What’s the single equivalent discount rate of the trade discount 5/4/1

The trade discount series "5/4/1" represents three successive discounts of 5%, 4%, and 1%, applied one after the other. To find the **single equivalent discount rate**, we need to combine these individual discounts.

The formula to calculate the equivalent discount is:

\[
\text{Equivalent Discount Rate} = 1 - \left( (1 - d_1) \times (1 - d_2) \times (1 - d_3) \right)
\]

Where:
- \( d_1 = 0.05 \) (5%)
- \( d_2 = 0.04 \) (4%)
- \( d_3 = 0.01 \) (1%)

Now, calculating step by step:

1. Subtract each discount from 1:
   - \( 1 - d_1 = 0.95 \)
   - \( 1 - d_2 = 0.96 \)
   - \( 1 - d_3 = 0.99 \)

2. Multiply these values together:
   \[
   0.95 \times 0.96 \times 0.99 = 0.90216
   \]

3. Subtract this result from 1:
   \[
   1 - 0.90216 = 0.09784
   \]

Thus, the **single equivalent discount rate** is approximately **9.784%**.

### Would you like more details on the calculation?

Here are five questions to consider next:
1. How does compounding affect multiple discounts?
2. Can you apply this method to larger series of discounts?
3. What happens if the discounts are larger percentages?
4. How does the order of applying discounts affect the final result?
5. What is the impact of the equivalent discount in retail?

**Tip:** Always remember that successive discounts don't simply add up but compound.

What’s the single equivalent discount rate of the trade discount 5/4/1?

Learn how to calculate the single equivalent discount rate for a 5/4/1 trade discount series, including the step-by-step process using percentage and compound discount formulas. Suitable for students in Grades 10-12 or business professionals dealing with trade discounts.

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