Calculating the Equivalent Single Discount from Successive Discounts
Understanding Equivalent Single Discount Calculations
When dealing with sales and pricing, it is important to understand how different discount levels affect the final price of an item. Specifically, the concept of an equivalent single discount from successive discounts is a valuable tool in business and financial analysis. This article explores the calculation method for this concept and provides step-by-step examples to clarify the process.
Methodology and Concept
When goods are sold with multiple successive discounts, it's not always clear what the equivalent single discount would be. This can be particularly important for customers and businesses that need to quickly determine the overall savings. The process involves calculating the effective price after each discount and then determining what single discount would achieve the same outcome.
Step-by-Step Example Calculation
Let's consider an example where an item has successive discounts of 20%, 10%, and 5%. We will calculate the equivalent single discount to these three successive discounts.
Start with the original price of the item, say Rs. 100.
Apply the first discount:
20% discount on Rs. 100 20 Amount payable after first discount 100 - 20 80Apply the second discount:
10% discount on Rs. 80 8 Amount payable after second discount 80 - 8 72Apply the third discount:
5% discount on Rs. 72 3.60 Final amount payable 72 - 3.60 68.40Calculate the overall discount:
Overall discount 100 - 68.40 31.60Therefore, the equivalent single discount of 20%, 10%, and 5% successive discounts is 31.60%.
Verification and Algorithm
To confirm the calculation, let's use another approach:
Assume the original price is Rs. 100. After the first discount:
20% off Rs. 100 20 Amount 100 - 20 80After the second discount:
10% off Rs. 80 8 Amount 80 - 8 72After the third discount:
5% off Rs. 72 3.60 Final amount 72 - 3.60 68.40Equivalent single discount:
100 - 68.40 31.60The final amount after each discount is equivalent to a single discount of 31.60%.
Conclusion
Understanding how to calculate the equivalent single discount from successive discounts is crucial in various financial and business contexts. This method not only simplifies decision-making but also enhances transparency for customers and businesses alike. Whether you're running a online store or analyzing financial statements, knowing the equivalent single discount ensures accuracy and efficiency in calculations.