# 1.1 Discounts

## LEARNING OBJECTIVES

- Solve problems involving a single trade discount rate or a series of trade discount rates.
- Calculate a single discount rate that is equivalent to a series of discounts.

You mutter in exasperation, “Why can’t they just set one price and stick with it?” Your mind boggles at all the competing discounts you encounter at the mall in your search for that perfect Batman toy for your nephew. Walmart is running their Rollback promotion and is offering a Batmobile for 25% off, regularly priced at $49.99. Toys R’ Us has an outlet in the parking lot where the regular price for the same toy is $59.99, but all Batman products are being cleared out at 40% off. You head over to The Bay for a warehouse clearance event that has the same toy priced at $64.99 but at 35% off. It is also Bay Days, which means you can scratch and win a further 10% to 20% off the sale price.

The **cost** of a product is the amount of money required to obtain the merchandise. If you are a consumer, the ticketed price tag on the product is your cost. If you are a reseller (also known as a *middleman* or *intermediary*), what you pay to your supplier for the product is your cost. If you are a manufacturer, then your cost equals all of the labor, materials, and production expenditures that went into creating the product.

A **discount** is a reduction in the price of a product. As a consumer, you are bombarded with discounts all the time. Retailers use various terms for discounts, including *sales* or *clearance*. If your business purchases a product from a supplier, any discount it receives lowers how much the business pays to acquire the product. When a business buys products, the price paid is the cost to the business. Therefore, a lower price means a lower cost.

If your business is the one selling the product, any discount offered lowers the selling price and reduces revenue per sale. Because the revenue must cover all costs and expenses associated with the product, the lower price means that the business reduces profits per sale. In business, it is common practice to express a discount as a percentage off the regular price.

The distribution of goods or products that are ultimately sold to consumers forms a chain, called a **merchandising chain** or **distribution chain**. For example, consider a manufacturer such as Kellogg Canada Inc. The distribution chain to get products from the manufacturer, in this case Kellogg Canada, to the consumer is illustrated in the top part of the image below. To distribute its products to various regions across Canada, Kellogg Canada uses various regional wholesalers. Each wholesaler then resells the product to retailers in its local trade area. Although some retailers (such as the Real Canadian Superstore) are very large, and Kellogg Canada distributes directly to these organizations, bypassing the wholesaler as represented by the blue arrow. Finally, consumers shop at these retailers and acquire Kellogg products.

The relationship of distribution to pricing is illustrated in the bottom part of the image above. Kellogg Canada sets a **list price** or **manufacturer’s suggested retail price**, known as the MSRP. This is a recommended retail price based on consumer market research. Because grocery retailers commonly carry thousands or tens of thousands of products, the MSRP helps the retailer to determine the retail price at which the product should be listed. In this case, assume a $2.00 MSRP for a particular product, which is the price consumers will pay for the product.

The retailer must pay something less than $2.00 to make money when selling the product. Kellogg Canada understands its distributors and calculates that to be profitable most retailers must pay approximately 40% less than the MSRP. Therefore, Kellogg Canada offers a 40% discount. If the retailer purchases directly from Kellogg, as illustrated by the yellow arrow, the price paid by the retailer to acquire the product is $2.00 less 40%, or $1.20. Smaller retailers acquire the product from a wholesaler for the same price. Thus, the retailer’s cost equals the wholesaler’s price (or Kellogg Canada’s price if the retailer purchases it directly from Kellogg).

The wholesaler’s price is $1.20. Again, Kellogg Canada, knowing that the wholesaler must pay something less than $1.20 to be profitable, offers an additional 20% discount exclusively to the wholesaler. So the price paid by the wholesaler to acquire the product from Kellogg Canada is $1.20 less 20%, or $0.96. This $0.96 forms Kellogg Canada’s price to the wholesaler, which equals the wholesaler’s cost.

