company a 8/9/14/2. company b 10/6/16/4. a. calculate the single equivalent discount rate for each company. b. which of the following companies, a or b, gives a higher discount? use the single equivalent discount rate to make your choice. round to the nearest hundredth

To solve this problem, we need to calculate the single equivalent discount rate for each company. The single equivalent discount rate \( r \) is calculated using the formula:

\[
r = 1 - (1 - d_1)(1 - d_2)\dots(1 - d_n)
\]

where \( d_1, d_2, \dots, d_n \) are the individual discount rates converted to their decimal form.

### Step 1: Convert the discount percentages to decimals
For each discount rate, convert the percentage to its decimal equivalent by dividing by 100.

**Company A:**
- \( d_1 = 8\% = 0.08 \)
- \( d_2 = 9\% = 0.09 \)
- \( d_3 = 14\% = 0.14 \)
- \( d_4 = 2\% = 0.02 \)

**Company B:**
- \( d_1 = 10\% = 0.10 \)
- \( d_2 = 6\% = 0.06 \)
- \( d_3 = 16\% = 0.16 \)
- \( d_4 = 4\% = 0.04 \)

### Step 2: Calculate the single equivalent discount rate

**For Company A:**
\[
r_A = 1 - (1 - 0.08)(1 - 0.09)(1 - 0.14)(1 - 0.02)
\]

**For Company B:**
\[
r_B = 1 - (1 - 0.10)(1 - 0.06)(1 - 0.16)(1 - 0.04)
\]

Let's calculate these values.

### Step 3: Perform the calculations

#### Company A:
\[
r_A = 1 - (0.92)(0.91)(0.86)(0.98)
\]

#### Company B:
\[
r_B = 1 - (0.90)(0.94)(0.84)(0.96)
\]

I will now calculate these values.### Step 4: Results

- The single equivalent discount rate for **Company A** is approximately **29.44%**.
- The single equivalent discount rate for **Company B** is approximately **31.78%**.

### Conclusion

**Company B** offers a higher discount because its single equivalent discount rate of 31.78% is greater than Company A's rate of 29.44%.

Would you like further details or have any questions about the calculations? 

Here are some related questions you might find interesting:
1. How does the order of discounts affect the single equivalent discount rate?
2. How can the single equivalent discount rate be used in cost comparison between suppliers?
3. What would the equivalent discount rate be if one company offered a flat 30% discount?
4. How does the equivalent discount rate change if the number of discounts increases?
5. What are some real-life examples where calculating the equivalent discount rate would be useful?

**Tip:** When calculating equivalent discount rates, always ensure the correct order of operations to avoid rounding errors.

Learn how to calculate the single equivalent discount rates for Company A (8%, 9%, 14%, 2%) and Company B (10%, 6%, 16%, 4%) using the single equivalent discount rate formula. Determine which company offers the higher discount with a step-by-step explanation. Suitable for students in Grades 10-12.

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