Understanding Compound Discounts on Clearance Items and Their Impact on Final Price

When a store has clearance items that have been marked down by 35%, they are often further discounted with an additional 40% off. This can be confusing for consumers, as the resulting price may not be immediately intuitive. This article provides a detailed explanation of how these discounts affect the final price you end up paying, along with practical examples. We will also explore how these discounts are calculated and provide insights into the potential impact of stacking them correctly.

Understanding Compound Discounts

Let's consider a scenario where a store has clearance items marked down by 35%. Then, they offer an additional 40% off the already discounted price. The question is, what percent of the original price do you end up paying?

Step-by-Step Calculation

Assuming the discounts are applied sequentially (i.e., the additional 40% is applied to the price after the initial 35% discount), the calculation works as follows:

First, let the original price of an item be ( p ). After a 35% discount, the price becomes: ( p times (1 - 0.35) 0.65p ). Next, an additional 40% discount is applied to the new price: ( 0.65p times (1 - 0.40) 0.65p times 0.60 0.39p ).

Thus, after both discounts, you end up paying 39% of the original price.

Example Calculation

Let's assume the original price of an item is $100.

After the first discount of 35%, the price becomes: $100 - 35% of $100 $100 - $35 $65. After the second discount of 40%, the price becomes: $65 - 40% of $65 $65 - $26 $39.

Therefore, if an item originally costs $100 and has a discount of 35% followed by an additional discount of 40%, you would end up paying $39, or 39% of the original price.

Stacking Discounts Correctly

It is important to note that the final price you pay can vary depending on whether the additional discount is applied to the already marked down price or the original price. In many cases, the additional discount is applied to the original price, not the marked down price. This means:

1. If the 40% discount is applied to the original price, the calculation would be: $100 times (1 - 0.35) times (1 - 0.40) $100 times 0.65 times 0.60 $39.

2. If the 40% discount is applied to the marked down price, the calculation would be: $100 times (1 - 0.35) times (1 - 0.60) $100 times 0.65 times 0.40 $26.

In this case, the discounts are stacked off the original price (OP), leading to a final price of 39% of the original price.

Conclusion

Compound discounts can be a powerful tool for stores to reduce prices and attract more customers, but they can also be misleading without a clear understanding of how they are applied. By following the steps outlined in this article, you can ensure you are paying the correct amount for clearance items and avoid any unexpected costs.

Whether you are a consumer looking to take advantage of these discounts or a retailer interested in optimizing your pricing strategy, understanding how compound discounts work is essential.