In summary, this discussion illustrates two key pricing concepts:

- Companies higher up in the distribution chain pay lower prices than those farther down the chain. Companies receive discounts off the MSRP based on their level in the distribution chain. This may result in multiple discounts, such as a wholesaler receiving both the retailer’s discount and an additional discount for being a wholesaler.
- One organization’s price becomes the next organization’s cost (assuming the typical distribution chaain structure):

[latex]\begin{eqnarray*}\text{Manufacturer’s Price}&=&\text{Wholesaler’s Cost}\\\text{Wholesaler’s Price}&=&\text{Retailer’s Cost}\\\text{Retailer’s Price}&=&\text{Consumer’s Cost}\end{eqnarray*}[/latex]

## Types of Discounts

Businesses or consumers are offered numerous types of discounts, of which five of the most common are trade, quantity, loyalty, sale, and seasonal.

**Trade Discount.**A**trade discount**is a discount offered to businesses only based on the type of business and its position in the distribution chain, such as a retailer, wholesaler, or any other member of the chain that resells the product. Consumers are ineligible for trade discounts. In the above example, two trade discounts are offered—a 40% retail trade discount and a second 20% wholesale trade discount. Typically, a business that is higher up in the distribution chain receives a combination of these trade discounts.**Quantity Discount.**A**quantity discount**, or volume discount, is a discount for purchasing larger quantities of a certain product.**Loyalty Discount.**A**loyalty discount**is a discount that a seller gives to a purchaser for repeat business. As a consumer, you see this regularly in marketing programs or with credit cards that offer cash back programs.**Sale Discount**. A**sale discount**is a temporary lowering of the price from a product’s regular selling price. Businesses put items on sale for a variety of reasons, such as selling excess stock or attracting shoppers.**Seasonal Discount**. A s**easonal discount**offered to consumers and businesses for purchasing products out of season. At the business level, manufacturers tend to offer seasonal discounts to encourage retailers, wholesalers, or distributors to purchase products before they are in season.

## Single Discounts

The price of a product after applying a single discount to the list price is called the **net price**. Figuring out the price after applying a single discount is called a net price calculation. When a business calculates the net price of a product, it is interested in what you still have to pay, not in what has been removed.

Given the list price ([latex]L[/latex]) of an item and a single discount ([latex]d[/latex]), the net price ([latex]N[/latex]) of the item is:

[latex]\begin{eqnarray*} N & = & L \times (1-d) \end{eqnarray*}[/latex]

where

**[latex]N[/latex] is the net price.**The net price is the price of the item after the discount is removed from the list price. It is a dollar amount representing what price remains after you have applied the discount.**[latex]L[/latex] is the list price.**The list price is the normal or regular dollar price of the item before any discounts. It is the MSRP or any dollar amount before you remove the discount.**[latex]d[/latex] is the discount rate.**The discount rate represents the percentage (in decimal format) of the list price that is deducted.

### NOTES

- In the net price formula, you take 1 and subtract the discount rate to determine the rate owing. For example, if you are eligible for a 20% discount, then you must pay 80% of the list price.
- The net price formula above requires the discount be given as percentage (i.e. 20% discount). Sometimes a discount is expressed as a dollar amount (i.e. take $5 off).

**discount amount**([latex]D[/latex]) is the actual dollar amount subtracted from the list price to get the net price. The discount amount is

**[latex]D[/latex] is the discount amount.****[latex]d[/latex] is the discount rate**. The discount rate represents the percentage (in decimal format) of the list price that is deducted.**[latex]L[/latex] is the list price.**The list price is the normal or regular dollar price of the item before any discounts.

An alternative formula for the discount amount is

[latex]\displaystyle{D=L-N}[/latex]

where

**[latex]D[/latex] is the discount amount.****[latex]L[/latex] is the list price**. The list price is the normal or regular dollar price of the item before any discounts.**[latex]N[/latex] is the net price.**The net price is the price of the item after the discount is removed from the list price.

### NOTES

- The last formula, [latex]D=L-N[/latex], can be rearrange to express the net price in terms of [latex]D[/latex] and [latex]L[/latex]: [latex]N=L-D[/latex].
- When working with single discounts, you are not always solving for the net price. Sometimes you must calculate the discount percent or the list price. At other times you know information about the discount amount but need to solve for list price, net price, or the discount rate. Ultimately, the formula that you use will depend on what information you have and what you are trying to find.
- Many of the pricing problems take multiple steps that combine various formulas, so you need to work through the problem systematically. In any pricing problem, you must understand which variables are provided and match them up to the known formulas. To get to your end goal, you must look for formulas in which you know all but one variable. In these cases, solving for variables will move you forward toward solving the overall pricing problem.

