Calculating Final Sale Prices with Discounts

Understanding how discounts affect the final sale price of an item is a fundamental concept in retail and economics. Whether you're a customer looking to calculate how much you're saving, or a business owner setting up discounts, knowing the correct formula is crucial. This article will walk you through different scenarios and provide the necessary formulas to calculate the final sale price after applying discounts.

Scenario 1: Basic 20% Discount on a $100 Item

Let's consider a simple example where a store offers a 20% discount on an item that originally costs $100. To find the final sale price, you can follow these steps:

Start with the original price: $100. Calculate the discount amount: 20% of $100. Subtract the discount from the original price.

The mathematical formula for this calculation is:

Final Price Original Price - (Original Price * Discount Rate)

Plugging in the numbers:

Final Price $100 - ($100 * 0.20) $100 - $20 $80

So, the final sale price after a 20% discount on a $100 item is $80.

Scenario 2: Additional Cash Discount

Sometimes, stores offer additional discounts to customers who choose to pay in cash. Let's say the initial discount is 20%, and there's an extra 10% discount if you pay in cash. If the original price of the item is $100, here's how you would calculate the final price:

Step 1: Calculate the price after the initial 20% discount:

Price after first discount $100 * (1 - 0.20) $100 * 0.80 $80

Step 2: Subtract the additional 10% cash discount:

Final Price $80 * (1 - 0.10) $80 * 0.90 $72

Thus, if you pay in cash, the final sale price is $72.

Complex Scenario: Initial Price and Final Sale Price Calculation

Occasionally, you might need to determine the original price based on the final sale price and the discount applied. For example, if the final sale price after a 20% discount is $94, here's how you can calculate the original price:

The formula to find the original price (OP) from the final sale price (SP) and the discount rate (D) is:

OP SP / (1 - D)

Substituting the given values:

OP $94 / (1 - 0.20) $94 / 0.80 $117.50

So, the original price of the item was $117.50.

Conclusion

Calculating the final sale price after applying discounts is a simple yet important task for both customers and business owners. By understanding and using the formulas discussed in this article, you can easily determine the final price of an item after a discount. This knowledge can help you make informed purchasing decisions and ensure accurate pricing in your own business.