Select methods for financial calculations

When performing calculations to complete different work requirements, a range of techniques can be used. These include:

• Multiplication
• Division
• Addition
• Subtraction
• Percentages
• Fractions
• Decimals
• Straight-line graphs

The process of multiplying a number by another number is called Multiplication. Multiplication is often referred to as ‘times’ (or repeated addition). The symbol used for Multiplication is '×'. The asterisk on your keyboard * is also used. When we multiply two numbers, the answer we get is called a ‘product’.

7 x 2 = 14

This is read as seven times two is equal to fourteen or simply, seven times two is fourteen. To multiply a large number with another number, we write the numbers vertically and multiply the larger number with the smaller number.¹⁰

Note: A product is the result of the Multiplication of two (or more) numbers.

\[ \begin{array}{@{}cr} & 765 \\ × & 9 \\ \hline & 8665 \end{array} \]

Write the smaller number, 9, under the larger number, 765, and then calculate the Multiplication. The answer is 6885.

Note: 9 × 5 = 45.

Step 1: So, place 5 units in the units column and carry the 4 (i.e. four tens) to the tens column.

Step 2: Calculate 9 × 6 and then add 4 to give 58 (i.e. 58 tens).

Step 3: Then place 8 in the tens column and carry 5 to the hundreds column.

Step 4: Finally, multiply 7 x 9 and add 5 to give 68 (i.e. 68 hundreds). Write this number down as shown above.

We use the 'times table' to find the product of the larger number with each digit in the multiplier, adding the results.

Add a zero for every place value after the multiplying digit. For example, if the multiplying digit is in the hundreds column, add two zero’s for the tens column and the units column.

For more examples on how to complete multiplication and long multiplication equations, please click here. 

Let’s test your knowledge of multiplication

You may use your calculator for this.

A bit of nostalgia, find below a times table chart to help refresh your memory of previous methods used.

Multiplying numbers in Excel

Microsoft Excel is a software program included in the Microsoft Office suite. It is used to create spreadsheets, which are documents in which data is laid out in rows and columns like a big table.

Accountants and bookkeepers use spreadsheets to carry out complex calculations quickly through the use of cell functions. Watch the video below to find out how Multiplication works in Excel.

Our next arithmetic operation, which is the complete opposite of Multiplication, is division.

Division is the action of separating something into parts or the process of being separated. It is breaking a number up into an equal number of parts.

If you take 25 things and put them into five equal-sized groups, there will be 5 things in each group. The answer is 5.

There are some signs that people may use to indicate division. The most common one is ÷, but the backslash / is also used. Sometimes people will write one number on top of another with a line between them. This is also called a fraction. ¹³

Let’s take this one step further. Division can also be expressed differently, For example, signs for "a divided by b":

a ÷ b
a/b
 

Each part of a division equation has a name. The three primary names are the dividend, the divisor, and the quotient:

• Dividend: The dividend is the number you are dividing up
• Divisor: The divisor is the number you are dividing by
• Quotient: the quotient is the answer

Example: 20 ÷ 4 = 5
Dividend = 20
Divisor = 4
Quotient = 5

Let’s test our knowledge with some division

You may use your calculator for this.

Watch the video below to find out how division works in Excel.

The process of calculating the total of two or more numbers or amounts is addition (often signified by the plus symbol "+"). The addition of two whole numbers is the total amount of those quantities combined.

The addition is finding the total, or sum, by combining two or more numbers.

Example: 8 + 3 = 11

There are four mathematical properties that involve addition. The properties are the commutative, associative, additive identity and distributive properties.

• Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4
• Associative property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2 + 3) + 4 = 2 + (3 + 4)
• Additive identity property: The sum of any number and zero is the original number. For example 5 + 0 = 5.
• Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For this, you need to use the rule of BODMAS meaning you need to complete the algorithm in the brackets before completing the equation outside of the brackets. For example 4 x (6 + 3) = 4 x 6 + 4 x 3 or using BODMAS 4x9.

For more information about Distributive property, check out this link. 

Watch the video below to find out how addition works in Excel.

Subtraction is a mathematical operation of removing objects from a collection. It is signified by the minus sign (−). For example, there are 5 balls, remove 2 balls, only 3 balls are left. Therefore, 5 − 2 = 3. Subtraction can also signify combining other physical and abstract quantities using different objects, including negative numbers, fractions, irrational numbers, vectors, decimals, functions, and matrices.

Subtraction is the opposite of addition. In mathematics, subtraction means taking something away from a group or number of things. When you subtract, what is left in the group becomes less.

There are three parts to a subtraction problem.

• The part you start with is called the minuend.
• The part being taken away is called the subtrahend.
• The part that is left after subtraction is known as the difference.

In the problem 5 - 2 = 3

the number '5' is the minuend, the number '2' is the subtrahend, and the number '3' is the difference.

Addition and subtraction are closely linked. Although addition is the opposite of subtraction, it is also true that every addition problem can be rewritten as a subtraction problem.