## EXAMPLE

A manufacturer that sells jeans directly to its retailers uses market research to find out it needs to offer a 25% trade discount. In doing so, the retailers will then be able to price the product at a list price of $59.99. What price should retailers pay for the jeans?

**Solution:**

**Step 1:** The given information is

[latex]\begin{eqnarray*}L&=&\$59.99\\d&=& 25\%\end{eqnarray*}[/latex]

**Step 2:** Solve for the net price.

[latex]\begin{eqnarray*}N & = & L \times (1-d) \\ &=&59.99\times(1–0.25)\\&=&59.99\times0.75\\&=&\$44.99\end{eqnarray*}[/latex]

The manufacturer should sell the jeans to the retailers for $44.99.

### NOTES

- Until you arrive at the final answer, avoid rounding any interim number, unless you have some special reason to do so.
- Round all dollar amounts to the nearest cent.
- Round all percentages to four decimals when in decimal format and two decimals when in percent format (i.e. 0.0523 or 5.23%).

## EXAMPLE

A retailer pays a net price of $27.50 for a winter jacket after receiving a retail trade discount of 45%. What was the list price of the jacket?

**Solution:**

**Step 1:** The given information is

[latex]\begin{eqnarray*}N&=&\$27.50\\d&=& 45\%\end{eqnarray*}[/latex]

**Step 2:** Solve for the list price.

[latex]\begin{eqnarray*}N & = & L \times (1-d) \\ 27.50 &=&L\times(1–0.45)\\27.50&=&L \times0.55\\\frac{27.50}{0.55} &=&L \\ \$50 & = & L \end{eqnarray*}[/latex]

The list price of the jacket was $50.

## EXAMPLE

You are shopping at a local sporting goods store for a new environmentally friendly water bottle. The price tag reads $14.75, which is $10.24 off the regular price. Determine the discount rate applied.

**Solution:**

**Step 1:** The given information is

[latex]\begin{eqnarray*}N&=&\$14.75\\D&=& \$10.24\end{eqnarray*}[/latex]

**Step 2:** Solve for the list price.

[latex]\begin{eqnarray*}N & = & L -D \\ 14.75 &=&L-10.24\\14.75+10.24&=&L\\ \$24.99 &=&L \end{eqnarray*}[/latex]

**Step 3:** Solve for the discount rate.

[latex]\begin{eqnarray*}D & = & d \times L \\ 10.24 &=& d \times 24.99\\ \frac{10.24}{24.99} &=& d \\ 0.4098 & = & d \\ 40.98\% & = & d \end{eqnarray*}[/latex]

The discount rate was 40.98%.

## TRY IT

A retailer sells shoes for $150. During a sale, a discount of 30% is offered. What is the net price of the shoes?

**Click to see Solution**

[latex]\begin{eqnarray*}N & = & L \times (1-d) \\ &=&150\times(1-0.3)\\&=&150\times 0.7 \\&=&\$105\end{eqnarray*}[/latex]

## TRY IT

A new model of cell phone is on sale for $750 after a discount of 15%. What was the list price of the cell phone?

**Click to see Solution**

[latex]\begin{eqnarray*}N & = & L \times (1-d) \\ 750&=&L \times(1-0.15)\\ 750 &=& L \times 0.85 \\ \frac{750}{0.85} & = & L \\ \$882.35 &=& L \end{eqnarray*}[/latex]

## TRY IT

A local food distributor lists a case of canned soup for $68.50. The distributor sells the case to a local grocery retailer for $52.35. What discount rate did the distributor offer the retailer?

