Introduction: Taxes and discounts are a natural extension of the application of percentages. These are probably the most frequent terms that come up during a conversation about shopping since they directly affect the amount of money involved. About a year ago, if you went to McDonalds to dine, you would have to pay a price that was more than the claimed price on the display. This was because a tax was applied on the food item when it was sold. The observant people picked up on it because the eatery would have a small asterix somewhere in the corner of the price display board saying, “*Prices are excluding taxes”.

The Big Idea: Taxes and Discounts

What are taxes?

By now, you must have heard about income tax, GST, service tax etc in daily conversations. Taxes are charges that are levied by the government on various items and services. A general example of this is sales tax. Sales tax is charged by the government on the sale of any given item. In recent years GST has also been introduced, while other taxes like excise duty, VAT, municipal tax, entertainment tax etc. have existed for a while now.

For example, let’s say an item cost Rs.500 and a sales tax of 5% was charged. What would be the bill amount?

\(\begin{align}&\mathrm{On}\;\mathrm{Rs}.100,\;\mathrm{the}\;\mathrm{tax}\;\mathrm{was}\;\mathrm{Rs}.5\\&\mathrm{So},\;\mathrm{on}\;\mathrm{Rs}.500,\;\mathrm{the}\;\mathrm{tax}\\&\qquad=\frac5{100}\times500=25\\&\mathrm{Adding}\;\mathrm{tax}\;\mathrm{to}\;\mathrm{the}\;\mathrm{listed}\;\mathrm{cost},\;\mathrm{bill}\;\mathrm{amount}\\&\qquad=500+25\\&\qquad=\mathrm{Rs.}525\end{align}\)

What are discounts?

We come across banners like “50% OFF” or “75% OFF” on a frequent basis. These are usually in place to attract customers like us and are usually put up in malls or big stores. Finding the discount is pretty simple; just subtract the sale price of the item from the marked price. When it comes to business, there is a term called trade discounts which applies when businessmen buy goods in large numbers. This is done to encourage bulk purchases which not only increases sales numbers but also clears the stock.

An easy example would be if you saw a 30% discount on an article with an MRP of Rs.800.

\(\begin{align}&\mathrm{Discount}\\& \qquad =\frac3{100}\times800\\& \qquad =\mathrm{Rs}.240\\\\&\mathrm{Final}\;\mathrm{price}\\& \qquad =800-240\\& \qquad =\mathrm{Rs.}560\end{align}\)

Why Taxes and Discounts? Why are they important?

Taxes are a way to provide for the the country’s infrastructure and government. They are used for maintaining national defences, building schools, transportation amenities, disaster relief and many other things that we might take for granted.

Discounts are a means to attract customers to any kind of business and everything in such regard boils down to increasing the consumer base of the business. They help in increasing the reputation of the organization, create positivity around the brand etc. Discounts may not always be all inclusive. For example, a restaurant might give discount to anyone who is considered a senior citizen while a comedy show might give a discount for attendees below the age of 18 years. All of this serves as an incentive for us to give our money to businesses.

Also, discount is calculated on selling price excluding taxes. Tax is applied on the amount arrived at after subtracting all the discount from selling price. E.g. If S is the selling price, D is the discount percentage, and T is the tax rate then:

[S x (1 D)] x (1 + T) and not [S x (1 + T)] x (1 D)

Suppose you are ordering a Pizza at Domino’s and it costs Rs.400. The restaurant is offering a discount of 30% on all dine in orders, so the final amount that it will come to, assuming the restaurant only charges 10% GST as tax is:

Base price = 400
Discount = 30% (D)
Discounted price = 400
(400 x 0.3) = 280
Tax = 10% (T)
Total = 280 + (280 x 0.1) = 308

So, you will end up paying a total of Rs.308 for your meal!

Let’s take a look at a very common scenario from our daily lives. It’s sale season, and Levi’s is offering a flat 20% discount on its entire catalogue. You buy a shirt which is listed at Rs.1200. Assuming that you have to pay a total tax of 18%, this is how much your bill ends up being:

Formulae for calculating taxes and discounts:

  • Billed amount = Cost of item + Sales Tax

  • Discount = Marked price  Sale price

  • Discount % = Discount/Marked Price x 10

A little tip to help you during the next mega sale:

Many a times, multiple discounts would be available on a single item. In such cases, we do not simply add the percentages. Let’s take an example of a bookstore which has a promotional sale going on. They are selling all books at a 25% discount on top of whatever discount is mentioned on individual books. Suppose you select a book with an MRP of Rs.500 and a 20% discount tag. In that case you would first get a discount of 20% on the book on which the cashier of the bookstore will add a discount of 25%. You can’t simply add both discount percentages together and get a 45% discount. Mathematically speaking:

\(\begin{align}&\mathrm{Initial\;price\;of\;book =Rs. 500}\\\\&\mathrm{Discount\;for\;individual\;book} \\& \qquad =20\%\\\\&\mathrm{Initial\;discount\;on\;book} \\& \qquad =\frac{20}{100}\times500 \\& \qquad =\mathrm{Rs}.\;100\;(\mathrm{On}\;\mathrm{Rs}.500)\\\\&\mathrm{Price\;of\;book\;after\;initial\;discount} \\& \qquad =\;500-100=\mathrm{Rs}.400\\\\&\mathrm{Store\;discount}=25\%\;(\mathrm{On}\;\mathrm{Rs}.400)\\&\mathrm{Final\;discount\;on\;book} \\& \qquad =\;\frac{25}{100}\times400 \\& \qquad =\mathrm{Rs}.100\\\\&\mathrm{Final\;discounted\;price\;of\;book} \\& \qquad =400-100 \\& \qquad =\mathrm{Rs.}300\end{align}\)

Tips and Tricks

  • Be careful when applying successive discounts. Discount percentages cannot be simply added. E.g. Two successive discounts of 5% is not equal to one discount of 10%
    For example, an item that costs Rs 2000 is discounted successively by 5%. First discount value will be 2000 x (5 ÷ 100) = Rs 100. Now the price has already reduced to Rs 1900. The second discount will be 1900 x (5 ÷ 100) = Rs 95. So, the final price of the item is Rs 1805. As you can see, this turns out to be slightly more expensive than a single discount of 10%.
  • Remember that discounts are calculated on the marked price (or listed price) of an item. Taxes are calculated on the final discounted price of the item and not on the marked price

 

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