 |1.0612 |1.0927 |1.1249 |1.1576 |1.1910 |1.2250 |1.2597 |1.2950 |1.3310 |1.3676 |1.4049 |1.4429 |1.4815 |1.5209 |1.5609 |1.7280 |1.9066 |1.9531 |2.1970 | |4 |1.0406 |1.0824 |1.1255 |1.1699 |1.2155 |1.2625 |1.3108 |1.3605 |1.4116 |1.4641 |1.5181 |1.5735 |1.6305 |1.6890 |1.7490 |1.8106 |2.0736 |2.3642 |2.4414 |2.8561 | |5 |1.0510 |1.1041 |1.1593 |1.2167 |1.2763 |1.3382 |1.4026 |1.4693 |1.5386 |1.6105 |1.6851 |1.7623 |1.8424 |1.9254 |2.0114 |2.1003 |2.4883 |2.9316 |3.0518 |3.7129 | | | | | | | | | | | | | | | | | | | | | | | |6 |1.0615 |1.1262 |1.1941 |1.2653 |1.3401 |1.4185 |1.5007 |1.5869 |1.6771 |1.7716 |1.8704 |1.9738 |2.0820 |2.1950 |2.3131 |2.4364 |2.9860 |3.6352 |3.8147 |4.8268 | |7 |1.0721 |1.1487 |1.2299 |1.3159 |1.4071 |1.5036 |1.6058 |1.7138 |1.8280 |1.9487 |2.0762 |2.2107 |2.3526 |2.5023 |2.6600 |2.8262 |3.5832 |4.5077 |4.7684 |6.2749 | |8 |1.0829 |1.1717 |1.2668 |1.3686 |1.4775 |1.5938 |1.7182 |1.8509 |1.9926 |2.1436 |2.3045 |2.4760 |2.6584 |2.8526 |3.0590 |3.2784 |4.2998 |5.5895 |5.9605 |8.1573 | |9 |1.0937 |1.1951 |1.3048 |1.4233 |1.5513 |1.6895 |1.8385 |1.9990 |2.1719 |2.3579 |2.5580 |2.7731 |3.0040 |3.2519 |3.5179 |3.8030 |5.1598 |6.9310 |7.4506 |10.604 | |10 |1.1046 |1.2190 |1.3439 |1.4802 |1.6289 |1.7908 |1.9672 |2.1589 |2.3674 |2.5937 |2.8394 |3.1058 |3.3946 |3.7072 |4.0456 |4.4114 |6.1917 |8.5944 |9.3132 |13.786 | | | | | | | | | | | | | | | | | | | | | | | |11 |1.1157 |1.2434 |1.3842 |1.5395 |1.7103 |1.8983 |2.1049 |2.3316 |2.5804 |2.8531 |3.1518 |3.4785 |3.8359 |4.2262 |4.6524 |5.1173 |7.4301 |10.657 |11.642 |17.922 | |12 |1.1268 |1.2682 |1.4258 |1.6010 |1.7959 |2.0122 |2.2522 |2.5182 |2.8127 |3.1384 |3.4985 |3.8960 |4.3345 |4.8179 |5.3503 |5.9360 |8.9161 |13.215 |14.552 |23.298 | |13 |1.1381 |1.2936 |1.4685 |1.6651 |1.8856 |2.1329 |2.4098 |2.7196 |3.0658 |3.4523 |3.8833 |4.3635 |4.8980 |5.4924 |6.1528 |6.8858 |10.699 |16.386 |18.190 |30.288 | |14 |1.1495 |1.3195 |1.5126 |1.7317 |1.9799 |2.2609 |2.5785 |2.9372 |3.3417 |3.7975 |4.3104 |4.8871 |5.5348 |6.2613 |7.0757 |7.9875 |12.839 |20.319 |22.737 |39.374 | |15 |1.1610 |1.3459 |1.5580 |1.8009 |2.0789 |2.3966 |2.7590 |3.1722 |3.6425 |4.1772 |4.7846 |5.4736 |6.2543 |7.1379 |8.1371 |9.2655 |15.407 |25.196 |28.422 |51.186 | | | | | | | | | | | | | | | | | | | | | | | |16 |1.1726 |1.3728 |1.6047 |1.8730 |2.1829 |2.5404 |2.9522 |3.4259 |3.9703 |4.5950 |5.3109 |6.1304 |7.0673 |8.1372 |9.3576 |10.748 |18.488 |31.243 |35.527 |66.542 | |17 |1.1843 |1.4002 |1.6528 |1.9479 |2.2920 |2.6928 |3.1588 |3.7000 |4.3276 |5.0545 |5.8951 |6.8660 |7.9861 |9.2765 |10.761 |12.468 |22.186 |38.741 |44.409 |86.504 | |18 |1.1961 |1.4282 |1.7024 |2.0258 |2.4066 |2.8543 |3.3799 |3.9960 |4.7171 |5.5599 |6.5436 |7.6900 |9.0243 |10.575 |12.375 |14.463 |26.623 |48.039 |55.511 |112.455 | |19 |1.2081 |1.4568 |1.7535 |2.1068 |2.5270 |3.0256 |3.6165 |4.3157 |5.1417 |6.1159 |7.2633 |8.6128 |10.197 |12.056 |14.232 |16.777 |31.948 |59.568 |69.389 |146.192 | |20 |1.2202 |1.4859 |1.8061 |2.1911 |2.6533 |3.2071 |3.8697 |4.6610 |5.6044 |6.7275 |8.0623 |9.6463 |11.523 |13.743 |16.367 |19.461 |38.338 |73.864 |86.736 |190.050 | | | | | | | | | | | | | | | | | | | | | | | |21 |1.2324 |1.5157 |1.8603 |2.2788 |2.7860 |3.3996 |4.1406 |5.0338 |6.1088 |7.4002 |8.9492 |10.804 |13.021 |15.668 |18.822 |22.574 |46.005 |91.592 |108.420 |247.065 | |22 |1.2447 |1.5460 |1.9161 |2.3699 |2.9253 |3.6035 |4.4304 |5.4365 |6.6586 |8.1403 |9.9336 |12.100 |14.714 |17.861 |21.645 |26.186 |55.206 |113.574 |135.525 |321.184 | |23 |1.2572 |1.5769 |1.9736 |2.4647 |3.0715 |3.8197 |4.7405 |5.8715 |7.2579 |8.9543 |11.026 |13.552 |16.627 |20.362 |24.891 |30.376 |66.247 |140.831 |169.407 |417.539 | |24 |1.2697 |1.6084 |2.0328 |2.5633 |3.2251 |4.0489 |5.0724 |6.3412 |7.9111 |9.8497 |12.239 |15.179 |18.788 |23.212 |28.625 |35.236 |79.497 |174.631 |211.758 |542.801 | |25 |1.2824 |1.6406 |2.0938 |2.6658 |3.3864 |4.2919 |5.4274 |6.8485 |8.6231 |10.835 |13.585 |17.000 |21.231 |26.462 |32.919 |40.874 |95.396 |216.542 |264.698 |705.641 | | | | | | | | | | | | | | | | | | | | | | | |30 |1.3478 |1.8114 |2.4273 |3.2434 |4.3219 |5.7435 |7.6123 |10.063 |13.268 |17.449 |22.892 |29.960 |39.116 |50.950 |66.212 |85.850 |237.376 |634.820 |807.794 |* | |35 |1.4166 |1.9999 |2.8139 |3.9461 |5.5160 |7.6861 |10.677 |14.785 |20.414 |28.102 |38.575 |52.800 |72.069 |98.100 |133.176 |180.314 |590.668 |* |* |* | |36 |1.4308 |2.0399 |2.8983 |4.1039 |5.7918 |8.1473 |11.424 |15.968 |22.251 |30.913 |42.818 |59.136 |81.437 |111.834 |153.152 |209.164 |708.802 |* |* |* | |40 |1.4889 |2.2080 |3.2620 |4.8010 |7.0400 |10.286 |14.974 |21.725 |31.409 |45.259 |65.001 |93.051 |132.782 |188.884 |267.864 |378.721 |* |* |* |* | |50 |1.6446 |2.6916 |4.3839 |7.1067 |11.467 |18.420 |29.457 |46.902 |74.358 |117.391 |184.565 |289.002 |450.736 |700.233 |* |* |* |* |* |* | |
Table A-2 Present Value Interest Factors for One Dollar Discounted at k Percent for n Periods: PVIF k,n = 1 / (1 + k)