**Click to see Solution**

[latex]\begin{eqnarray*}N & = & L \times (1-d) \\ 52.35&=&68.50 \times(1-d)\\ \frac{52.35}{68.50} &=& 1-d \\ 0.76423... & = & 1-d \\ d & = & 1-0.76423... \\ d & = & 0.2358 \\ d & = & 23.58\% \end{eqnarray*}[/latex]

## Multiple Discounts

You are driving down the street when you see a large sign at Old Navy that says, “Big sale, take an additional 25% off already reduced prices!” In other words, products on sale (the first discount) are being reduced by an additional 25% (the second discount).

Businesses commonly receive more than one discount when they make a purchase. Consider a transaction in which a business receives a 30% trade discount as well as a 10% volume discount. First, you have to understand that this is **NOT** a 30% + 10% = 40% discount. The second discount is always applied to the net price **after** the first discount is applied. Therefore, the second discount has a smaller base upon which it is calculated. If there are more than two discounts, you deduct each subsequent discount from continually smaller bases.

Given the list price of an item and a series of discounts, the net price of the item is

[latex]\begin{eqnarray*} N & = & L \times (1-d_1) \times (1-d_2) \times \cdots \times (1-d_n) \end{eqnarray*}[/latex]

where

**[latex]N[/latex] is the net price.**The net price is the price of the item after all of the discounts have been deducted.**[latex]L[/latex] is the list price.**The list price is the normal or regular dollar price of the item before any discounts.**[latex]d_1[/latex] is the first discount rate, [latex]d_2[/latex] is the second discount rate, and so on to [latex]d_n[/latex] the [latex]n[/latex]th discount rate.**The discount rate represents the percentage (in decimal format) of the list price that is deducted. When there is more than one discount, you must extend beyond the [latex]N=L\times(1−d)[/latex] formula by multiplying another discount expression. These discounts are represented by the same [latex]d[/latex] symbol. However, each discount receives a subscript to make its symbol unique. Therefore, the first discount receives the symbol of [latex]d_1[/latex], the second discount receives the symbol [latex]d_2[/latex], and so on. Recall that the symbol [latex]n[/latex] represents the number of pieces of data (a count), so you can expand or contract this formula to the exact number of discounts being offered.

It is often difficult to understand exactly how much of a discount is being received when multiple discounts are involved. Often it is convenient to summarize the multiple discount percentages into a single percentage. This makes it easier to calculate the net price and aids in understanding the discount benefit. Simplifying multiple percent discounts into a single percent discount is called finding the **single equivalent discount**. Whether you apply the multiple discounts or just the single equivalent discount, you arrive at the same net price.

To convert multiple discount percentages into a single equivalent discount percent

[latex]\displaystyle{d_e=1-\left[(1-d_1) \times (1-d_2) \times \cdots (1-d_n)\right]}[/latex]

where

**[latex]d_e[/latex] is the single equivalent discount rate.**That is, [latex]d_e[/latex] is equal to the series of multiple discounts. Recall that taking [latex](1 − d)[/latex] calculates what you pay. Therefore, if you take 1, which represents the entire amount, and reduce it by what you pay, the rate left over must be what you did not pay. In other words, it is the discount rate.**[latex]d_1[/latex] is the first discount rate, [latex]d_2[/latex] is the second discount rate, and so on to [latex]d_n[/latex] the [latex]n[/latex]th discount rate.**Because there are multiple discounts, each discount receives a numerical subscript to give it a unique identifier. You can expand or contract the formula to the exact number of discounts being offered.

### NOTES

- As noted above, the single equivalent discount rate is NOT equal to the sum of the discounts. That is, if you have a series of 30%, 10% and 5% discounts, the single equivalent discount is actually 40.15%, and NOT 45%.
- The order of the discounts
**does not**matter in determining the net price. Remember from the rules of BEDMAS that you can complete multiplication in any order. In other words, it does not matter if you take 30% first followed by 10% or 10% first followed by 30%. - Notice in the single equivalent discount formula that the list price and the net price are not involved in the calculation of the single equivalent discount.

## EXAMPLE

A retail dealership purchases some snowmobiles to stock in its stores. Examining the merchandising terms of the manufacturer, the dealership notices that it would be eligible to receive a 35% trade discount, a 15% volume discount, and a 3% loyalty discount. Because it is June and snowmobiles are out of season, the manufacturer offers a seasonal discount of 12% for purchases made before June 30.

