Single Equivalent Rate:
What is a Single Equivalent Rate?
In financial mathematics and retail pricing, the Single Equivalent Rate (SER) represents a single percentage that yields the same final value as a series of successive percentages applied one after another.
A common misconception is that you can simply add percentages together. For example, a 20% discount followed by a 10% discount is not equal to a 30% total discount. Because the second percentage is applied to the already reduced amount, the total effect is slightly less than the sum. This calculator helps you determine the true effective rate.
Why Percentages Are Not Additive
When multiple rates are applied sequentially, the base value changes after every step.
- Successive Discounts: The equivalent single discount is always less than the sum of the individual discounts.
- Successive Increases: The equivalent single increase is always more than the sum of the individual increases (due to compounding).
The Formula
To calculate the single equivalent discount rate ($d_{eq}$) for a series of discounts ($d_1, d_2, d_3…$):
To calculate the single equivalent surcharge rate ($i_{eq}$) for a series of increases ($i_1, i_2, i_3…$):
Real-World Example
Imagine an item costs 100.
Discount 1: 20% off. The price becomes 80.
Discount 2: An additional 10% off the new price (80). 10% of 80 is 8.
Final Price: 80 – 8 = 72.
The total reduction was 28 (from 100 to 72). Therefore, the Single Equivalent Discount Rate is 28%, not 30%.
When to Use This Calculator
- Retail Shopping: Checking the real savings when a store offers "Take an extra 20% off sale items".
- Business Pricing: Calculating the net effect of successive price hikes or tax layers.
- Supply Chain: Understanding trade discounts applied in chains (e.g., Manufacturer → Wholesaler → Retailer).