Taxes

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax. In this lesson, we will study the tax computation when the selling price or price before tax is given. We calculate tax on a product by multiplying the tax rate with the product's net selling price.

Tax amount = \($(S.P. \times \dfrac{Tax\ rate}{100})\)

Tax is the amount paid by the people to the government for goods and services provided. In any tax transaction, there are two parties involved - a taxpayer and a tax collector. A taxpayer is a person or an organization who is paying the tax to the government. A tax collector is a government or any middleman collecting tax on behalf of the government.

The first known tax transaction took place around 3000–2800 BC in Ancient Egypt. In India, taxes were introduced in 1860 by Sir James Wilson to meet the Government's losses based on the Military Mutiny of 1857. Taxes have generally been around since the beginning of civilization or history. While the Civil War led to the creation of the first income tax in the U.S., the federal income tax as we know it was officially enacted in 1913. You may have heard terms like income tax, value-added tax, service tax, etc. The formula used to calculate tax on the selling price is given below:

Tax amount = \($(S.P. \times \dfrac{Tax\ rate}{100})\)

Let's consider an example. Let’s say an item costs $50, and a sales tax of 5% was charged. What would be the bill amount?

Let’s first find 5% of 50.

5/100×50 = 2.5

Now let’s add this amount to the cost price, $50+ $2.5 = $52.5. The total bill amount, including taxes, would be $52.5

When the tax amount and the selling price (S.P.) of an item are given, and we have to calculate the tax rate, then we can use the following formula:

Tax rate = \(\dfrac{Tax\ amount}{Price\ before\ tax}\times 100\%\)

Consider the following example. You purchase a mobile phone whose price before tax is $200, and the tax paid on it is $20. Then, the rate of tax paid on that mobile can be calculated by using the above formula. 

Tax rate = (Tax amount/Price before tax) × 100

Tax rate = ($20/$200) × 100

Tax rate = 10%

Let’s now try and understand how taxes are levied on a discounted product. 

• Discount is calculated on the selling price, excluding taxes. 
• The tax is applied on the amount arrived at after subtracting the discount value from the selling price. 

Consider the following scenario. You have ordered a pizza at a restaurant, and it costs $12. The restaurant is offering a discount of 30% on all dine-in orders. Hence, assuming the restaurant only charges 10% service tax, the final amount is calculated in the following way. First, calculate the discounted price. Discount = 30/100 × 12 = $3.6

Final Bill Amount = $12 - $3.6 = $8.4

Remember, the tax is charged at a discounted price. We know that 10% service tax was charged on the final amount.

10/100 × 8.4 = $0.84

Final Amount = $8.4 + $0.84 = $9.24

There are two types of taxes. They are direct and indirect taxes. Taxes paid by the citizens directly to the government are direct taxes. For example, income tax, corporate tax, etc., are categorized as direct taxes. Taxes paid by the people but not directly collected by the government are indirect taxes. For example, sales tax, entertainment tax, excise duty, etc., are categorized as indirect taxes. 

Indirect taxes are collected by the people who sell goods or services. These include shop owners and business people, who then further pay the indirect tax to the government. Indirect tax can be passed from one entity to another.

We calculate tax on the marked price when the seller sells an item at the marked price without any discount. In that case, the marked price and the selling price are the same. Thus, tax is calculated on the marked price. For example, if the marked price on a chair is $1200 and 8% tax is to be paid to the shopkeeper, then the amount of tax to be paid to the shopkeeper can be calculated as:

Tax amount = ${M.P. × (Tax rate/100)}

                    = ${1200 × (8/100)}

                    = $(12 × 8)

                    = $96

Therefore, We need to pay $96 as a tax on the chair's purchase at a marked price of $1200.

Always remember that only when the final selling price is the same as the marked price of the item purchased, we calculate tax on the marked price. Otherwise, we calculate tax on the net amount that the customer is paying to buy a product or a service.

Important Notes

• Tax is always calculated on the item's final selling price after considering discounts, if available on the item.
• There are two major categories of taxes, and they are direct tax and indirect tax.
• Tax is a real-life application of the percentage concept.
• We should always compare the tax rate and not the tax amount, as the prices before tax are different for different products.

Challenging Question on Taxes

Now let's try to solve this challenging question related to taxes.

• Which brand of bag is charging more tax?

Related Articles on Taxes

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• Rate Definition
• Percentages
• Profit and Loss
• Simple interest
• Compound Interest
• Discounts
• Unitary Method

How to Calculate Tax on a Product?

To calculate tax on a product, we multiply the tax rate by its net selling price. Tax amount = ${S.P. × (Tax rate/100)

What Are Taxes?

The amount paid by the people to the government for goods and services provided is called tax which is further utilized by the government for public welfare activities.

What Is the Difference Between Cost Price and Selling Price?

Cost price is when an article is purchased, and selling price is when an article is sold.

What Is the Meaning of Marked Price?

Marked price is the price set by the shopkeeper on the label of the article. It is set by adding the profit margin to the cost price of the article.

What Is the Formula to Calculate the Rate of Tax on a Product?

The formula to calculate the rate of tax is given below:

Tax rate = (Tax amount/Price before tax) × 100%

What Are the Different Types of Taxes?

There are two types of taxes: direct tax and indirect tax.

What Is a Direct Tax?

Direct tax refers to the tax directly paid to the government by the customer. Examples of direct taxes include income tax, corporate tax, wealth tax, etc.