- If the list price for the snowmobiles is $12,399 and the dealership purchases this item on June 15, what price would the dealership pay?
- What single discount is equivalent to the series of four discounts offered?

**Solution:**

**Step 1:** The given information is

[latex]\begin{eqnarray*}L&=&\$12,399\\d_1&=& 35\% \\ d_2 & = & 15\% \\ d_3 & = & 3\% \\ d_4 & = & 12\%\end{eqnarray*}[/latex]

**Step 2:** Solve for the net price.

[latex]\begin{eqnarray*}N & = & L \times (1-d_1) \times (1-d_2) \times (1-d_3) \times (1-d_4) \\ &=& 12,399 \times (1-0.35) \times (1-0.15) \times (1-0.03) \times (1-0.12) \\ &=& 12,399 \times 0.65 \times 0.85 \times 0.97 \times 0.88\\ &=& \$5,847.54 \end{eqnarray*}[/latex]

**Step 3:** Solve for the single equivalent discount rate.

[latex]\begin{eqnarray*}d_e & = & 1-\left[(1-d_1) \times (1-d_2) \times (1-d_3) \times (1-d_4) \right] \\ &=& 1-\left[(1-0.35) \times (1-0.15) \times (1-0.03) \times (1-0.12)\right]\\ &=& 1-(0.65 \times 0.85 \times 0.97 \times 0.88) \\ & = & 1-0.471614 \\ & = & 0.528386 \\ & = & 52.8386\% \end{eqnarray*}[/latex]

The net price of the snowmobiles was $5,847.54. The single equivalent discount rate was 52.84%.

### NOTE

In the previous example, because you know the list price ($12,399) and the net price ($5,847.54), you could solve for the single equivalent discount by solving for [latex]d[/latex] in [latex]N=L \times (1-d)[/latex]:

[latex]\begin{eqnarray*} N & = & L \times (1-d) \\ 5,847.54 & = & 12,399 \times (1-d) \\ \frac{5,847.54}{12,399} & = & 1-d \\ 0.47161384 & = & 1-d \\ d & = & 0.528386 \end{eqnarray*}[/latex]

## EXAMPLE

An advertisement claims that at 60% off, you are saving $18. However, today there is an additional 20% off. What price should you pay for this item? What percent savings does this represent?

**Solution:**

**Step 1:** The given information is

[latex]\begin{eqnarray*}D_1&=&\$18\\d_1&=& 60\% \\ d_2 & = & 20\%\end{eqnarray*}[/latex]

**Step 2:** Solve for the list price.

[latex]\begin{eqnarray*}D_1 & = & d_1 \times L \\ 18 &=& 0.6 \times L \\ \frac{18}{0.6} &=& L \\ \$30 &=& L \end{eqnarray*}[/latex]

**Step 3:** Solve for the net price.

[latex]\begin{eqnarray*}N & = & L \times (1-d_1) \times (1-d_2) \\ &=& 30 \times (1-0.6) \times (1-0.2) \\ &=& 30 \times 0.4 \times 0.8 \\ &=& \$9.60 \end{eqnarray*}[/latex]

**Step 4:** Solve for the single equivalent discount rate.

[latex]\begin{eqnarray*}d_e & = & 1-\left[(1-d_1) \times (1-d_2) \right] \\ &=& 1-\left[(1-0.6) \times (1-0.2)\right]\\ &=& 1-(0.4 \times 0.8) \\ & = & 1-0.32 \\ & = & 0.68 \\ & = & 68\% \end{eqnarray*}[/latex]

You should pay $9.60 for the item, which represents a 68% savings.

## EXAMPLE

An online store sells a pair of shoes for $73.50 less a 15% discount. A department store sells the same shoes for $87.25 less a 20% discount.

- What is the net price of the shoes at the online store?
- What additional discount does the department store have to offer to match the price offered by the online store?

