4.03 Discounts, fees and markups
Introduction
We have already learned about percent increase and percent decrease. We will now apply these concepts to real life situations like calculating discounts, markups and markdowns, and fees.
Discounts and markdowns
Everyone will have seen stores advertising, "25\% off", or "pay less when you pay cash." These are both examples of discounts. A discount is a reduction in price, or a percent decrease. Businesses often use discount sales to encourage people to buy from them so it's important to be able to calculate discounts to make sure you're getting a great deal.
Another example of a percent decrease is a markdown, which is an amount by which we lower the selling price. Markdown is seen when businesses give out coupons, and have special sales events to encouage more customers to purchase.
Let's look at the following example on how we apply percent decrease to calculate a discount.
Examples
Example 1
Steph is going to buy a hat that is marked at 75\% off. The original price is \$36.
What is the value of the discount in dollars?
What is the price that Emily will pay for the dress?
Discounts and markdowns are examples of percent decreases. We subtract the amount of discount or markdown from the original price to find the sale price. We can also multiply the original price by 100\%-\text{percent decrease} to get the sale price.
Fees and markups
On the other hand, we can have a percent increase like a markup. This is when the price is increased to cover the cost. For example, if we buy a cellphone for \$200, we may sell it with 5\% markup to earn a profit.
We may also apply percent increase in additional fees, which is a charge or payment for professional services. For example, a service fee for hotel services or a fee to use a credit card.
Markdowns and discounts involve lowering the costs for consumers, to increase the quantity that people may purchase. Markups and fees imply an increase in the cost, increasing the profit for the supplier.
Examples
Example 2
A brush set which costs \$75 is marked up by 20\%. What is the markup amount for the brush set?
Example 3
A contractor was hired to build a house which will cost \$300\,000. The contractor also includes a service fee of \$45\,000 for the overall cost of the contract.
What percent of the cost of the house is the contractor's percentage fee?
Fees and markups are examples of percent increases. We add the fee or the markup to the original price to find the full price. We can also multiply the original cost by 100\% + \text{percent increase} to find the full price.