Period |1% |2% |3% |4% |5% |6% |7% |8% |9% |10% |11% |12% |13% |14% |15% |16% |20% |24% |25% |30% | |1 |0.9901 |0.9804 |0.9709 |0.9615 |0.9524 |0.9434 |0.9346 |0.9259 |0.9174 |0.9091 |0.9009 |0.8929 |0.8850 |0.8772 |0.8696 |0.8621 |0.8333 |0.8065 |0.8000 |0.7692 | |2 |0.9803 |0.9612 |0.9426 |0.9246 |0.9070 |0.8900 |0.8734 |0.8573 |0.8417 |0.8264 |0.8116 |0.7972 |0.7831 |0.7695 |0.7561 |0.7432 |0.6944 |0.6504 |0.6400 |0.5917 | |3 |0.9706 |0.9423 |0.9151 |0.8890 |0.8638 |0.8396 |0.8163 |0.7938 |0.7722 |0.7513 |0.7312 |0.7118 |0.6931 |0.6750 |0.6575 |0.6407 |0.5787 |0.5245 |0.5120 |0.4552 | |4 |0.9610 |0.9238 |0.8885 |0.8548 |0.8227 |0.7921 |0.7629 |0.7350 |0.7084 |0.6830 |0.6587 |0.6355 |0.6133 |0.5921 |0.5718 |0.5523 |0.4823 |0.4230 |0.4096 |0.3501 | |5 |0.9515 |0.9057 |0.8626 |0.8219 |0.7835 |0.7473 |0.7130 |0.6806 |0.6499 |0.6209 |0.5935 |0.5674 |0.5428 |0.5194 |0.4972 |0.4761 |0.4019 |0.3411 |0.3277 |0.2693 | | | | | | | | | | | | | | | | | | | | | | | |6 |0.9420 |0.8880 |0.8375 |0.7903 |0.7462 |0.7050 |0.6663 |0.6302 |0.5963 |0.5645 |0.5346 |0.5066 |0.4803 |0.4556 |0.4323 |0.4104 |0.3349 |0.2751 |0.2621 |0.2072 | |7 |0.9327 |0.8706 |0.8131 |0.7599 |0.7107 |0.6651 |0.6227 |0.5835 |0.5470 |0.5132 |0.4817 |0.4523 |0.4251 |0.3996 |0.3759 |0.3538 |0.2791 |0.2218 |0.2097 |0.1594 | |8 |0.9235 |0.8535 |0.7894 |0.7307 |0.6768 |0.6274 |0.5820 |0.5403 |0.5019 |0.4665 |0.4339 |0.4039 |0.3762 |0.3506 |0.3269 |0.3050 |0.2326 |0.1789 |0.1678 |0.1226 | |9 |0.9143 |0.8368 |0.7664 |0.7026 |0.6446 |0.5919 |0.5439 |0.5002 |0.4604 |0.4241 |0.3909 |0.3606 |0.3329 |0.3075 |0.2843 |0.2630 |0.1938 |0.1443 |0.1342 |0.0943 | |10 |0.9053 |0.8203 |0.7441 |0.6756 |0.6139 |0.5584 |0.5083 |0.4632 |0.4224 |0.3855 |0.3522 |0.3220 |0.2946 |0.2697 |0.2472 |0.2267 |0.1615 |0.1164 |0.1074 |0.0725 | | | | | | | | | | | | | | | | | | | | | | | |11 |0.8963 |0.8043 |0.7224 |0.6496 |0.5847 |0.5268 |0.4751 |0.4289 |0.3875 |0.3505 |0.3173 |0.2875 |0.2607 |0.2366 |0.2149 |0.1954 |0.1346 |0.0938 |0.0859 |0.0558 | |12 |0.8874 |0.7885 |0.7014 |0.6246 |0.5568 |0.4970 |0.4440 |0.3971 |0.3555 |0.3186 |0.2858 |0.2567 |0.2307 |0.2076 |0.1869 |0.1685 |0.1122 |0.0757 |0.0687 |0.0429 | |13 |0.8787 |0.7730 |0.6810 |0.6006 |0.5303 |0.4688 |0.4150 |0.3677 |0.3262 |0.2897 |0.2575 |0.2292 |0.2042 |0.1821 |0.1625 |0.1452 |0.0935 |0.0610 |0.0550 |0.0330 | |14 |0.8700 |0.7579 |0.6611 |0.5775 |0.5051 |0.4423 |0.3878 |0.3405 |0.2992 |0.2633 |0.2320 |0.2046 |0.1807 |0.1597 |0.1413 |0.1252 |0.0779 |0.0492 |0.0440 |0.0254 | |15 |0.8613 |0.7430 |0.6419 |0.5553 |0.4810 |0.4173 |0.3624 |0.3152 |0.2745 |0.2394 |0.2090 |0.1827 |0.1599 |0.1401 |0.1229 |0.1079 |0.0649 |0.0397 |0.0352 |0.0195 | | | | | | | | | | | | | | | | | | | | | | | |16 |0.8528 |0.7284 |0.6232 |0.5339 |0.4581 |0.3936 |0.3387 |0.2919 |0.2519 |0.2176 |0.1883 |0.1631 |0.1415 |0.1229 |0.1069 |0.0930 |0.0541 |0.0320 |0.0281 |0.0150 | |17 |0.8444 |0.7142 |0.6050 |0.5134 |0.4363 |0.3714 |0.3166 |0.2703 |0.2311 |0.1978 |0.1696 |0.1456 |0.1252 |0.1078 |0.0929 |0.0802 |0.0451 |0.0258 |0.0225 |0.0116 | |18 |0.8360 |0.7002 |0.5874 |0.4936 |0.4155 |0.3503 |0.2959 |0.2502 |0.2120 |0.1799 |0.1528 |0.1300 |0.1108 |0.0946 |0.0808 |0.0691 |0.0376 |0.0208 |0.0180 |0.0089 | |19 |0.8277 |0.6864 |0.5703 |0.4746 |0.3957 |0.3305 |0.2765 |0.2317 |0.1945 |0.1635 |0.1377 |0.1161 |0.0981 |0.0829 |0.0703 |0.0596 |0.0313 |0.0168 |0.0144 |0.0068 | |20 |0.8195 |0.6730 |0.5537 |0.4564 |0.3769 |0.3118 |0.2584 |0.2145 |0.1784 |0.1486 |0.1240 |0.1037 |0.0868 |0.0728 |0.0611 |0.0514 |0.0261 |0.0135 |0.0115 |0.0053 | | | | | | | | | | | | | | | | | | | | | | | |21 |0.8114 |0.6598 |0.5375 |0.4388 |0.3589 |0.2942 |0.2415 |0.1987 |0.1637 |0.1351 |0.1117 |0.0926 |0.0768 |0.0638 |0.0531 |0.0443 |0.0217 |0.0109 |0.0092 |0.0040 | |22 |0.8034 |0.6468 |0.5219 |0.4220 |0.3418 |0.2775 |0.2257 |0.1839 |0.1502 |0.1228 |0.1007 |0.0826 |0.0680 |0.0560 |0.0462 |0.0382 |0.0181 |0.0088 |0.0074 |0.0031 | |23 |0.7954 |0.6342 |0.5067 |0.4057 |0.3256 |0.2618 |0.2109 |0.1703 |0.1378 |0.1117 |0.0907 |0.0738 |0.0601 |0.0491 |0.0402 |0.0329 |0.0151 |0.0071 |0.0059 |0.0024 | |24 |0.7876 |0.6217 |0.4919 |0.3901 |0.3101 |0.2470 |0.1971 |0.1577 |0.1264 |0.1015 |0.0817 |0.0659 |0.0532 |0.0431 |0.0349 |0.0284 |0.0126 |0.0057 |0.0047 |0.0018 | |25 |0.7798 |0.6095 |0.4776 |0.3751 |0.2953 |0.2330 |0.1842 |0.1460 |0.1160 |0.0923 |0.0736 |0.0588 |0.0471 |0.0378 |0.0304 |0.0245 |0.0105 |0.0046 |0.0038 |0.0014 | | | | | | | | | | | | | | | | | | | | | | | |30 |0.7419 |0.5521 |0.4120 |0.3083 |0.2314 |0.1741 |0.1314 |0.0994 |0.0754 |0.0573 |0.0437 |0.0334 |0.0256 |0.0196 |0.0151 |0.0116 |0.0042 |0.0016 |0.0012 |* | |35 |0.7059 |0.5000 |0.3554 |0.2534 |0.1813 |0.1301 |0.0937 |0.0676 |0.0490 |0.0356 |0.0259 |0.0189 |0.0139 |0.0102 |0.0075 |0.0055 |0.0017 |0.0005 |* |* | |36 |0.6989 |0.4902 |0.3450 |0.2437 |0.1727 |0.1227 |0.0875 |0.0626 |0.0449 |0.0323 |0.0234 |0.0169 |0.0123 |0.0089 |0.0065 |0.0048 |0.0014 |* |* |* | |40 |0.6717 |0.4529 |0.3066 |0.2083 |0.1420 |0.0972 |0.0668 |0.0460 |0.0318 |0.0221 |0.0154 |0.0107 |0.0075 |0.0053 |0.0037 |0.0026 |0.0007 |* |* |* | |50 |0.6080 |0.3715 |0.2281 |0.1407 |0.0872 |0.0543 |0.0339 |0.0213 |0.0134 |0.0085 |0.0054 |0.0035 |0.0022 |0.0014 |0.0009 |0.0006 |* |* |* |* | |[pic][pic][pic][pic][pic][pic]
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