**Solution:**

**Step 1:** The given information for the online store is

[latex]\begin{eqnarray*}L &=&\$73.50\\d&=& 15\% \end{eqnarray*}[/latex]

**Step 2:** Solve for the net price at the online store.

[latex]\begin{eqnarray*}N & = & L \times (1-d) \\ &=& 73.50 \times (1-0.15) \\ &=& 73.50 \times 0.85 \\ &=& \$62.48 \end{eqnarray*}[/latex]

**Step 3:** The department store needs to have the same net price as the online store: $62.48. The given information for the department store is

[latex]\begin{eqnarray*}L &=&\$87.25\\N & = & \$62.48 \\ d_1&=& 20\% \end{eqnarray*}[/latex]

**Step 4:** Solve for the second discount rate.

[latex]\begin{eqnarray*}N & = & L \times (1-d_1) \times (1-d_2) \\ 62.48 &=& 87.25 \times (1-0.2) \times (1-d_2) \\ 62.48 &=& 87.25 \times 0.8 \times (1-d_2) \\ 62.48 &=& 69.80 \times (1-d_2) \\ \frac{62.48}{69.80} & = & 1-d_2 \\ 0.89512894 & = & 1-d_2 \\ d_2 & = & 0.10487106 \\ d_2 & = & 10.49\% \end{eqnarray*}[/latex]

The net price at the online store is $62.48. The department store needs to offer an additional discount of 10.49% to match the net price of the online store.

## TRY IT

A retailer purchases coats for a net price of $75 after discounts of 20% and 5%. What was the list price of the coats?

**Click to see Solution**

[latex]\begin{eqnarray*}N & = & L \times (1-d_1) \times (1-d_2) \\ 75 &=& L \times (1-0.2) \times (1-0.0.5) \\ 75 &=& L \times 0.8 \times 0.95 \\ 75 & = & L \times 0.76 \\ \frac{75}{0.76} & = & L \\ \$98.68 &=& L \end{eqnarray*}[/latex]

## TRY IT

What single discount is equivalent to the series of discounts 40%, 18% and 3%?

**Click to see Solution**

[latex]\begin{eqnarray*}d_e & = & 1-\left[(1-d_1) \times (1-d_2) \times (1-d_3) \right] \\ &=& 1-\left[(1-0.4) \times (1-0.18) \times (1-0.03)\right]\\ &=& 1-(0.6 \times 0.82 \times 0.97) \\ & = & 1-0.47724 \\ & = & 0.52276 \\ & = & 52.276\% \end{eqnarray*}[/latex]

## TRY IT

An electronics stores sells a tablet for $799 less discounts of 30% and 8%. An online store sells the same tablet for $849 less a 25% discount. What additional discount does the online store need to have to match the price offered by the electronics store?

**Click to see Solution**

[latex]\begin{eqnarray*} N & = & L \times (1-d_1) \times (1-d_2) \\ & = & 799 \times (1-0.3) \times (1-0.08) \\ & = & 799 \times 0.7 \times 0.92 \\ & = & \$514.56 \end{eqnarray*}[/latex]

[latex]\begin{eqnarray*} N & = & L \times (1-d_1) \times (1-d_2) \\ 514.56 & = & 849 \times (1-0.25) \times (1-d_2) \\ 514.56 & = & 849 \times 0.75 \times (1-d_2) \\ 514.56 & = & 636.75 \times (1-d_2) \\ \frac{514.56}{636.75} & = & 1-d_2 \\ 0.808104 & = & 1-d_2 \\ d_2 & = & 0.191896 \\ d_2 & = & 19.19\% \end{eqnarray*}[/latex]

**Exercises**

- What is the net price of an item with a list price of $980 after a discount of 42%? What is the total discount amount?

**Click to see Answer**net price=$568.40, discount amount=$411.60

- What is the list price of an item with a net price of $366.05 and discounts of 18%, 4%, and 7%? What is the total discount amount? What single discount rate is equivalent to the series of discounts given?

**Click to see Answer**list price=$500, discount amount=$133.95, single discount rate=26.7904%

- A wholesaler of stereos normally qualifies for a 35% trade discount on all electronic products purchased from its manufacturer. If the list price of a stereo is $399.95, what net price will the wholesaler pay?

