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The term commercial mathematics is a combination of two words, commerce and math. Commerce relates to the concept of trade, business, etc., whereas mathematics deals with the calculation and analysis of these concepts. In this article, we will explore the idea of commercial mathematics.
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Commercial math is the branch of mathematics that focus on the calculation of profits, discounts, taxes, percentages, and many others terms related to money. It was first developed in the early 3rd millennium BCE in the Mesopotamian and Egyptian civilizations for trade and commerce.
The use of commercial mathematics in today's world is mainly related to the banking and financial sectors. The term “commercial” itself refers to business, trade, or activities intended to generate a profit.
Commercial math is mainly used in the banking and finance sectors, as it deals with trade and commerce-related subjects. Even though banking and financial sectors are major users of commercial math, it is not limited to them. The main functions of commercial math:
Since we have already discussed the primary uses and the definition of commercial mathematics, let us discuss the essential topics in commercial mathematics:
All businesses work on the basic principle of profit and loss. Business can be simply defined as the act of conducting trade, and in trade, there is either a profit or a loss.
Profit is the money a business retains after paying all its expenses. It is an important performance metric to understand the business’s financial gains. Profit is the value remaining after reducing the selling price from the cost price. The mathematical expression for profit is given by:
Profit = Selling Price - Cost Price
To find out how much profit was made compared to the cost, we use the formula,
Profit Percentage = \( \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \)
When a product is sold for an amount less than the original cost, it is said to be a loss. The formula for calculating loss is expressed as:
Loss = Cost Price - Selling Price
Let's understand these terms using an example.
Example: We bought a toy for ₹160 and sold it for ₹200. What percentage of profit did we make?
Solution:
Given:
Cost Price (CP) = ₹160
Selling Price (SP) = ₹200
So we made a profit of 25%.
Simple interest is the interest added or the extra money that is to be paid while returning borrowed money. It is only applicable on the original amount of money borrowed.
Simple interest depends on three factors:
So using these factors we have a formula to calculate the simple interest:
Simple interest (SI) = \( {{P \times T\times R} \over 100}\)
Now, let's use an example to understand what simple interest is and how it works.
Example: A person borrowed Rs 5000 and promised to pay the bank back in 3 years with a 5% interest per year. Calculate the simple interest.
The interest earned on both the original amount and the interest that has already been added is called compound interest.
Compound interest can be calculated using:
So there are two formulas for calculating the amount:
Now, after finding the amount, compound interest can be calculated by using formula:
\(\text{Compound Interest = Amount - Principal}\)
Here are a few examples that use these formulas:
Example 1: Rohan put ₹ 1500 in the bank at 15% interest per year, compounded quarterly, for two years. Find the compound interest.
\(A = 1500 (1.0375)^8\)
\(A = 1500 (1.3425) = 2013.75\)
Example 2: Now Rohan put ₹3000 in the bank at 12% interest per year, compounded annually, for three years. Find the compound interest.
\( A = 3000 (1.404928)\)
\(A = ₹4214.784\)
Calculating compound interest:
\( = 4214.784 - 3000 \\= ₹1214.784\)
The following table gives the differences between simple interest and compound interest.
Simple interest | Compound interest |
Simple Interest is the extra money you earn, or you have to pay, on the original amount over a fixed period of time. |
|
SI is calculated only on the principal amount. | CI is calculated both on the principal and the previously earned interest. |
Return is less. | Return is higher. |
The principal amount always remains constant. | Principal amount can keep varying during the time period. |
The reduction in the price of an object or a set of objects is referred to as a discount. It is a widely used technique employed by businesspeople to attract both existing and new customers. A discount can be expressed in terms of a percentage reduction or as a flat money discount.
We use a following formula to calculate the discount:
Calculating a discount is done in two cases:
When the marked price and selling price are both given, we use the discount formula, which is calculated by subtracting the selling price from the marked price. Another case is when the discount percentage is given, we use the discount percentage formula.
Let's use these formulas in real-life examples to get a better understanding:
Example: A PlayStation 5 costs around $450, but it is being sold for $360. Find the discount amount and the discount percentage.
Given:
Marked Price = $450
Selling Price = $360
So there is a 20% discount on the PlayStation 5.
Tax is the amount of money that is collected from eligible individuals and organizations that are liable to pay and is transferred to the government. The money is used for the development and welfare of the country.
A formula used to calculate tax is:
\(\text{Tax amount} = \text {Selling Price} \times {{{\text{Tax Rate}} \over 100}}\)
There are two types of taxes :
Direct Tax - These are paid directly to the government, like when you get your salary a small portion of it goes to the government.
Indirect Tax - These taxes are paid to businesses, which then pays the government. Sales tax is an example of indirect tax.
Goods and Services Tax (GST) is the price that is added to various products and services that are bought and sold. This is then collected by the government, which would be used for public.
GST has formulas of its own as well. The formulas are:
Let's use these in some examples
Example 1: You buy a shirt that costs you around ₹500, the GST rate is 13%. Find the total amount after GST.
Given:
GST = 13%
Price = ₹500
So the price of the shirt after GST is ₹565.
Ratio is a way of comparing two quantities, whereas proportion states the equality of two ratios. The concept of ratio and proportion is widely used in daily life as well as in commerce and science.
What is Ratio?
Two quantities compared with each other is what we call ratio. It tells us how much one thing is compared to another.
