Formula of cost original price, selling price, mark up, mark up rate, markdown, markdown rate, gross margin, gross margin rate

Here are the formulas for each of the requested terms related to pricing and profitability:

1. **Original Price (Cost Price, \(C\))**:
   The original price is the price at which the item is purchased or manufactured.  
   \[
   C = \text{Cost Price}
   \]

2. **Selling Price (\(S\))**:
   The selling price is the price at which the item is sold to customers.  
   \[
   S = \text{Selling Price}
   \]

3. **Markup (\(M\))**:
   Markup is the difference between the selling price and the original price (cost price).  
   \[
   M = S - C
   \]

4. **Markup Rate (\(MR\))**:
   The markup rate is the percentage increase of the cost price to reach the selling price.  
   \[
   MR = \left( \frac{M}{C} \right) \times 100 = \left( \frac{S - C}{C} \right) \times 100
   \]

5. **Markdown (\(Md\))**:
   Markdown refers to the reduction in the selling price from the original or listed price.  
   \[
   Md = \text{Original Selling Price} - \text{New Selling Price}
   \]

6. **Markdown Rate (\(MdR\))**:
   Markdown rate is the percentage decrease from the original selling price.  
   \[
   MdR = \left( \frac{Md}{\text{Original Selling Price}} \right) \times 100
   \]

7. **Gross Margin (\(GM\))**:
   Gross margin is the difference between the selling price and the cost price, similar to markup, but focusing on profit.  
   \[
   GM = S - C
   \]

8. **Gross Margin Rate (\(GMR\))**:
   The gross margin rate is the percentage of the selling price that is profit.  
   \[
   GMR = \left( \frac{GM}{S} \right) \times 100 = \left( \frac{S - C}{S} \right) \times 100
   \]

### Summary of Formulas:
- **Original Price**: \(C\)
- **Selling Price**: \(S\)
- **Markup**: \(M = S - C\)
- **Markup Rate**: \(MR = \left( \frac{S - C}{C} \right) \times 100\)
- **Markdown**: \(Md = \text{Original Selling Price} - \text{New Selling Price}\)
- **Markdown Rate**: \(MdR = \left( \frac{Md}{\text{Original Selling Price}} \right) \times 100\)
- **Gross Margin**: \(GM = S - C\)
- **Gross Margin Rate**: \(GMR = \left( \frac{S - C}{S} \right) \times 100\)

Would you like more detailed explanations or specific examples for any of these terms?

Here are 5 relative questions:
1. How does increasing the markup rate affect the gross margin rate?
2. What happens to the selling price if you apply a markdown after markup?
3. Can the markdown rate exceed 100%? Why or why not?
4. How is gross margin different from profit margin?
5. Why might a business choose a lower markup rate but aim for a higher gross margin rate?

**Tip**: Monitoring both markup and markdown rates helps businesses balance profits and competitiveness effectively.

Discover the key formulas for calculating cost, selling price, markup, markdown, and gross margin. This guide provides step-by-step explanations for markup and markdown rates, gross margin percentages, and profitability analysis. Ideal for students in Grades 9-12 or college-level courses.

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