**Click to see Answer**$259.97

- Mary is shopping at the mall where she sees a sign that reads, “Everything in the store is 30% off, including sale items!” She wanders in and finds a blouse on the clearance rack. A sign on the clearance rack states, “All clearance items are 50% off.” If the blouse is normally priced at $69.49, what price should Mary pay for it?

**Click to see Answer**$24.32

- A distributor sells some shoes directly to a retailer. The retailer pays $16.31 for a pair of shoes that has a list price of $23.98. What trade discount percent is the distributor offering to its retailers?

**Click to see Answer**31.99%

- A retailer purchases supplies for its head office. If the retailer pays $16.99 for a box of paper and was eligible for a 15% volume discount, what was the original list price for the box of paper?

**Click to see Answer**$19.99

- Mountain Equipment Co-op has purchased a college backpack for $29 after discounts of 30%, 8%, and 13%. What is the list price for the backpack? What single discount is equivalent to the three discounts?

**Click to see Answer**list price=$51.76, single discount rate=43.97%

- Walmart purchased the latest CD recorded by Selena Gomez. It received a total discount of $10.08 off the list price for the CD, which represents a discount percent of 42%.
- What was the list price?
- What was the net price paid for the CD?

**Click to see Answer**a. $24; b. $13.92

- Best Buy just acquired an HP Pavilion computer for its electronics department. The net price on the computer is $260.40 and Best Buy receives discounts of 40% and 38%.
- What single discount is equivalent to the two discounts?
- What is the list price?
- What is the total discount amount?

**Click to see Answer**a. 62.8%; b. $700; c. $439.60

- TELUS retails a Samsung cellphone at the list price of $399.99. TELUS can purchase the phone from its supplier and receive a 20% trade discount along with a 5% volume discount.
- What is the single equivalent percent discount?
- What net price does TELUS pay for the phone?
- How much of a discount in dollars does this represent?

**Click to see Answer**a. 24%; b. $303.99; c. $96

- A wholesaler offers the following discounts: 10% seasonal discount for all purchases made between March 1 and May 1, 15% cumulative quantity discount whenever more than 5,000 units are purchased in any month, 5% loyalty discount for customers who have made regular purchases every month for at least one year, and a 33% trade discount to any retailer. Ed’s Retail Superstore makes a purchase of 200 watches, list price of $10, from the wholesaler on April 29. This month alone, Ed’s has ordered more than 5,000 watches. However, Ed’s has purchased from the wholesaler for only the past six months. Determine the total price that Ed’s should pay for the watches.

**Click to see Answer**$1,026

- Sk8 is examining an invoice. The list price of a skateboard is $109.00, and the invoice states it received a trade discount of 15% and quantity discount of 10% as well as a loyalty discount. However, the amount of the loyalty discount is unspecified.
- If Sk8 paid $80.88 for the skateboard, what is the loyalty discount percent?
- If the loyalty discount is applied after all other discounts, what amount of loyalty dollars does Sk8 save per skateboard?

**Click to see Answer**a. 3%; b. $2.50

- Currently, a student can qualify for up to six different tuition discounts at a local college based on such factors as financial need or corporate sponsorships. Mary Watson just applied to the college and qualifies for all six discounts: 20%, 15%, 23%, 5%, 3%, and 1%.
- She is confused and wants the college to tell her what single discount percent she is receiving. What should the college tell her?
- If her total list tuition comes to $6,435.00, how much should she pay?

**Click to see Answer**a. 52.23%; b. $3,073.82

- Sumandeep is very loyal to her local hairstylist. Because she is loyal, her hairstylist gives her three different discounts: 10%, 5%, and 5%. These discounts amount to $14.08 in savings.
- What was the list price her hairstylist charged her?
- What amount did she pay her hairstylist?
- If her hairstylist increases prices by 5%, what are the list price, net price, and total discount amount?

**Click to see Answer**a. $74.99; b. $60.91; c. list price=$78.74, net price=$63.96, discount amount=$14.78

#### Attribution

“4.1: Figuring Out the Cost: Discounts” from Introduction to Business Math by Margaret Dancy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

“6.1: Figuring Out the Cost: Discounts” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.