We write ratio as:
a:b (we read it is ‘a' is to b’)
Example 1: We mix 2 cups of milk with 3 cups of water. What is the ratio?
Solution: The ratio is 2:3
This means that for every 2 cups of milk, there will be 3 cups of water.
What is Proportion?
Proportions is a concept of showing if two values are in ratio or not.
We write proportion as:
\({{a} \over b}\) = \( {{c} \over d}\)
Example 2: If 2 cups of sugar is added to 4 cups of milk, then how many cups of sugar is required for 8 cups of milk?
Solution: \({{2} \over 4}\) = \( {{x} \over 8}\)
Now we solve for x by cross multiplying:
\( 2 \times 8 = 4 \times x \\ \space \\ 16 = 4x \\ \space \\ x = \frac{16}{4} \\ \space \\ x = 4 \)
So 4 cups of sugar is needed for 8 cups of milk.
Two people coming together and starting a business arrangement, sharing the profit and losses, is what we call a partnership.
The amount of money a partner invests in the company decides how much profit or loss each partner gets. Usually, partnerships are formed among large companies like Ben & Jerry's or Apple.
How are the profits shared between partners?
The distribution of profits among partners according to the investment made by each business partner is called profit-sharing.
To calculate profit-sharing, the formula is given by:
\(\text{Partner's Share} = \frac{\text{Partner's Investment} \space \times \space \text{Total Profit}}{\text{Total Investment}} \)
Example 1: So two partners Pam and Tam start a business. Pam invests $3000 and Tam invests $2000. The total profit is, $5000. Find out each partner’s share.
\(\text{Tam’s share } = \frac{2000 \times 5000}{5000} = $2000 \)
Final profit: Pam gets ₹3000 and Tam gets ₹2000.
This topic is all about the amount of work done in a said time by a person or a group of people.
Here are some of the key points to remember:
Work: Any given task that must be completed.
Some formulas for work and time are:
\(\text{Efficiency} = \frac{\text{Work}}{\text{Time}} \)
Let's understand this through an example
Example 1: Andy is a salesman who can complete his task in 10 days. How efficient is Andy in his work, and how much would he be able to complete in 4 days?
Solution:
\( \text{Work} = \frac{1}{4} × 4 = 0.4 \)
So, Andy’s efficiency is \(\frac{1}{10} \) of the work per day, and in 4 days he will be able to complete only 40% of the work.
We use time, speed, and distance to understand how fast an object moves from point to another and how long it would take to get there.
The following image provides a better visualization of time, distance and speed formula:
Let’s use these formulas in an example
Example 1: A car is travelling from point A to point B at a speed of 60 km/h. How much time will it take to travel 180kms?
Solution: We will use the time formula:
\(\text{Time} = \frac{\text{Distance}}{\text{Speed}} \)
Time = \(\frac{180}{60} \)
Time = 3 hours
To travel 180kms, the car will take 3 hours at a speed of 60 km/h
Learning commercial math can definitely feel overwhelming as there are a lot of formulas and concepts to learn. Here are some tips and tricks to know that will make studying these concepts much easier.
c. Time, Speed, and Distance:
\(Distance = speed × time\)
\(\text{Speed} = \frac{\text{Distance}}{\text{Time}} \)
\(\text{Time} = \frac{\text{Distance}}{\text{Speed}} \)
Using percentage shortcuts for calculations can help you to solve problems faster:
10% of a number: You just need to move the decimal point one place to its left.
Example: 10% of 500 = 50
1% of a number: Over here, we have to just divide the number by 100.
Example 1% of 3000 = 3000/100 = 30
Practice solving with real world examples: Using real world examples would definitely help you understand how formulas work.
Make sure to understand and apply ratios and proportions: Go step by step, simplify the ratios or fractions first and then cross multiply when it comes to solving for proportions.
Be careful about successive changes: In situations where there are multiple discounts or losses, it is essential to subtract or add accordingly based on the question. Not every time is the discount or loss applied to the original price.
Making mistakes is common when learning commercial math. However, it can be avoided if the mistakes are identified well in advance. Some of them are mentioned here:
We need commercial math to calculate profit, losses, or discounts. Every business also needs to pay tax to the government.
Here are some ways we apply Commercial Math in Real life:
These are some of the few areas in our daily lives where commercial math is widely used.
Anil bought a bicycle for ₹1500. He then sold it for ₹1800. What is Anil’s profit? Also calculate the percentage of profit.
Profit is ₹300
Profit percentage = 20%.
\(\text {Profit} = 1800 - 1500 = 300 \\ \space \\ \text {Profit} \% = \frac{300}{1500} × 100\)
Anil earns a profit of 20%.
Find the compound interest on $15000 at 5% per year for 3 years.
Compound interest is $2364.375
The compound interest is $2364.375.
A dress costs around $2000 but is sold at a 20% discount. Find the selling price of the dress.
$1600
The selling price of the dress is $1600.
A car travels at a speed of 80 km/h. How far will the car travel in 6 hours?
480 km
Using Distance formula:
\(\text{Distance = Speed × Time}\\ \space \\ \text{Distance = 80 × 6 = 480 km}\)
The car will travel 480km in 6 hours.
A school has 100 boys and 80 girls. Calculate the ratio between boys and girls. Also, if the school plans to increase the number of boys and girls in the same ratio, how many boys will there be if the number of girls increases to 110?
137.5 rounded to 138
So the ratio is 5:4 and the number of boys would be 138 boys.
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