In addition, you probably learned something like the following: if 3 + 2 = 5, then 2 + 3 = 5. In other words, you can change the order of the numbers you add and get the same answer. This cannot be done in subtraction. For example, 5 - 3 and 3 - 5 do not equal the same value.

One subtraction method is to use a diagram showing what you start with, what you are taking away and what you are left with.

When subtracting numbers with two or more digits, it is important to write the numbers one on top of the other. This is so that the same place values are lined up, as shown in the problem.

\[ \begin{array}{@{}cr} & 37 \\ − & 25 \\ \hline & 12 \end{array} \]

You then subtract, starting with the digit's farthest to the right. So, in this problem, you would start with 7 - 5 and place the difference, 2, below the numbers. Then you would subtract 3 - 2 and place the difference, 1, below those numbers. This gives you the solution 37 - 25 = 12.

Subtraction follows some significant patterns. It is anticommutative, implying that changing the order of the numbers will change the answer. It is not associative, meaning that when more than two numbers are subtracted, the order in which subtraction is completed matters. When you subtract 0, it does not change a number. The subtraction also obeys predictable rules concerning related operations such as addition and Multiplication. These rules can be confirmed, starting with the subtraction of integers and generalising up through the real numbers and beyond.

Next, let's see how you go with some subtraction

Again, you may use your calculator for this.

Watch the video below to find out how subtraction works in Excel.

BODMAS is an acronym that represents the order of mathematical operations. When a sum contains multiple numbers and operations, you need to know which part to solve first in order to solve it in the correct order. If you don't, you'll get an incorrect answer. Therefore, it is important to understand BODMAS when doing mathematical calculations.

BODMAS stands for:

1. Brackets (any part contained in brackets comes first)
2. Order (operations containing powers or square roots)
3. Division
4. Multiplication
5. Addition
6. Subtraction

Using BODMAS

Brackets

4 x (5+2) = ?

Firstly, you need to do the calculation inside the brackets and then multiply the answer by 4.

5 + 2 = 7
4 x 7 = 28

If you ignore the brackets and do the calculation from left to right, you will get a different answer.

4 x 5 = 20 + 2 = 22

Order

After brackets, do anything involving a power or a square root next.

4⁴ + 8 = ?
4⁴ 4 x 4 = 16
18 + 8 = 24

Division and Multiplication

The next step is division and Multiplication. When you have one of each in the equation, then the rule is you start from the left and work across to the right.

12 ÷ 4 + 5 x 3 =?
12 ÷ 4 = 3
5 x 3 = 15
3 + 15 = 18

Addition and Subtraction

Finally, you calculate any addition or subtraction.

9 + 9 – 8 + 10 =?
9 + 9 = 18
18 - 8 = 10
10 + 10 = 20

When making basic mathematical equations, a handheld calculator is a tool often used to make simple math calculations. The calculator supports the following operations:

• Addition (key '+')
• Subtraction (key '-')
• Multiplication (key 'x')
• Division (key '/' ÷)

Most calculators today have the following operations, which you need to know how to use⁹:

Financial calculators

There are different types of financial calculators. Some financial calculators combine the basic to advanced financial functions, and some have math and science-related functions as well.

The most important functions of a financial calculator are:

• Payment calculations 
• Determining the rate of interest for various transactions
• Calculations for determining the current or the upcoming value of a loan

Features of Financial calculators

Financial calculators usually have five important keys that represent the ‘variables’ in various calculations:

• “N” key is used for the number of periods
• “I” key implies the periodic interest rate
• “PV” key stands for the Present Value
• “PMT” key is used to calculate the Payment
• “FV” key is used to calculate the Future Value

Now let’s start looking into the trickier stuff that Maths is all about!

Percent means "per 100", or divided by 100. Dividing by 100 moves the decimal point two places to the left e.g. 24% = 24/100 = 0.24

A percentage, in mathematics, is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviations "pct.", "pct". A percentage is a dimensionless number (pure number).

Percent is an abbreviation for the Latin ‘per centum’, meaning for each 100.

• 100%, then, means 100 for each 100, which is all
• 100% of 12 is 12
• 50% is another way of saying half because 50% means 50 for each 100, which is half. 50% of 12 is 6

If we think of an amount being divided into one hundred equal parts, that is, into hundredths, then a percent is a number of hundredths. 32% is 32 hundredths.

A simple calculator can be used to calculate percentages even though it might not have a '%' key. Multiply the number by the percentage fraction.

To calculate 9% of 25000, multiply 25000 by 9/100; that is, multiply 25000 by 0.09.

If your calculator does not have a percent key and you want to add a percentage to a number, multiply that number by 1 plus the percentage fraction. For example 25000+9% = 25000 x 1.09 = 27250. To subtract 9 percent, multiply the number by 1 minus the percentage fraction. Example: 25000 - 9% = 25000 x 0.91 = 22750.

