For the last 12 years, DiDi has been receiving a 20/10/5 series discount. Find the equivalent single discount rate.
Equivalent single discount rate = __________

To find the equivalent single discount rate for a series discount, we need to use the following formula:

\[
\text{Equivalent Single Discount Rate} = 1 - (1 - d_1) \times (1 - d_2) \times (1 - d_3) \times \ldots \times (1 - d_n)
\]

Where \( d_1, d_2, d_3, \dots \) are the individual discounts expressed as decimals.

For a 20/10/5 series discount:

- \( d_1 = 20\% = 0.20 \)
- \( d_2 = 10\% = 0.10 \)
- \( d_3 = 5\% = 0.05 \)

Substituting these values into the formula:

\[
\text{Equivalent Single Discount Rate} = 1 - (1 - 0.20) \times (1 - 0.10) \times (1 - 0.05)
\]

\[
= 1 - (0.80) \times (0.90) \times (0.95)
\]

\[
= 1 - (0.684)
\]

\[
= 0.316
\]

So, the equivalent single discount rate is **31.6%**.

Would you like any further details or have any questions? Here are some related questions:

1. How would the equivalent discount rate change with different discount values?
2. Can the equivalent discount rate be higher than the highest individual discount in a series?
3. How do we compute the equivalent discount rate if more than three discounts are applied?
4. What is the formula to convert an equivalent discount rate back into a series discount?
5. How do equivalent discount rates compare to applying all discounts separately?

**Tip:** Always convert percentage discounts to decimals when performing calculations.

Learn how to calculate the equivalent single discount rate for a 20/10/5 series discount with step-by-step guidance and examples. This problem involves converting multiple discounts into a single equivalent discount rate, covering key concepts in discounts and mathematical formulas.

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