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When Calculating The Successive Discounts of 15 and 10

Reviewed by Calculator Editorial Team

When applying multiple discounts to an item, the discounts are applied successively to the remaining price after each previous discount. This guide explains how to calculate successive discounts of 15% and 10%, including the formula, step-by-step instructions, and practical examples.

How to Calculate Successive Discounts

Successive discounts are applied one after another to the remaining price of an item. To calculate the final price after two discounts, you need to apply each discount sequentially to the current price.

Step-by-Step Calculation

  1. Start with the original price of the item.
  2. Apply the first discount to the original price.
  3. Calculate the new price after the first discount.
  4. Apply the second discount to the new price.
  5. Calculate the final price after both discounts.

Important Note

The order of discounts matters. Applying a 15% discount followed by a 10% discount is not the same as applying a 10% discount followed by a 15% discount.

The Formula

The formula for calculating successive discounts is:

Final Price = Original Price × (1 - First Discount) × (1 - Second Discount)

Where:

  • Original Price = The starting price of the item
  • First Discount = The first discount rate (e.g., 15%)
  • Second Discount = The second discount rate (e.g., 10%)

For example, if the original price is $100, the first discount is 15%, and the second discount is 10%, the final price would be:

$100 × (1 - 0.15) × (1 - 0.10) = $100 × 0.85 × 0.90 = $76.50

Worked Example

Let's calculate the final price of an item with an original price of $200, a first discount of 15%, and a second discount of 10%.

  1. Original Price = $200
  2. First Discount = 15% → $200 × 0.15 = $30 discount → New Price = $200 - $30 = $170
  3. Second Discount = 10% → $170 × 0.10 = $17 discount → Final Price = $170 - $17 = $153

Using the formula: $200 × (1 - 0.15) × (1 - 0.10) = $200 × 0.85 × 0.90 = $153

Verification

The final price of $153 is correct. Applying the discounts successively gives the same result as using the formula.

Common Mistakes

When calculating successive discounts, it's easy to make these common mistakes:

  • Adding Discounts: Adding the two discounts (15% + 10% = 25%) and applying a single 25% discount is incorrect. The discounts are applied to different amounts.
  • Incorrect Order: Applying the larger discount first can result in a different final price than applying the smaller discount first.
  • Rounding Errors: Rounding intermediate values can lead to incorrect final prices. Always work with precise decimal values.

To avoid these mistakes, always apply each discount sequentially to the current price and use the correct formula.

FAQ

How do I calculate successive discounts of 15% and 10%?

Use the formula: Final Price = Original Price × (1 - First Discount) × (1 - Second Discount). For example, $100 × 0.85 × 0.90 = $76.50.

Is the order of discounts important?

Yes, the order matters. Applying a 15% discount followed by a 10% discount gives a different result than applying a 10% discount followed by a 15% discount.

Can I add the two discounts together?

No, you cannot simply add the two discounts (15% + 10% = 25%). The discounts are applied to different amounts, so you must apply them successively.

How do I handle rounding in successive discounts?

Always work with precise decimal values. Round the final price only at the end of the calculation to avoid rounding errors.