Triple Discount Calculator

What is a Triple Discount?

A Triple Discount refers to the practice of applying three consecutive discounts to the price of an item. This marketing strategy is often seen in clearance sales, where a store offers an initial discount (e.g., 20% off), an additional discount for loyalty members (e.g., 10% off), and a final discount at checkout (e.g., 5% off coupon).

It is important to note that consecutive discounts are not additive. For example, a 20% discount followed by a 10% discount and a 5% discount does not equal a 35% total discount. Instead, each discount is applied to the declining balance, resulting in an effective discount rate of 31.6%.

The Consecutive Discount Formula

To find the final price after three consecutive discounts, use the following formula:

Where:

• Original Price: The initial price of the item before any discounts.
• d₁: The first discount rate (as a decimal).
• d₂: The second discount rate (as a decimal).
• d₃: The third discount rate (as a decimal).

Step-by-Step Calculation Example

Let's say you buy a jacket originally priced at $100. The store offers three consecutive discounts of 20%, 10%, and 5%. Here is how the final price is calculated:

1. First Discount (20% off): $$\text{Price}_1 = \$100 \times (1 - 0.20) = \$80.00 \quad (\text{You save } \$20.00)$$
2. Second Discount (10% off the new price): $$\text{Price}_2 = \$80.00 \times (1 - 0.10) = \$72.00 \quad (\text{You save } \$8.00)$$
3. Third Discount (5% off the second price): $$\text{Final Price} = \$72.00 \times (1 - 0.05) = \$68.40 \quad (\text{You save } \$3.60)$$

Your total savings are $\$100.00 - \$68.40 = \$31.60$. The effective discount rate is $31.6\%$.