Percentage increase and decrease

To calculate the % that an amount has increased, you first need to calculate the difference between the two numbers you are comparing. The percent increase formula is:

Percent increase = [(new value - original value)/original value] * 100

Example

John has an investment that last year was valued at $1,250. This year the value has increased to $1,445. Calculate the % increase.

[(1,445 - 1,250)/1,250] * 100
(195/1,250) * 100
0.156 * 100
Increase = 15.6 %

To calculate the % that an amount has decreased, the percent decrease formula is:

Percent decrease = [(original value - new value)/original value] * 100

Example

James has an investment that last year was valued at $1,445. This year the value has decreased to $1,300. Calculate the % decrease.

[(1,445 - 1,300)/1,445] * 100
(145/1,445) * 100
0.10 * 100
Decrease = 10%

Now, let's see how you go with finding out the percentage for this equation. Again, you may use your calculator for this.

In this next section, we are going to explore the world of Fractions. Fractions are for counting ‘part’ of something. A fraction is a part of a whole.

The top number tells how many slices you have. The bottom number shows how many slices the pizza was cut into.

Types of fractions

Proper fractions have a numerator (top number) less than its denominator (bottom number).

Example:

\begin{equation} \frac{4}{7} \end{equation} \begin{equation} \frac{2}{3} \end{equation}

Improper fractions have a numerator (the top number) greater than its denominator (the bottom number).

Examples:

\begin{equation} \frac{9}{8} \end{equation} \begin{equation} \frac{21}{15} \end{equation}

Mixed numbers consist of a whole number and a proper fraction together.

Examples:

\begin{equation} 3\frac{2}{5} \end{equation}

The top number is the Numerator; it is the number of parts you have. The bottom number is the denominator; it is the number of parts the whole is divided into.

Some fractions may look different but are really the same, for example 4/8, 2/4 and 1/2.

It is usually best to show an answer using the simplest fraction (1/2 in this case). That is called Simplifying or Reducing the Fraction.

You can add fractions easily if the bottom number (the denominator) is the same:

1/4 + 1/4 = 2/4 = 1/2

Ok now it is your turn, work out the fraction question below. 

One of the most significant signs/symbols you will use in the world of finance is the decimal point.

A decimal is any number in our base-ten number system. Specifically, we will be using numbers with one or more digits to the right of the decimal point in this module. The decimal point is used to separate the one's place from the tenths place in decimals. (It is also used to separate dollars from cents in money.) As we move to the right of the decimal point, each number place is divided by 10.

Decimals are used in situations that require more precision than whole numbers can provide. An example of this is money: Three and one-fourth dollars is an amount between 3 dollars and 4 dollars. So we use decimals to write this amount as $3.25.

A decimal may have both a whole-number part and a fractional part. The whole-number part of a decimal are those digits to the left of the decimal point. The fractional part of a decimal is represented by the digits to the right of the decimal point. The decimal point is used to separate these parts.

Consider the following number:

\begin{equation} 57\frac{49}{100} \end{equation}

Below we have expressed it in expanded form and decimal form.

Mixed number

\begin{equation} 57\frac{49}{100} \end{equation}

Expanded form

\begin{equation} (5 × 10) + (7 × 1) + 4 ×\frac{1}{10} + 9 ×\frac{1}{100} \end{equation}

Decimal form

57.49

As you can see, it is easier to write it in decimal form. So let's look at this decimal number in a place-value chart to understand better how decimals work.

A line graph shows the change in value over time. Line graphs appear as a jagged line going across the page. The height of the line above the time marked on the axis tells you how high the value is. A line graph might be used by a business to track its profits or project its interest payments over the life of a loan.

The idea of a line graph is to show how a value changes in response to another value – often, but not always, time.

The equation of a straight line is usually:

y = mx + b

• y = how far up
• x = how far along
• m = slope or gradient (how steep the line is)
• b = the Y Intercept (where the line crosses the Y axis)

Simple interest can be represented by a straight-line graph with a positive gradient.

The graph video below demonstrates how to construct a simple interest graph to illustrate the amount of interest you would pay over the life of the loan.

Line graphs are one of the standard graph options in Excel. They are ideal for tracking trends and predicting the results of data in yet-to-be-recorded time periods, for example, the amount of interest paid over the life of a loan. Excel offers several different variations of the line graph:

• Line: If there is more than one data series, each data series is plotted individually.
• Stacked Line: This option requires more than one data set. Each additional set is added to the first, so the top line is the total of the ones below it. Therefore, the lines will never cross.
• 100% Stacked Line: This graph is similar to a stacked line graph, but the Y-axis depicts percentages rather than an absolute value. The top line will always appear straight across the top of the graph, and a period’s total will be 100 percent.
• Marked Line Graph: The marked versions of each 2-D graph add indicators at each data point.
• 3D Line: Similar to the basic line graph but represented in a 3D format.

To find out more about construction line graphs in Excel, click on the following link.

How to Make Line Graphs in Excel | Smartsheet