Calculate The Final Price Of A Washing Machine After Successive Discounts Of 5% And 15% Are Applied To An Original Price Of $800.
In the realm of retail, understanding how discounts impact the final price of an item is crucial for both consumers and businesses. This article delves into a practical scenario involving successive discounts applied to a washing machine in a wholesale store. Let's explore how to calculate the final price after applying two discounts sequentially.
Understanding Successive Discounts
When dealing with successive discounts, it's essential to grasp that each discount is applied to the price after the previous discount. This means that the second discount isn't calculated on the original price but on the reduced price after the first discount. This method of calculation can sometimes lead to a final price lower than what one might initially expect if simply adding the discounts together.
The Scenario: Washing Machine Discounts
Let's consider the scenario presented: A washing machine in a wholesale store is priced at $800. The store is running a promotional campaign, offering two successive discounts. The first discount is 5%, and the second discount is 15%. The challenge is to determine the final price of the washing machine after both discounts are applied.
Step-by-Step Calculation
To accurately calculate the final price, we'll break down the process into steps:
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Calculate the First Discount: The initial discount is 5% of the original price. To find this, we multiply the original price by the discount percentage:
Discount Amount = Original Price * Discount Percentage Discount Amount = $800 * 0.05 Discount Amount = $40
The first discount amounts to $40. 2. Subtract the First Discount: Next, we subtract the discount amount from the original price to find the price after the first discount:
```
Price After First Discount = Original Price - Discount Amount
Price After First Discount = $800 - $40
Price After First Discount = $760
```
After the first 5% discount, the price of the washing machine is $760.
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Calculate the Second Discount: Now, we calculate the second discount, which is 15% of the price after the first discount ($760):
Second Discount Amount = Price After First Discount * Second Discount Percentage Second Discount Amount = $760 * 0.15 Second Discount Amount = $114
The second discount amounts to $114. 4. Subtract the Second Discount: Finally, we subtract the second discount amount from the price after the first discount:
```
Final Price = Price After First Discount - Second Discount Amount
Final Price = $760 - $114
Final Price = $646
```
Therefore, the final price of the washing machine after both discounts is $646.
The Impact of Successive Discounts
The final price of $646 is significantly lower than the original price of $800. This demonstrates the impact of successive discounts. If we were to simply add the discount percentages (5% + 15% = 20%) and apply that to the original price, we would get a different result:
Combined Discount Amount = Original Price * Combined Discount Percentage
Combined Discount Amount = $800 * 0.20
Combined Discount Amount = $160
Price After Combined Discount = $800 - $160
Price After Combined Discount = $640
In this case, the result would be $640, which is slightly lower than the actual final price of $646 when applying discounts successively. This difference highlights the importance of understanding the correct method for calculating successive discounts.
Practical Implications for Consumers
For consumers, understanding how successive discounts work is essential for making informed purchasing decisions. When evaluating deals involving multiple discounts, it's crucial to calculate the final price step-by-step to accurately assess the savings. Retailers often use successive discounts as a marketing strategy to attract customers, making it even more important for consumers to be able to calculate the actual final price.
Business Strategies and Discounting
From a business perspective, offering successive discounts can be an effective way to boost sales and clear inventory. However, it's crucial for businesses to carefully consider the discount percentages to ensure profitability. Understanding the impact of successive discounts on the bottom line is vital for effective pricing strategies.
Conclusion
In summary, the final price of the washing machine after successive discounts of 5% and 15% is $646. This example illustrates the importance of accurately calculating successive discounts by applying each discount to the price after the previous discount. For consumers, this knowledge empowers them to make informed purchasing decisions, while for businesses, it aids in developing effective pricing and promotional strategies. Understanding the mathematics behind discounts is a valuable skill in both personal finance and business management.
Exploring Further Applications of Percentage Calculations
Percentage calculations, like the ones we've used to determine the final price of the washing machine, are not just limited to retail scenarios. They are fundamental in various aspects of finance, economics, and everyday life. Let's delve into some additional applications to appreciate the versatility and importance of understanding percentages.
Financial Investments and Returns
In the world of finance, percentages are extensively used to calculate investment returns. Whether it's stocks, bonds, or mutual funds, investors often assess the performance of their investments in terms of percentage gains or losses. For instance, if an investor purchases a stock for $100 and sells it for $110, the percentage return can be calculated as follows:
Return = (Selling Price - Purchase Price) / Purchase Price * 100
Return = ($110 - $100) / $100 * 100
Return = 10%
This means the investor has made a 10% return on their investment. Understanding these percentage calculations is crucial for making informed investment decisions.
Interest Rates and Loans
When it comes to loans and interest rates, percentages play a pivotal role. Interest rates, often expressed as annual percentage rates (APRs), determine the cost of borrowing money. For example, if you take out a loan of $10,000 with an APR of 5%, you'll need to pay interest on the borrowed amount. The interest can be calculated as:
Annual Interest = Loan Amount * Interest Rate
Annual Interest = $10,000 * 0.05
Annual Interest = $500
In this case, the annual interest on the loan would be $500. Understanding how interest rates are calculated helps borrowers assess the total cost of a loan and compare different financing options.
Sales Tax and Value Added Tax (VAT)
Percentages are also fundamental in calculating sales tax and Value Added Tax (VAT). These taxes are typically levied as a percentage of the sale price of goods and services. For instance, if the sales tax rate is 8% and you purchase an item for $50, the sales tax amount would be:
Sales Tax = Sale Price * Tax Rate
Sales Tax = $50 * 0.08
Sales Tax = $4
So, the total cost of the item, including sales tax, would be $54. Similarly, VAT is a consumption tax applied in many countries, and understanding how it is calculated is essential for both consumers and businesses.
Statistical Analysis and Data Interpretation
In statistical analysis, percentages are used to represent proportions and relative changes in data. For example, if a survey indicates that 60% of respondents prefer a particular product, this percentage provides a clear and concise way to understand the proportion of people with that preference. Percentages are also used to express growth rates, market shares, and other key metrics in various fields, including business, economics, and social sciences.
Everyday Life Scenarios
Beyond these specific applications, percentages are prevalent in numerous everyday life scenarios. Calculating tips at restaurants, understanding discounts at retail stores, and determining proportions in recipes all involve percentage calculations. Having a solid grasp of percentages empowers individuals to make informed decisions and navigate financial and practical situations with confidence.
The Importance of Mathematical Literacy
The ability to work with percentages is a crucial aspect of mathematical literacy. It enables individuals to understand financial information, make sound decisions, and participate effectively in a data-driven world. Whether you are a student, a professional, or a consumer, mastering percentage calculations is an invaluable skill.
Conclusion: The Ubiquity of Percentages
In conclusion, percentages are a fundamental mathematical concept with widespread applications across diverse fields. From calculating discounts in retail to assessing investment returns in finance, percentages provide a versatile tool for understanding proportions, changes, and relative values. Developing proficiency in percentage calculations is essential for making informed decisions and navigating the complexities of the modern world. The scenario of calculating the final price of a washing machine with successive discounts serves as a practical illustration of the broader significance of percentages in everyday life and professional contexts.
Calculate the final price of a washing machine after successive discounts of 5% and 15% are applied to an original price of $800.
Calculating Final Price Washing Machine with Successive Discounts