Formula For 3 Successive Discount

Decoding the Formula for 3 Successive Discounts: A Comprehensive Guide

Understanding successive discounts is crucial for anyone navigating the world of sales and promotions. Whether you're a savvy shopper looking for the best deal or a business owner strategizing pricing, mastering the calculation of successive discounts, especially three successive discounts, is essential. This article provides a comprehensive guide to calculating three successive discounts, explaining the formula, its applications, and offering practical examples to solidify your understanding. We'll explore the underlying logic and offer tips to avoid common pitfalls.

Understanding Successive Discounts

A successive discount refers to a series of discounts applied one after another. Unlike a single discount, each successive discount is applied to the remaining price after the previous discount has been deducted. This makes the overall discount slightly different than simply adding the individual percentages together. This is because each subsequent discount is calculated on a smaller base amount.

Imagine a store offering a 20% discount, followed by a 10% discount, and finally a 5% discount. Applying these discounts successively will result in a lower final price than if you simply added 20% + 10% + 5% = 35% and applied that single discount. This is the key concept to grasp when working with successive discounts.

The Formula for 3 Successive Discounts

Let's denote the original price as 'P'. The three successive discounts are represented as percentages: d1, d2, and d3. To calculate the final price after three successive discounts, we use the following formula:

Final Price = P * (1 - d1/100) * (1 - d2/100) * (1 - d3/100)

Let's break this down:

• P: This represents the original price of the item.
• (1 - d1/100): This part calculates the price after the first discount. We subtract the discount percentage (d1) divided by 100 from 1 to get the remaining percentage. For example, if d1 is 20%, this becomes (1 - 20/100) = 0.8.
• (1 - d2/100): Similarly, this calculates the price after the second discount, applied to the price remaining after the first discount.
• (1 - d3/100): This represents the final discount calculation, applied to the price remaining after the second discount.

Step-by-Step Calculation with Examples

Let's illustrate the formula with a practical example:

Example 1: A laptop originally costs $1000. The store offers three successive discounts: 15%, 10%, and 5%. What is the final price?

Step 1: Identify the values:

• P = $1000
• d1 = 15%
• d2 = 10%
• d3 = 5%

Step 2: Apply the formula:

Final Price = 1000 * (1 - 15/100) * (1 - 10/100) * (1 - 5/100)

Final Price = 1000 * (1 - 0.15) * (1 - 0.10) * (1 - 0.05)

Final Price = 1000 * 0.85 * 0.90 * 0.95

Final Price = $726.75

Therefore, the final price of the laptop after the three successive discounts is $726.75.

Example 2: A dress is priced at $50. It's subject to discounts of 25%, 12%, and 8%. Find the final price.

Step 1: Identify the values:

• P = $50
• d1 = 25%
• d2 = 12%
• d3 = 8%

Step 2: Apply the formula:

Final Price = 50 * (1 - 25/100) * (1 - 12/100) * (1 - 8/100)

Final Price = 50 * 0.75 * 0.88 * 0.92

Final Price = $30.36

The final price of the dress is $30.36.

Calculating the Overall Discount Percentage

While the formula above directly calculates the final price, you might also want to know the overall discount percentage. This is calculated as follows:

Overall Discount Percentage = 100% - [(Final Price / Original Price) * 100%]

Using Example 1:

Overall Discount Percentage = 100% - [($726.75 / $1000) * 100%]

Overall Discount Percentage = 100% - 72.675%

Overall Discount Percentage = 27.325%

The overall discount applied is approximately 27.325%. Note that this is not simply the sum of the individual discounts (15% + 10% + 5% = 30%).

Common Mistakes to Avoid

• Adding percentages directly: The most common mistake is adding the discount percentages together. Remember, each discount is applied to the remaining balance, not the original price.
• Incorrect order of operations: Ensure you follow the order of operations (PEMDAS/BODMAS) correctly. Multiplication and division should be performed before addition and subtraction.
• Using decimal numbers incorrectly: Make sure to convert percentages to decimals accurately before applying the formula.

Advanced Applications and Variations

The formula can be extended to handle more than three successive discounts. Simply add additional terms of the form (1 - dn/100) for each additional discount (dn).

Furthermore, this concept isn't limited to retail pricing. Successive discounts or reductions can be applied in various financial calculations, such as compound interest (where interest is added and then further interest is calculated on the new total) or depreciation models (where the value of an asset decreases over time by a certain percentage each period).

Frequently Asked Questions (FAQ)

Q: Can I use this formula for more than three successive discounts?

A: Yes, you can easily extend the formula to include as many successive discounts as needed. Just add another (1 - dn/100) term for each additional discount.

Q: What if the discounts are not in percentage but in a fixed amount?

A: In that case, you'd subtract the fixed amount from the price after each discount. The formula would be different, and you would need to calculate each step individually rather than using a single formula.

Q: Does the order of the discounts matter?

A: Yes, the order of successive discounts does matter. Applying a 10% discount followed by a 20% discount will yield a different final price than applying a 20% discount followed by a 10% discount. Always apply discounts in the order they are presented.

Conclusion

Calculating three successive discounts might seem complex at first, but with a clear understanding of the formula and a step-by-step approach, it becomes straightforward. Remember to avoid common mistakes like adding percentages directly. Mastering this concept will empower you to make informed decisions as a consumer or effectively manage pricing strategies as a business professional. The ability to quickly and accurately calculate successive discounts is a valuable skill with broad applications in various fields.